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Bounded excitons in transition metal dichalcogenides monolayers lead to numerous opto-electronic applications, which require a detailed understanding of the exciton dynamics. The dynamical properties of excitons with finite momentum transfer $\textbf{Q}$ can be investigated experimentally using electron energy-loss (EEL) spectroscopy. The EEL spectrum depends on the response function of the material which in turn is determined by the exciton energies and eigenvectors in the exciton band structure. In this work, we utilize ab initio density-functional theory plus Bethe-Salpeter equation (DFT+BSE) approach to explore the exciton band structure and also $\textbf{Q}$-resolved EEL spectrum in monolayer ${\mathrm{WSe}}_{2}$. In particular, we carefully examine the discrepancies and connections among the existing EEL spectrum formulas for quasi-two-dimensional (2D) systems, and establish a proper definition of the EEL spectrum, which is then used to calculate the EEL spectra of monolayer ${\mathrm{WSe}}_{2}$. We find that remarkably, the dispersion of the calculated lowest-energy EELS peaks for the in-plane momentum transfer follows almost precisely the non-parabolic upper band of the lowest bright A exciton, and also agrees well with the previous experiment. Furthermore, we show that only the bright exciton with its electric dipole being parallel to the direction of the transfered momentum is excited, i.e., EEL spectroscopy selectively probes bright exciton bands. This explains why only the upper band of the A exciton, which is a longitudinal exciton with an in-plane dipole moment, was observed in the previous experiment. Our findings will stimulate further EEL experiments to measure other branches of the exciton band structure, such as the parabolic lower band of the A exciton, and hence will lead to a better understanding of the exciton dynamics in quasi-2D materials., Comment: 15 pages, 6 figures and 3 tables

In a multi-valley electronic band structure, lifting of the valley degeneracy is associated with rotational symmetry breaking in the electronic fluid, and may emerge through spontaneous symmetry breaking order, or through a large response to a small external perturbation such as strain. In this work we use scanning tunneling microscopy to investigate an unexpected rotational symmetry breaking in Landau levels formed in the unusual floating surface band of ZrSiS. We visualize a ubiquitous splitting of Landau levels into valley-polarized sub-levels. We demonstrate methods to measure valley-selective Landau level spectroscopy, to infer unknown Landau level indices, and to precisely measure each valley's Berry phase in a way that is agnostic to the band structure and topology of the system. These techniques allow us to obtain each valley's dispersion curve and infer a rigid valley-dependent contribution to the band energies. Ruling out spontaneous symmetry breaking by establishing the sample-dependence of this valley splitting, we explain the effect in terms of residual strain. A quantitative estimate indicates that uniaxial strain can be measured to a precision of $ \lt 0.025 \% $. The extreme valley-polarization of the Landau levels results from as little as $ \sim 0.1 \% $ strain, and this suggests avenues for manipulation using deliberate strain engineering., Comment: 13 pages, 9 figures (plus 13 pages, 9 figures)

Nonlinear optical (NLO) responses of noncentrosymmetric nonmagnets have drawn a lot of attention in the past decades because of their significance in materials characterization, green energy and device applications. However, the magnetism-induced NLO responses have rarely been studied so far. In this paper, we first extend the numerical calculation friendly formula by Rashkeev $\textit{et al.}$ [Phys. Rev. B $\textbf{57}$, 3905 (1998)] for second harmonic generation (SHG) in nonmagnetic materials to include magnetic systems and then calculate the magnetism-induced NLO responses of BiFeO$_3$, a multiferroic that exhibits both ferroelectricity and antiferromagnetic (AFM) ordering at room temperature and has a band gap that falls in the visible frequency region. First, we find that the calculated magnetism-induced SHG susceptibilities are large and the SHG intensity is tunable with the reversal of magnetization. In particular, we find a strong magnetic contrast of the SHG signal of approximately 440% at SHG photon energy of 4.82 eV, thus enabling a magnetic control of the SHG in BiFeO$_3$. Also, because of the sensitivity of the SHG signal to the direction of the N\'eel vector, the SHG can be utilized to detect the reversal of the N\'eel vector in the AFM materials, which is an important issue for AFM spintronics. Second, the calculated BPVE in BiFeO$_3$ are also strong, being larger than some well-known NLO compounds such as BaTiO$_3$, GaAs, CdS and CdSe. Finally, we analyse the origins of the prominent features in the NLO response spectra in terms of the calculated quantum geometric quantities. Our interesting findings suggest that the magnetism-driven NLO responses in BiFeO$_3$ are significant, anisotropic and tunable, and that understanding the magnetism-driven components of both SHG and BPVE is essential for their applications in, e.g., multiferroic-based photovoltaic devices.

We perform a systematic ab initio study on phonon-mediated superconductivity in the transition-metal-based superconductors Sc$_6M$Te$_2$ ($M$ = Fe, Co, Ni). Firstly, our charge analysis reveals significant electron transfer from Sc to $M$ due to the substantial difference in the electronegativity, filling the 3$d$ orbitals of $M$ and suppressing magnetic instability. Secondly, we show that Sc$_6$FeTe$_2$ exhibits strong lattice anharmonicity. Moreover, for $M =$ Fe and Co, we find low-frequency soft phonon bands of $M$ which can be interpreted as "rattling phonons" in the framework formed by Sc. While not observed in the case of $M=$ Ni, the rattling phonons give rise to a prominent peak or plateau in the Eliashberg spectral function and enhance the pairing instability. By reproducing the experimental trend of superconducting transition temperatures, our study underscores the potential of designing phonon-mediated superconductors by strategically combining non-superconducting and magnetic transition-metal elements., Comment: 13 pages, 10 figures

The identification of distinct charge transport features, deriving from nontrivial bulk band and surface states, has been a challenging subject in the field of topological systems. In topological Dirac and Weyl semimetals, nontrivial conical bands with Fermi-arc surface states give rise to negative longitudinal magnetoresistance due to chiral anomaly effect and unusual thickness dependent quantum oscillation from Weyl-orbit effect, which were demonstrated recently in experiments. In this work, we report the experimental observations of large nonlinear and nonreciprocal transport effects for both longitudinal and transverse channels in an untwinned Weyl metal of SrRuO$_3$ thin film grown on a SrTiO$_{3}$ substrate. From rigorous measurements with bias current applied along various directions with respect to the crystalline principal axes, the magnitude of nonlinear Hall signals from the transverse channel exhibits a simple sin$\alpha$ dependence at low temperatures, where $\alpha$ is the angle between bias current direction and orthorhombic [001]$_{\rm o}$, reaching a maximum when current is along orthorhombic [1-10]$_{\rm o}$. On the contrary, the magnitude of nonlinear and nonreciprocal signals in the longitudinal channel attains a maximum for bias current along [001]$_{\rm o}$, and it vanishes for bias current along [1-10]$_{\rm o}$. The observed $\alpha$-dependent nonlinear and nonreciprocal signals in longitudinal and transverse channels reveal a magnetic Weyl phase with an effective Berry curvature dipole along [1-10]$_{\rm o}$ from surface states, accompanied by 1D chiral edge modes along [001]$_{\rm o}$., Comment: 27 pages, 6 figures

We perform a systematic \textit{ab initio} density functional study of the superconductivity, electronic and phononic band structures, electron-phonon coupling and elastic constants of all four possible structures of niobium nitride $\beta$-Nb$_2$N as well as Nb-rich $\gamma$-Nb$_4$N$_3$ and N-rich $\beta^\prime$-Nb$_4$N$_5$. First of all, we find that all four structures of $\beta$-Nb$_2$N are superconductors with superconducting transition temperatures ($T_c$) ranging from 0.6 K to 6.1 K, depending on the structure. This explains why previous experiments reported contradicting $T_c$ values for $\beta$-Nb$_2$N. Furthermore, both $\gamma$-Nb$_4$N$_3$ and $\beta^\prime$-Nb$_4$N$_5$ are predicted to be superconductors with rather high $T_c$ of 8.5 K and 15.3 K, respectively. Second, the calculated elastic constants and phonon dispersion relations show that all the considered niobium nitride structures are mechanically and dynamically stable. Moreover, the calculated elastic moduli demonstrate that all the niobium nitrides are hard materials with bulk moduli and hardness being comparable to or larger than the well-known hard sapphire. Third, the calculated band structures reveal that the nitrides possess both type I and type II Dirac nodal points and are thus topological metals. Finally, the calculated electron-phonon coupling strength, superconductivity and mechanical property of the niobium nitrides are discussed in terms of their underlying electronic structures and also Debye temperatures. The present \textit{ab initio} study thus indicates that $\beta$-Nb$_2$N, $\gamma$-Nb$_4$N$_3$ and $\beta^\prime$-Nb$_4$N$_5$ are hard superconductors with nontrivial band topology and are promising materials for exploring exotic phenomena due to the interplay of hardness, superconductivity and nontrivial band topology., Comment: 12 pages, 4 tables and 6 figures

We perform {\it ab initio} many-body calculations to investigate the exciton shift current in small diameter zigzag BN nanotubes and also single BN sheet, using the GW plus Bethe-Salpeter equation (GW-BSE) method with the newly developed efficient algorithms. Our GW-BSE calculations reveal a giant in-gap peak in the shift current spectrum in all the studied BN systems due to the excitation of the A exciton. The peak value of the excitonic shift current is more than three times larger than that of the quasiparticle shift current, and is attributed to the gigantic enhancement of the optical dipole matrix element by the A exciton resonance. The effective exciton shift current conductivity is nearly ten times larger than the largest shift conductivity observed in ferroelectric semiconductors. Importantly, the direction of the shift current in the BN nanotubes is found to be independent of the tube chirality ($n,0$) (or diameter), contrary to the simple rule of $ sgn(J_\text{shift})=\text{mod}(n,3)$ predicted by previous model Hamiltonian studies. Finally, our {\it ab initio} calculations also show that the exciton excitation energies decrease significantly with the decreasing diameter due to the curvature-induced orbital rehybridization in small diameter zigzag BN nanotubes., Comment: 12 pages, 8 figures and 2 tables

The recent discovery of long-range magnetic order in atomically thin films has triggered particular interest in two-dimensional (2D) van der Waals (vdW) magnetic materials. In this paper, we perform a systematic theoretical study of the magneto-optical Sch\"{a}fer-Hubert effect (MOSHE) in 2D vdW antiferromagnetic \textit{M}PS$_3$ (\textit{M} = Mn, Fe, Ni) with multifold intralayer and interlayer magnetic orders. The formula for evaluating the MOSHE in 2D magnets is derived by considering the influence of a non-magnetic substrate. The MOSHE of monolayer and bilayer \textit{M}PS$_3$ are considerably large ($>2^{\circ}$), originating from the strong anisotropy of in-plane optical conductivity. The Sch\"{a}fer-Hubert rotation angles are surprisingly insensitive to the orientations of the N\'{e}el vector, while the Sch\"{a}fer-Hubert ellipticities are identified to be a good criterion to distinguish different interlayer magnetic orders. Our work establishes a theoretical framework for exploring novel 2D vdW magnets and facilitates the promising applications of the 2D \textit{M}PS$_3$ family in antiferromagnetic nanophotonic devices.

Chiral multifold fermions are quasi-particles that appear only in chiral crystals such as transition metal silicides in the cubic B20 structure (i.e., the CoSi family), and they may show exotic physical properties. Here we study the injection and shift photoconductivities and also the related geometrical quantities for several types of chiral multifold fermions, including spin-1/2 as well as pseudospin-1 and -3/2 fermions, dubbed as Kramers Weyl, triple point and Rarita-Schwinger-Weyl (RSW) fermions, respectively. We utilize the minimal symmorphic model to describe the triple point fermions (TPF). We also consider the more realistic model Hamiltonian for the CoSi family including both linear and quadratic terms. We find that circular injection currents are quantized as a result of the Chern numbers carried by the multifold fermions within the linear models. Surprisingly, we discover that in the TPF model, linear shift conductivities are proportional to the pseudo spin-orbit coupling and independent of photon frequency. In contrast, for the RSW and Kramer Weyl fermions, the linear shift conductivity is linearly proportional to photon frequency. The numerical results agree with the power-counting analysis for quadratic Hamiltonians. The frequency independence of the linear shift conductivity could be attributed to the strong resonant symplectic Christoffel symbols of the flat bands. Moreover, the calculated symplectic Christoffel symbols show significant peaks at the nodes, suggesting that the shift currents are due to the strong geometrical response near the topological nodes.

We propose a time-reversal-even spin generation in second order of electric fields, which dominates the current induced spin polarization in a wide class of centrosymmetric nonmagnetic materials, and leads to a novel nonlinear spin-orbit torque in magnets. We reveal a quantum origin of this effect from the momentum space dipole of the anomalous spin polarizability. First-principles calculations predict sizable spin generations in several nonmagnetic hcp metals, in monolayer TiTe$_{2}$, and in ferromagnetic monolayer MnSe$_{2}$, which can be detected in experiment. Our work opens up the broad vista of nonlinear spintronics in both nonmagnetic and magnetic systems., Comment: 4 pages, 2 figures

Materials carrying topological surface states (TSS) provide a fascinating platform for the hydrogen evolution reaction (HER). Based on systematic first-principles calculations for $A_3 B$ ($A$ = Ni, Pd, Pt; $B$ = Si, Ge, Sn), we propose that topological electric polarization characterized by the Zak phase can be crucial to designing efficient catalysts for the HER. For $A_3 B$, we show that the Zak phase takes a nontrivial value of $\pi$ in the whole (111) projected Brillouin zone, which causes quantized electric polarization charge at the surface. There, depending on the adsorption sites, the hydrogen (H) atom hybridizes with the TSS rather than with the bulk states. When the hybridization has an intermediate character between the covalent and ionic bond, the H states are localized in the energy spectrum, and the change in the Gibbs free energy ($\Delta G$) due to the H adsorption becomes small. Namely, the interaction between the H states and the substrate becomes considerably weak, which is a highly favorable situation for the HER. Notably, we show that $\Delta G$ for Pt$_3$Sn and Pd$_3$Sn are just -0.066 and -0.092 eV, respectively, which are almost half of the value of Pt., Comment: 12 pages, 6 figures

Photonic topological phases offering unprecedented manipulation of electromagnetic waves have attracted much research interest which, however, have been mostly restricted to a single band gap. Here, we report on the experimental discovery of hybrid topological photonic crystals which host simultaneously quantum anomalous Hall and valley Hall phases in different photonic band gaps. The underlying hybrid topological phase manifests itself in the edge responses as the coexistence of the chiral edge states and valley Hall edge states in different frequency ranges. We experimentally verify such an emergent phenomenon and show that such a feature enables novel multiplexing of photon transport in the edge channels. Our study reveals a situation with coexisting topology of distinct nature in a single photonic system that may enable frequency-dependent filtering and manipulation of topological edge photons.

Bismuth is an archetypal semimetal with gigantic spin-orbit coupling and it has been a major source material for the discovery of seminal phenomena in solid state physics for more than a century. In recent years, spin current transports in bismuth have also attracted considerable attention. In this paper, we theoretically study both spin Hall effect (SHE) and spin Nernst effect (SNE) in bismuth, based on relativistic band structure calculations. First, we find that there are three independent tensor elements of spin Hall conductivity (SHC) and spin Nernst conductivity (SNC), namely, $Z_{yx}^z$, $Z_{xz}^y$, and $Z_{zy}^x$. We calculate all the elements as a function of the Fermi energy. Second, we find that all SHC tensor elements are large, being $\sim$1000 ($\hbar$/e)(S/cm) and comparable to that of platinum. Furthermore, because of its low electrical conductivity, the corresponding spin Hall angles are gigantic, being $\sim$20%. Third, all the calculated SNC tensor elements are also pronounced, being comparable to that [$\sim$0.13 ($\hbar$/e)(A/m-K)] of gold, although they are several times smaller than platinum and $\beta$-Ta. Finally, in contrast to Pt and Au where $Z_{yx}^z = Z_{xz}^y = Z_{zy}^x$, the SHE and SNE in bismuth are strongly anisotropic, i.e., $Z_{yx}^z$, $Z_{xz}^y$ and $Z_{zy}^x$ differ significantly. Consequently, the Hall voltages due to the inverse SHE and SNE from the different conductivity elements could cancel each other and thus result in a small spin Hall angle if polycrystalline samples are used, which may explain why the measured spin Hall angles ranging from nearly 0 to 25% have been reported. We hope that these interesting findings would stimulate further spin current experiments on bismuth using highly oriented single crystal specimens., Comment: 8 pages, 3 figures

Transition metal monosilicides CoSi, CoGe, RhSi and RhGe in the chiral cubic B20 structure have recently been found to host unconventional chiral fermions beyond spin-1/2 WFs, and also exhibit exotic physical phenomena such as long Fermi arc surface states, GME and quantized CPGE. Thus, exploring novel spin-related transports in these unconventional chiral fermion semimetals may open a new door for spintronics and spin caloritronics. In this paper, we study the intrinsic SHE and SNE in the CoSi family based on ab initio relativistic band structure calculations. First, we find that unlike nonchiral cubic metals, the CoSi family have two independent nonzero SHC (SNC) tensor elements, namely, $\sigma_{xy}^z$ and $\sigma_{xz}^y$ ($\alpha_{xy}^z$ and $\alpha_{xz}^y$) instead of one element. Furthermore, the SHC ($\sigma_{xy}^z$ and $\sigma_{xz}^y$) and helicity of the chiral structure are found to be correlated, thus enabling SHE detection of structural helicity and also chiral fermion chirality. Second, the intrinsic SHE and SNE in some of the CoSi family are large. In particular, the calculated SHC of RhGe is as large as -140 ($\hbar$/e)(S/cm). The calculated SNC of CoGe is also large, being -1.3 ($\hbar$/e)(A/m K) at room temperature. Due to their semimetallic nature with low electrical conductivity, these topological semimetals may have large spin Hall and spin Nernst angles, being comparable to that of Pt metal. The SHC and SNC of these compounds can also be increased by raising or lowering $\mu$ to, e.g., the topological nodes, via either chemical doping or electrical gating. Our findings thus indicate that the CoSi family not only would provide a material platform for exploring novel spin-transports and exotic phenomena in unconventional chiral fermion semimetals but also could be promising materials for developing better spintronic and spin caloritronic devices.

Photodetection is an indispensable function of optoelectronic devices in modern communication and sensing systems. Contrary to the near-infrared/visible regions, the fast and sensitive photodetectors operated at room temperature for the far-infrared/terahertz regions are not well developed despite a possibly vast range of applications. The bulk photovoltaic effect (BPVE) in single-phase noncentrosymmetric materials based on the shift current mechanism enables less-dissipative energy conversion endowed with instantaneous responsivity owing to the quantum-mechanical geometric phase of electronic states. Nevertheless, the small-band-gap material for the low-energy BPVE inevitably suffers from the thermal noise due to the intrinsically high conductivity. Here, we demonstrate the shift current induced by soft-phonon excitations without creation of electron-hole pairs in the archetypal ferroelectric BaTiO3 by using the terahertz light, whose energy scale is three orders of magnitude smaller than the electronic band gap. At and above room temperature, we observe appreciable photocurrents caused by the soft-phonon excitation as large as that for electronic excitation and their strong phonon-mode dependence. The observed phonon-driven BPVE can be well accounted for by the shift current model considering the electron-phonon coupling in the displacement-type ferroelectrics as supported by the first-principles calculation. Our findings establish the efficient quantum BPVE arising from low-energy elementary excitations, suggesting the novel principle for the high-performance terahertz photodetectors., Comment: 25 pages, 8 figures

Weyl semimetals (WSMs) have recently stimulated intensive interest because they exhibit fascinating physical properties and also promise exciting technological applications. So far, however, the few conrmed magnetic WSMs generally have a large number of Weyl points either located away from the Fermi level (EF ) or shrouded by nontopological Fermi surface pockets. Based on first principles density functional theory calculations, we establish cubic double perovskite BaEuNiOsO6 to be a high Curie temperature (Tc) ferromagnetic WSM with magnetization along the [111] direction, just two pairs of Weyl points at the EF and Tc = 325 K. The strong ferromagnetism is attributed to the strong ferromagnetic Ni 3d-Eu 4f-Os 5d coupling induced by the substitution of half of Ba atoms with Eu atoms in double perovskite Ba2NiOsO6. Moreover, the momentum separation of one Weyl point pair is large, thus giving rise to not only a long (001) surface Fermi arc but also large anomalous Hall conductivity. Intriguingly, as a unique physical result of a ferromagnetic WSM, the (111) BaEuNiOsO6 monolayer superlattice (BaEuNiOsO6)/(BaTiO3)10, being its (111) quantum-well structure, is found to be a high temperature (Tc = 210 K) Chern insulator with a large band gap of 190 meV. Therefore, cubic double perovskite BaEuNiOsO6 will provide a superior high temperature material plotform for exploring fundamental physics of Weyl fermions and its (111) monolayer superlattices will offer a high temperature magnetic topological insulator for studying exotic quantum phenomena such as quantum anomalous Hall effect.

The simulation of fermionic relativistic physics, e.g., Dirac and Weyl physics, has led to the discovery of many unprecedented phenomena in photonics, of which the optical-frequency realization is, however, still challenging. Here, surprisingly, we discover that the woodpile photonic crystals commonly used for optical frequency applications host exotic fermion-like relativistic degeneracies: a Dirac nodal line and a fourfold quadratic point, as protected by the nonsymmorphic crystalline symmetry. Deforming the woodpile photonic crystal leads to the emergence of type-II Dirac points from the fourfold quadratic point. Such type-II Dirac points can be detected by its anomalous refraction property which is manifested as a giant birefringence in a slab setup. Our findings provide a promising route towards 3D optical Dirac physics in all-dielectric photonic crystals.

Recently, atomically thin PdSe$_2$ semiconductors with rare pentagonal Se-Pd-Se monolayers were synthesized and were also found to possess superior properties such as ultrahigh air stability, and high carrier mobility, thus offering a new family of two-dimensional (2D) materials for exploration of 2D semiconductor physics and for applications in advanced opto-electronic and nonlinear photonic devices. In this work, we systematically study the nonlinear optical (NLO) responses [namely, bulk photovoltaic effect (BPVE), second-harmonic generation (SHG) and linear electric-optic (LEO) effect] of noncentrosymmetric bilayer (BL) and four-layer (FL) PdS$_2$ and PdSe$_2$ by applying the first-principles density functional theory with the generalized gradient approximation plus scissors-correction. First of all, the shift current conductivity is in the order of 130 $\mu$A/V$^2$, being very high compared to known BPVE materials. Similarly, their injection current susceptibilities are in the order of 100$\times$10$^8$A/V$^2$s, again being large. Secondly, the SHG coefficients ($\chi^{(2)}$) of these materials are also large, being one order higher than that of the best-known few-layer group 6B transition metal dichalcogenides. For example, the maximum magnitude of $\chi^{(2)}$ can reach 1.4$\times$10$^3$ pm/V for BL PdSe$_2$ at 1.9 eV and 1.2$\times$10$^3$ pm/V at 3.1 eV for BL PdS$_2$. Thirdly we find significant LEO coefficients for these structures in the low photon energy. All these indicate that 2D PdX$_2$ semiconductors will find promising NLO applications. Fourthly, we find that the large BPVE and SHG of the few-layer PdX$_2$ structures are due to strong intralayer directional covalent bonding and also 2D quantum confinement.

The geometry of quantum states is well-established as a basis for understanding the response of electronic systems to static electromagnetic fields, as exemplified by the theory of the quantum and anomalous Hall effects. However, it has been challenging to relate quantum geometry to resonant optical responses. The main obstacle is that optical transitions involve a pair of states, while existing geometrical properties are defined for a single state. As a result, a concrete geometric understanding of optical responses has so far been limited to two-level systems, where the Hilbert space is completely determined by a single state and its orthogonal complement. Here, we construct a general theory of Riemannian geometry for resonant optical processes by identifying transition dipole moment matrix elements as tangent vectors. This theory applies to arbitrarily high-order responses, suggesting that optical responses can generally be thought of as manifestations of the Riemannian geometry of quantum states. We use our theory to show that third-order photovoltaic Hall effects are related to the Riemann curvature tensor and demonstrate an experimentally accessible regime where they dominate the response., Comment: 14+4 pages, 3 figures, accepted version

The spin chirality, created by magnetic atoms, has been comprehensively understood to generate and control the magneto-optical effects. In comparison, the role of the crystal chirality that relates to nonmagnetic atoms has received much less attention. Here, we theoretically discover the crystal chirality magneto-optical (CCMO) effects, which depend on the chirality of crystal structures that originates from the rearrangement of nonmagnetic atoms. We show that the CCMO effects exist in many collinear antiferromagnets, such as RuO$_{2}$ and CoNb$_{3}$S$_{6}$, which has a local and global crystal chirality, respectively. The key character of the CCMO effects is the sign change if the crystal chirality reverses. The magnitudes of the CCMO spectra can be effectively manipulated by reorienting the N\'eel vector with the help of an external electric field, and the spectral integrals are found to be proportional to magnetocrystalline anisotropy energy., Comment: 6 pages, 4 figs

Few layers Fe$_3$GeTe$_2$ is currently the only atomically thin ferromagnetic metal, and thus has drawn huge attention in the field of two-dimensional (2D) magnetism. In this paper, we perform a systematic first principle study on the electronic structure, magnetic anisotropy energy (MAE), and magneto-optical (MO) effects in monolayer (ML), bilayer (BL) and trilayer (TL) as well as bulk Fe$_3$GeTe$_2$. All the considered structures of Fe$_3$GeTe$_2$ are predicted to have large MAE of order $\sim$3.0 meV/f.u., being larger than reported 2D ferromagnetic semiconductors Cr$_2$Ge$_2$Te$_6$ and CrI$_3$ and also being comparable to that of FePt which has the largest MAE among the transition metal alloys. This large MAE thus stabilizes the long range ferromagnetic order down to atomically thin layers and also suggests promising applications of 2D Fe$_3$GeTe$_2$ in high density data storage. Furthermore, the calculated magneto-optical spectra show large magnetic circular dichroism, thus resulting in large MO Kerr rotation and Faraday rotation angles. In visible frequency range, Kerr rotation angles up to $\sim$1.0$^\circ$ for TL Fe$_3$GeTe$_2$ are found. Such values are larger than famous MO transition metal alloy MnBi. Also, large Faraday rotation angles are predicted for all considered Fe$_3$GeTe$_2$ structures. In particular, ML Fe$_3$GeTe$_2$ has a Faraday rotation angle of -156$^\circ$/$\mu m$, which is three times larger than famous MO oxide Bi$_3$Fe$_5$O$_{12}$. These important findings are analysed in terms of the calculated orbital-decomposed density of states and dipole selection rule derived from the group theory. Our findings thus suggest that few layers and bulk Fe$_3$GeTe$_2$ are promising MO materials and could be widely applied to nano MO devices in the future.

Few-layer selenium and tellurium films have been recently prepared, and they provide a new platform to explore novel properties of two-dimensional (2D) elemental materials. In this work, we have performed a systematic first-principles study on the electronic, linear, and nonlinear optical (NLO) properties of atomically thin selenium and tellurium films within the density-functional theory with the generalized gradient approximation plus scissors correction using the band gaps from the relativistic hybrid Heyd-Scuseria-Ernzerhof functional calculations. Interestingly, we find that few-layer Se and Te possess large second-harmonic generation (SHG), linear electro-optic effect, and bulk photovoltaic effect. In particular, trilayer (TL) Te possesses large SHG coefficient, being more than 65 times larger than that of GaN, a widely used NLO material. Bilayer (BL) Te has huge static SHG coefficient, being more than 100 times larger than that of GaN. Furthermore, monolayer (ML) Se possesses large SHG coefficient. Moreover, we predict that TL Te exhibits strong bulk photovoltaic effect (BPVE), being greater than that of GeS, a polar system with the largest BPVE found so far. Although the shift current conductivities of bulk and 2D Se are comparable, the shift current conductivities of TL Te are five times larger than those of bulk Te. Finally, an analysis of the calculated electronic band structures indicates that the strong NLO responses of 2D Se and Te materials are primarily derived from their low-dimensional structures with high anisotropy, directional covalent bonding, lone-pair electrons, and relatively small band gaps. These findings provide a practical strategy to search for excellent NLO and BPVE materials., Comment: 15pages 12figures

Antiferromagnetism (AF) in AB'-stacked centrosymmetric bilayer (BL) CrI$_3$ breaks both spatial inversion ($P$) and time-reversal ($T$) symmetries but maintains the combined $PT$ symmetry, thus inducing novel second-order nonlinear optical (NLO) responses such as second-harmonic generation (SHG), linear electric-optic effect (LEO) and bulk photovoltaic effect (BPVE). In this work, we calculate AF-induced NLO responses of the BL CrI$_3$ based on the density functional theory with the generalized gradient approximation (GGA) plus onsite Coulomb correlation (U), i.e., the GGA+U method. Interestingly, we find that the magnetic SHG, LEO and photocurrent in the AF BL CrI$_3$ are huge, being comparable or even larger than that of the well-known nonmagnetic noncentrosymmetric semiconductors. For example, the calculated SHG coefficients are in the same order of magnitude as that of MoS$_2$ monolayer (ML), the most promising 2D material for NLO devices. The calculated LEO coefficients are almost three times larger than that of MoS$_2$ ML. The calculated NLO photocurrent in the CrI$_3$ BL is among the largest values predicted so far for the BPVE materials. On the other hand, unlike nonmagnetic semiconductors, the NLO responses in the AF BL CrI$_3$ are nonreciprocal and also switchable by rotating magnetization direction. Therefore, our interesting findings indicate that the AF BL CrI$_3$ will not only provide a valuable platform for exploring new physics of low-dimensional magnetism but also have promising applications in magnetic NLO and LEO devices such as frequency conversion, electro-optical switches, and light signal modulators as well as high energy conversion efficiency photovoltaic solar cells., Comment: 10 pages, 7 figures

The quaternary arsenide compounds XCuYAs (X=Zr, Hf; Y= Si, Ge) belong to the vast family of the 1111-type quaternary compounds, which possess outstanding physical properties ranging from $p$-type transparent semiconductors to high-temperature Fe-based superconductors. In this paper, we study the electronic structure topology, spin Hall effect (SHE) and spin Nernst effect (SNE) in these compounds based on density functional theory calculations. First we find that the four considered compounds are Dirac semimetals with the nonsymmorphic symmetry-protected Dirac line nodes along the Brillouin zone boundary $A$-$M$ and $X$-$R$ and low density of states (DOS) near the Fermi level ($E_F$). Second, the intrinsic SHE and SNE in some of these considered compounds are found to be large. In particular, the calculated spin Hall conductivity (SHC) of HfCuGeAs is as large as -514 ($\hbar$/e)(S/cm). The spin Nernst conductivity (SNC) of HfCuGeAs at room temperature is also large, being -0.73 ($\hbar$/e)(A/m-K). Moreover, both the magnitude and sign of the SHC and SNC in these compounds can be manipulated by varying either the applied electric field direction or spin current direction. The SHE and SNE in these compounds can also be enhanced by tuning the Fermi level via chemical doping or electric gating. Finally, a detailed analysis of the band-decomposed and $k$-resolved spin Berry curvatures reveals that these large SHC and SNC as well as their notable tunabilities originate largely from the presence of a large number of spin-orbit coupling-gapped Dirac points near the Fermi level as well as the gapless Dirac line-nodes, which give rise to large spin Berry curvatures. Our findings thus suggest that the four XCuYAs compounds not only provide a valuable platform for exploring the interplay between SHE, SNE and band topology but also have promising applications in spintronics and spin caloritronics.

Higher-order topology yields intriguing multidimensional topological phenomena, while Weyl semimetals have unconventional properties such as chiral anomaly. However, so far, Weyl physics remain disconnected with higher-order topology. Here, we report the theoretical discovery of higher-order Weyl points and thereby the establishment of such an important connection. We demonstrate that higher-order Weyl points can emerge in chiral materials such as chiral tetragonal crystals as the intermediate phase between the conventional Weyl semimetal and 3D higher-order topological phases. Higher-order Weyl semimetals manifest themselves uniquely by exhibiting concurrent chiral Fermi-arc surface states, topological hinge states, and the momentum-dependent fractional hinge charge, revealing a novel class of higher-order topological phases., Comment: 4+ pages, 4 figures

We study the low-frequency properties of the bulk photovoltaic effect in topological semimetals. The bulk photovoltaic effect is a nonlinear optical effect that generates DC photocurrents under uniform irradiation, allowed by noncentrosymmetry. It is a promising mechanism for a terahertz photodetection based on topological semimetals. Here, we systematically investigate the low-frequency behavior of the second-order optical conductivity in point-node semimetals. Through symmetry and power-counting analysis, we show that Dirac and Weyl points with tilted cones show the leading low-frequency divergence. In particular, we find new divergent behaviors of the conductivity of Dirac and Weyl points under circularly polarized light, where the conductivity scales as $\omega^{-2}$ and $\omega^{-1}$ near the gap-closing point in two and three dimensions, respectively. We provide a further perspective on the low-frequency bulk photovoltaic effect by revealing the complete quantum geometric meaning of the second-order optical conductivity tensor. The bulk photovoltaic effect has two origins, which are the transition of electron position and the transition of electron velocity during the optical excitation, and the resulting photocurrents are respectively called the shift current and the injection current. Based on an analysis of two-band models, we show that the injection current is controlled by the quantum metric and Berry curvature, whereas the shift current is governed by the Christoffel symbols near the gap-closing points in semimetals. Finally, for further demonstrations of our theory beyond simple two-band models, we perform first-principles calculations on magnetic Dirac semimetal MnGeO$_3$and Weyl semimetal PrGeAl. Our work brings out new insights into the structure of nonlinear optical responses as well as for the design of semimetal-based terahertz photodetectors., Comment: 27 pages, 10 figures, first-principles calculations added

The magneto-optical (MO) effects not only are a powerful probe of magnetism and electronic structure of magnetic solids but also have valuable applications in high-density data-storage technology. Yttrium iron garnet (Y$_3$Fe$_5$O$_{12}$) (YIG) and bismuth iron garnet (Bi$_3$Fe$_5$O$_{12}$) (BIG) are two widely used magnetic semiconductors with strong magneto-optical effects and have also attracted the attention for fundamental physics studies. In particular, YIG has been routinely used as a spin current injector. In this paper, we present a thorough theoretical investigation on magnetism, electronic, optical and MO properties of YIG and BIG, based on the density functional theory with the generalized gradient approximation plus onsite Coulomb repulsion. We find that both semiconductors exhibit large MO effects with their Kerr and Faraday rotation angles being comparable to that of best-known MO materials such as MnBi. Especially, the MO Kerr rotation angle for bulk BIG reaches -1.2$ ^{\circ}$ at photon energy $\sim2.4$ eV, and the MO Faraday rotation angle for BIG film reaches -74.6 $ ^{\circ}/\mu m$ at photon energy $\sim2.7$ eV. Furthermore, we also find that both valence and conduction bands across the MO band gap in BIG are purely spin-down states, i.e., BIG is a single spin semiconductor. These interesting findings suggest that the iron garnets will find valuable applications in semiconductor MO and spintronic nanodevices. The calculated optical conductivity spectra, MO Kerr and Faraday rotation angles agree well with the available experimental data. The main features in the optical and MO spectra of both systems are analyzed in terms of the calculated band structures especially by determining the band state symmetries and the main optical transitions at the $\Gamma$ point in the Brillouin zone.

In this work, we present a comparative first principles study of mechanical properties, electronic structure, phonon dispersion relation, electron-phonon coupling and magnetism in three isostructural superconductors, namely, ThFeAsN, ThCoAsN and ThNiAsN. Experimentally, ThFeAsN and ThNiAsN show superconducting properties, while ThCoAsN has not been synthesized. Our calculated elastic constants show that all these systems are mechanically stable. Significant differences in the electronic structures of these three compounds in terms of density of states, band structures and Fermi surfaces, are found. Our phonon calculations reveal that all the systems including ThCoAsN, are dynamically stable. Phonon dispersion relations indicate that the optical modes of all the three systems are almost the same while there are significant variations in the low frequency manifold consisting of mixed modes. The electron-phonon coupling constants and superconducting transition temperatures calculated based on the Eliashberg formalism, predict a rather high $T_c$ of 6.4 K for ThCoAsN and also a $T_c$ of 3.4 K for ThNiAsN which agrees well with the experimental value of 4.3 K. Nevertheless, we find a $T_c$ of 0.05 K for ThFeAsN, which is much smaller than the experimental $T_c$ of $\sim$30 K. However, a simple analysis considering the amplifying effects of spin density wave order and out-of-plane soft phonon modes suggests that the $T_c$ could be increased considerably to $\sim$10 K. Finally, we also discuss the effect of anion As height on the electronic structures and study possible magnetic states in these three compounds., Comment: accepted for publication in the Phys. Rev. B

In this paper, we present pressure dependent structural parameters and electronic structure of ThFeAsN superconductor. There are no anomalies in the structural parameters as well as elastic constants with hydrostatic pressure which is consistent with the experiments. We study the electronic structure of this compound at different external pressures in terms of density of states, band structure and Fermi surface. Density of states at the Fermi level, coming from Fe-d orbitals follows the same trend as that of the superconducting transition temperature (T$_c$) as a function of hydrostatic pressure. We also observe a pressure induced orbital selective Lifshitz transition in ThFeAsN compound which is quite different from the Lifshitz transitions observed in the other families of Fe-based superconductors. Fermi surfaces of ThFeAsN specially hole like Fermi surfaces at $\Gamma$ point are altered significantly with pressure. This modification of Fermi surface topology with pressure seems to play the major role in the reduction of T$_c$ with pressure in ThFeAsN superconductor. Spin-orbit coupling does not affect the Lifshitz transition but it modifies the energy ordering of bands near $\Gamma$ point at higher pressure.

Organic-inorganic hybrid halide perovskites have ignited tremendous interests for photovoltaic applications. However, their nonlinear optical response has not been studied although many of these structures lack the centrosymmetry and exhibit ferroelectricity. In this work, we employ our developed large-scale parallel, first-principles simulation tool (ArchNLO) to explore second-order nonlinear optical properties of a typical family of organic-inorganic hybrid halide perovskites, CH3NH3MX3 (M= Ge, Sn, Pb; X=Cl, Br, I). We find that these hybrid perovskites exhibit second harmonic generation and linear electro-optic effect. The nonlinear optical effects are strongly influenced by the types and positions of cations/anions and corresponding band gaps. Particularly, the distorted cubic phase, which is essentially triclinic, of CH3NH3SnI3 shows significant second harmonic generation and electro-optic effect, which are comparable with those widely used materials, such as GaAs. These second-order optical properties of organic-inorganic hybrid halide perovskites and their low-temperature, solution-based fabrication pave the way for achieving and implementing nonlinear optical devices with low cost., Comment: 29 pages, 9 figures, and 3 tables

Dirac semimetals (DSMs) are three dimensional analogue to graphene with symmety enforced bulk Dirac nodes. Among various DSMs, ZrSiS has been attracting more interests recently, due to its three dimensional Dirac nodal line protected by the nonsymmorphic symmetry. It actually belongs to a large family of isostructural compounds with unique quantum phenomenon. Here we present a comprehensive study of the first principle calculation, angle-resolved photoemission spectroscopy (ARPES) measurements, and scanning tunneling microscope (STM) experiments on ZrGeTe, a member of the ZrSiS family with stronger spin-orbit coupling (SOC). Our band structure calculation shows the existence of floating gapless surface states at $\bar{X}$ with Rashba splitted helical spin texture, which are confirmed by our ARPES measurements. We also perform quasiparticle scattering interference (QPI) imaging and find several q-vectors, with two Umklapp scattering vectors not observed in other family compounds. All the q-vectors can be identified with joint density of states (JDOS) simulation. Our results demonstrate the interesting electronic structure of ZrGeTe and might benefit the potential application by utilizing its exotic quantum states in the future., Comment: 12 pages, 5 figures

The ZrSiS-type compounds are Dirac semimetals and have been attracting considerable interest in recent years due to their topological electronic properties and possible applications. In particular, gapped Dirac nodes can possess large spin Berry curvatures and thus give rise to large spin Hall effect (SHE) and spin Nernst effect (SNE), which may be used to generate pure spin current for spintronics and spin caloritronics without applied magnetic field or magnetic material. In this paper we study both SHE and SNE in ZrXY (X = Si, Ge; Y = S, Se, Te) based on \textit{ab initio} relativistic band structure calculations. Our theoretical calculations reveal that some of these compounds exhibit large intrinsic spin Hall conductivity (SHC) and spin Nernst conductivity (SNC). The calculated SHC of ZrSiTe is as large as -755 ($\hbar$/e)(S/cm). Since the electric conductivity of these Dirac semimetals are much smaller than that of platinum which has the largest intrinsic SHC of $\sim$2200 ($\hbar$/e)(S/cm), this indicates that they will have a larger spin Hall angle than that of platinum. Remarkably, we find that both the magnitude and sign of the SHE and SNE in these compounds can be significantly tuned by changing either the electric field direction or spin current direction and may also be optimized by slightly varying the Fermi level via chemical doping. Analysis of the calculated band- and $k$-resolved spin Berry curvatures show that the large SHE and SNE as well as their remarkable tunabilities originate from the presence of many slightly spin-orbit coupling-gapped Dirac nodal lines near the Fermi level in these Dirac semimetals. Our findings suggest that the ZrSiS-type compounds are promising candidates for spintronic and spin caloritronic devices, and will certainly stimulate further experiments on these Dirac semimetals., Comment: 9 pages, 6 figures

Controlling light propagation using artificial photonic crystals and electromagnetic metamaterials is an important topic in the vibrant field of photonics. Notably, chiral edge states on the surface or at the interface of photonic Chern insulators can be used to make reflection-free waveguides. Here, by both theoretical analysis and electromagnetic simulations, we demonstrate that gyromagnetic hyperbolic metamaterials (GHM) are photonic Chern insulators with superior properties. As a novel mechanism, the simultaneous occurrence of the hyperbolic and gyromagnetic effects in these metamaterials is shown to open the large topological band gaps with gap Chern number of one. Importantly, unlike many other photonic Chern insulators, the GHM Chern insulators possess non-radiative chiral edge modes on their surfaces, and thus allow to fabricate unidirectional waveguides without cladding metals which generally incurr considerable Ohmic loss. Furthermore, the photonic edge states in the proposed Chern insulators are robust against disorder on a wide range of length scales, in strong contrast to crystalline topological insulators, and the light flow direction on the surface of the Chern insulators can be easily flipped by switching the direction of an applied magnetic field. Fascinatingly, we find that negative refraction of the topological surface wave occurs at the boundary between the GHMs with the opposite signs of gyromagnetic parameters. Finally, we show that compared with other photonic topological materials such as chiral hyperbolic materials, the present GHM Chern insulators can be much easier to fabricate.

Resulting from strong magnetic anisotropy two-dimensional ferromagnetism was recently shown to be stabilized in chromium triiodide, CrI$_3$, in the monolayer limit. While its properties remain largely unexplored, it provides a unique material-specific platform to unveil its electromagnetic properties associated with coupling of modes. Indeed, trigonal symmetry in the presence of out-of-plane magnetization results in a non-trivial structure of the conductivity tensor, including the off-diagonal terms. In this paper, we study the surface electromagnetic waves localized in a CrI$_3$-based structure using the results of {\it ab initio} calculations for the CrI$_3$ conductivity tensor. In particular, we provide an estimate for the critical angle corresponding to the surface plasmon polariton generation in the Kretschmann-Raether configuration by a detailed investigation of reflectance spectrum as well as the magnetic field distribution for different CrI$_3$ layer thicknesses. We also study the bilayer structure formed by two CrI$_3$ layers separated by a SiO$_2$ spacer and show that the surface plasmon resonance can be achieved at the interface between CrI$_3$ and air depending on the spacer thickness., Comment: 11 pages, 6 figures

We carry out a first-principles investigation on magnetism, electronic structure, magneto-optical effects and topological property of newly grown cubic double perovskite Ba2NiOsO6 and its (111) (Ba2NiOsO6)/(BaTiO3)10 superlattice, based on the density functional theory with the generalized gradient approximation (GGA) plus onsite Couloumb interactions. Interestingly, we find that both structures are rare ferromagnetic (FM) semiconductors with estimated Curie temperatures of ~150 and 70 K, respectively. The calculated near-neighbor exchange coupling parameters reveal that the ferromagnetism is driven by exotic FM coupling between Ni and Os atoms, which is due to the FM superexchange interaction caused by the abnormally strong hybridization between the half-filled Nieg and unoccupied Os eg orbitals. The strong spin-orbit coupling (SOC) on the Os atom is found to not only open the semiconducting gap but also produce a large antiparallel orbital magnetic moment on the Os atom, thus reducing the total magnetization from 4.0 uB/f.u.

In normal metals, the magnetic-moment of impurity-spins disappears below a characteristic Kondo temperature, TK. This marks the formation of a polarized cloud of conduction band electrons that screen the magnetic moment . In contrast, moments embedded in insulators remain unscreened at all temperatures. This raises the question about the fate of magnetic-moments in intermediate, pseudogap systems, such as graphene. In these systems coupling between the local moment and the conduction band electrons is predicted to drive a quantum phase-transition between a local-moment phase and a Kondo-screened singlet phase as illustrated in Fig. 1A. However, attempts to experimentally confirm these predictions and their intriguing consequences such as the ability to electrostatically tune magnetic-moments, have been elusive. Here we report the observation of Kondo screening and the quantum phase-transition between screened and unscreened phases of vacancy magnetic-moments in graphene. Using scanning-tunneling-microscopy (STM), spectroscopy (STS) and numerical-renormalization-group (NRG) calculations, we identified Kondo-screening by its spectroscopic signature and mapped the quantum phase-transition as a function of coupling strength and chemical potential. We show that the coupling strength can be tuned across this transition by variations in the local curvature and furthermore that the transition makes it possible to turn the magnetic-moment on and off with a gate voltage., Comment: 28 pages 9 figures. arXiv admin note: substantial text overlap with arXiv:1711.06942

Trigonal selenium and tellurium crystalize in helical chain-like structures and thus possess interesting properties such as current-induced spin polarization, gyrotropic effects and nonlinear optical responses. By performing systematic ab initio calculations based on density functional theory in the generalized gradient approximation plus scissors correction, we study their linear and nonlinear optical (NLO) properties. We find that the two materials exhibit significant second-harmonic generation (SHG) and linear electro-optic (LEO) effect. In particular, the SHG coefficients of tellurium are huge in the photon energy range of 0 ~ 3 eV, with the magnitudes of SHG(xxx) being as large as 3640 pm/V, which are about sixteen times larger than that of GaN, a widely used NLO material. On the other hand, trigonal selenium is found to possesses large LEO coefficients r(xxx,0) which are more than six times larger than that of GaN.Therefore, trigonal tellurium and selenium may find valuable applications in NLO and LEO devices such as frequency conversion, electro-optical switch and light signal modulator.The energy positions and shapes of the principal features in the calculated optical dielectric functions of both materials agree rather well with the available experimental ones, and are also analyzed in terms of the calculated band structures especially symmetries of the involved band states and dipole transition selection rules.

Noncollinear antiferromagnets (AFMs) have recently attracted a lot of attention owing to the potential emergence of exotic spin orders on geometrically frustrated lattices, which can be characterized by corresponding spin chiralities. By performing first-principles density functional calculations together with group-theory analysis and tight-binding modelling, here we systematically study the spin-order dependent anomalous Hall effect (AHE) and magneto-optical effect (MOE) in representative noncollinear AFMs Mn$_{3}X$N ($X$ = Ga, Zn, Ag, and Ni). The symmetry-related tensor shape of the intrinsic anomalous Hall conductivity (IAHC) for different spin orders is determined by analyzing the relevant magnetic point groups. We show that while only the ${xy}$ component of the IAHC tensor is nonzero for right-handed spin chirality, all other elements, $\sigma_{xy}$, $\sigma_{yz}$, and $\sigma_{zx}$, are nonvanishing for a state with left-handed spin chirality owing to lowering of the symmetry. Our tight-binding arguments reveal that the magnitude of IAHC relies on the details of the band structure and that $\sigma_{xy}$ is periodically modulated as the spin rotates in-plane. The IAHC obtained from first principles is found to be rather large, e.g., it amounts to 359 S/cm in Mn$_{3}$AgN. By extending our analysis to finite frequencies, we calculate the optical isotropy [$\sigma_{xx}(\omega)\approx\sigma_{yy}(\omega)\approx\sigma_{zz}(\omega)$] and the magneto-optical anisotropy [$\sigma_{xy}(\omega)\neq\sigma_{yz}(\omega)\neq\sigma_{zx}(\omega)$] of Mn$_{3}X$N. We argue that the spin-order dependent AHE and MOE are indispensable in detecting complex spin structures in noncollinear AFMs., Comment: 13 pages, 7 figures

The rapid development of topological photonics and acoustics calls for accurate understanding of band topology in classical waves, which is not yet achieved in many situations. Here, we present the Wilson-loop approach for exact numerical calculation of the topological invariants for several photonic/sonic crystals. We demonstrate that these topological photonic/sonic crystals are topological crystalline insulators with fragile topology, a feature which has been ignored in previous studies. We further discuss the bulk-edge correspondence in these systems with emphasis on symmetry broken on the edges.

The latest discovery of ferromagnetism in atomically thin films of semiconductors Cr$_2$Ge$_2$Te$_6$ and CrI$_3$ has unleashed numerous opportunities for fundamental physics of magnetism in two-dimensional (2D) limit and also for technological applications based on 2D magnetic materials. In this paper, we present a comprehensive theoretical study of the magnetic, electronic, optical and magneto-optical(MO) properties of multilayers [monolayer(ML), bilayer and trilayer] and bulk CrI$_3$, based on the density functional theory with the generalized gradient approximation plus on-site Coulomb repulsion scheme. Interestingly, all the structures are found to be single-spin ferromagnetic(FM) semiconductors. They all have a large out-of-plane magnetic anisotropy energy(MAE) of $\sim$0.5 meV/Cr. These large MAEs suppress transverse spin fluctuations and thus stabilize long-range magnetic orders at finite temperatures down to the ML limit. They also exhibit strong MO effects with their Kerr and Faraday rotation angles being comparable to that of best-known bulk MO materials. The shape and position of the main features in the optical and MO spectra are found to be nearly thickness-independent although the magnitude of Kerr rotation angles increases monotonically with the film thickness. Magnetic transition temperatures estimated based on calculated exchange coupling parameters, calculated optical conductivity, MO Kerr and Faraday rotation angles agree quite well with available experimental data. The calculated MAE as well as optical and MO properties are analyzed in terms of the calculated orbital-decomposed densities of states, band state symmetries and dipole selection rules. Our findings of large out-of-plane MAEs and strong MO effects in these single-spin FM semiconducting CrI$_3$ ultrathin films suggest that they will find valuable applications in semiconductor MO and spintronic nanodevices.

Quantum anomalous Hall (QAH) phases in magnetic topological insulators are characterized by the scattering-free chiral edge currents protected by their nontrivial bulk band topology. To fully explore these intriguing phenomena and application of topological insulators, high temperature material realization of QAH phases is crucial. In this paper, based on extensive first-principles density functional theory calculations, we predict that perovskite bilayers (LaXO$_3$)$_{2}$ (X = Pd, Pt) imbedded in the (111) (LaXO$_3$)$_{2}$/(LaAlO$_3$)$_{10}$ superlattices are high Curie temperature ferromagnets that host both QAH and Dirac semimetal phases, depending on the biaxial strain and onsite electron correlation. In particular, both the direction (the sign of Chern number) and spin-polarization of the chiral edge currents are tunable by either onsite electron correlation or biaxial in-plane strain. Furthermore, the nontrivial band gap can be enhanced up to 92 meV in the LaPdO$_3$ bilayer by the compressive in-plane strain, and can go up to as large as 242 meV when the Pd atoms are replaced by the heavier Pt atoms. Finally, the microscopic mechanisms of the ferromagnetic coupling and other interesting properties of the bilayers are uncovered by analyzing their underlying electronic band structures.

Reflecting the fundamental interactions of polarized light with magnetic matter, magneto-optical effects are well known since more than a century. The emergence of these phenomena is commonly attributed to the interplay between exchange splitting and spin-orbit coupling in the electronic structure of magnets. Using theoretical arguments, we demonstrate that topological magneto-optical effects can arise in noncoplanar antiferromagnets due to the finite scalar spin chirality, without any reference to exchange splitting or spin-orbit coupling. We propose spectral integrals of certain magneto-optical quantities that uncover the unique topological nature of the discovered effect. We also find that the Kerr and Faraday rotation angles can be quantized in insulating topological antiferromagnets in the low-frequency limit, owing to nontrivial global properties that manifest in quantum topological magneto-optical effects. Although the predicted topological and quantum topological magneto-optical effects are fundamentally distinct from conventional light-matter interactions, they can be measured by readily available experimental techniques., Comment: 10 pages, 5 figures

Dirac nodal line semimetals represent a new state of quantum matters in which the electronic bands touch to form a closed loop with linear dispersion. Here, we report a combined study on ZrSiS by density functional theory calculation, scanning tunneling microscope (STM) and magneto-transport measurements. Our STM measurements reveal the spectroscopic signatures of a diamond-shaped Dirac bulk band and a surface band on two types of cleaved surfaces as well as a spin polarized surface band at ${\bar{\Gamma}}$ at E~0.6eV on S-surface, consistent with our band calculation. Furthermore, we find the surface termination does not affect the surface spectral weight from the Dirac bulk bands but greatly affect the surface bands due to the change in the surface orbital composition. From our magneto-transport measurements, the primary Shubnikov de-Haas frequency is identified to stem from the hole-type quasi-two-dimensional Fermi surface between {\Gamma} and X. The extracted non-orbital magnetoresistance (MR) contribution D($\theta$, H) yields a nearly H-linear dependence, which is attributed to the intrinsic MR in ZrSiS. Our results demonstrate the unique Dirac line nodes phase and the dominating role of Zr-d orbital on the electronic structure in ZrSiS and the related compounds.

By performing systematic $ab$ $initio$ density functional calculations, here we study two relativity-induced properties of atomically thin ferromagnetic (FM) Cr$_2$Ge$_2$Te$_6$ films [monolayer (ML), bilayer (BL) and trilayer (TL) as well as bulk], namely, magnetic anisotropy energy (MAE) and magneto-optical (MO) effects. Competing contributions of both magneto-crystalline anisotropy energy (C-MAE) and magnetic dipolar anisotropy energy (D-MAE) to the MAE, are computed. Calculated MAEs of these materials are large, being in the order of $\sim$0.1 meV/Cr. Interestingly, we find that the out-of-plane magnetic anisotropy is preferred in all the systems except the ML where an in-plane magnetization is favored because here the D-MAE is larger than the C-MAE. Crucially, this explains why long-range FM order was observed in all the few-layer Cr$_2$Ge$_2$Te$_6$ except the ML because the out-of-plane magnetic anisotropy would open a spin-wave gap and thus suppress magnetic fluctuations so that long-range FM order could be stabilized at finite temperature. In the visible frequency range, large Kerr rotations up to $\sim$1.0 deg in these materials are predicted and they are comparable to that observed in famous MO materials such as PtMnSb and Y$_3$Fe$_5$O$_{12}$. Moreover, they are $\sim$100 times larger than that of 3$d$ transition metal MLs deposited on Au surfaces. Faraday rotation angles in these 2D materials are also large, being up to $\sim$120 deg/$\mu$m, and are thus comparable to the best-known MO semiconductor Bi$_3$Fe$_5$O$_{12}$. These findings thus suggest that with large MAE and MO effects, atomically thin Cr$_2$Ge$_2$Te$_6$ films would have potential applications in novel magnetic, MO and spintronic nanodevices.

In this paper, we investigate the electronic band structure, lattice dynamics and electron-phonon interaction in $\delta$-NbN, $\varepsilon$-NbN and WC-NbN by performing systematic ab initio calculations based on DFT-GGA. The calculated electronic band structures show that all three polytypes are metallic with the Nb $d$-orbital dominated energy bands near the Fermi level ($E_F$). The calculated phonon dispersion relations of $\delta$-NbN are in good agreement with neutron scattering experiments. The electron-phonon coupling ($\lambda$) in $\delta$-NbN ($\lambda=0.98$) is much stronger than in $\varepsilon$-NbN ($\lambda=0.16$) and WC-NbN ($\lambda=0.11$). This results in a much higher superconducting transition temperature ($T_c =18.2$ K) than in $\varepsilon$-NbN and WC-NbN ($T_c \le 1.0$ K). The stronger $\lambda$ and higher $T_c$ in $\delta$-NbN are attributed to its large density of states at $E_F$ and small Debye temperature. The calculated $T_c$ of $\delta$-NbN is in good agreement with the experimental values. However, the predicted $T_c$ of $\varepsilon$-NbN is much smaller than the recent experiment (11.6 K) but agrees well with the earlier experiment. Finally, the calculated relativistic band structures reveal that all three NbN polytypes are topological metals. Specifically, $\varepsilon$-NbN and $\delta$-NbN are, respectively, type-I and type-II Dirac metals, while WC-NbN is an emergent topological metal that has rare triply degenerate nodes. All these results indicate that all the three NbN polytypes should be hard superconductors with nontrivial band topology that would provide valuable opportunities for studying fascinating phenomena arising from the interplay of band topology and superconductivity., Comment: All 4 NbN polytypes are now studied. All 7 figures are revised and new Fig. 8 is added. The manuscript has been substantially revised

We study the magnetic properties in the vicinity of a single carbon defect in a monolayer of graphene. We include the unbound $\sigma$ orbital and the vacancy induced bound $\pi$ state in an effective two-orbital single impurity model. The local magnetic moments are stabilized by the Coulomb interaction as well as a significant ferromagnetic Hund's rule coupling between the orbitals predicted by a density functional theory calculation. A hybridization between the orbitals and the Dirac fermions is generated by the curvature of the graphene sheet in the vicinity of the vacancy. We present results for the local spectral function calculated using Wilson's numerical renormalization group approach for a realistic graphene band structure and find three different regimes depending on the filling, the controlling chemical potential, and the hybridization strength. These different regions are characterized by different magnetic properties. The calculated spectral functions qualitatively agree with recent scanning tunneling spectra on graphene vacancies., Comment: 18 pages, 15 figures

The symmetry considerations that imply a non-zero anomalous Hall effect (AHE) in certain non-collinear antiferromagnets also imply both non-zero orbital magnetization and a net spin magnetization. We have explicitly evaluated the orbital magnetizations of several anomalous Hall effect antiferromagnets and find that they tend to dominate over spin magnetizations, especially so when spin-orbit interactions are weak. Because of the greater relative importance of orbital magnetization the coupling between magnetic order and an external magnetic field is unusual. We explain how magnetic fields can be used to manipulate magnetic configurations in these systems, pointing in particular to the important role played by the response of orbital magnetization to the Zeeman-like spin exchange fields., Comment: 5 pages + supplementary materials; revised version

We study the optical properties of bi-anisotropic optical waveguides with nontrivial topological structure in wavevector space, placed in an ordinary dielectric matrix. We derive an exact analytical description of the eigenmodes of the systems with arbitrary parameters that allows us to investigate topologically protected surface states (TPSS) in details. In particular, we find that the TPSS on the waveguides would disappear (1) if their radius is smaller than a critical radius due to the dimensional quantization of azimuthal wavenumber, and also (2) if the permittivity of the host-medium exceeds a critical value. Interestingly, we also find that the TPSS in the waveguides have negative refraction for some geometries. We have found a TPSS phase diagram that will pave the way for development of the topological waveguides for optical interconnects and devices., Comment: 21 pages, 16 figures