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The $GW$ approximation is a widely used framework for studying correlated materials, but it struggles with certain limitations, such as its inability to explain pseudogap phenomena. To overcome these problems, we propose a systematic theoretical framework for Green's function corrections and apply it specifically to the $GW$ approximation. In this new theory, the screened potential is reconnected to the physical response function, i.e. the covariant response function proposed in \cite{cGW_2023}, rather than using the RPA formula. We apply our scheme to calculate Green's function, the spectral function, and the charge compressibility in the two-dimensional Hubbard model. Our scheme yields significant qualitative and quantitative improvements over the standard $GW$ method and successfully captures the pseudogap behavior., Comment: 13 pages, 5 figures

High-$T_c$ cuprates are characterized by strong spin fluctuations, which give rise to antiferromagnetic and pseudogap phases and may be key to the high superconducting critical temperatures observed in these materials. Experimental studies have revealed significant changes in the Hall coefficient $R_H$ across these phases, a phenomenon closely related to both spin fluctuations and changes in the Fermi surface morphology. Using the perturbation correction to Gaussian approximation (PCGA), we investigate the two-dimensional(2D) square-lattice single-band Hubbard model and obtain the self-energy with a finite imaginary part due to scattering. We calculate the density dependence of the Hall number $n_H=1/(qR_H)$. For small hole (or electron) doping $p$ (or $x$), our numerical results show that $n_H$ transitions from $p$ to $1+p$ for hole-doped systems, and from $-x$ to $1-x$ for electron-doped systems -- both in agreement with experimental findings. Furthermore, we discuss the correlation between phase boundaries and the observed peculiar changes in the Hall number., Comment: 9 pages, 6 figures

The transport of Bloch electrons under strong fields is traditionally understood through two mechanisms: intraband Bloch oscillations and interband Zener tunneling. Here we propose a new oscillation mechanism induced by the interband quantum metric, which would significantly affect the electron dynamics under strong fields. By considering the multiband dynamics to the second order of the density matrix, we reveal that quantum metric-induced oscillations (QMO) persist regardless of band dispersion, even in exactly flat bands. The resultant drift current can reach a magnitude comparable to the Bloch oscillations-induced drift current in systems where interband tunneling is negligible. Notably, the {QMO}-induced drift current increases linearly with electric field strength under the constraints of time-reversal or spatial-inversion symmetry, emerging as the primary delocalized current. We further show that both one-dimensional and two-dimensional superlattices are potential platforms for investigating QMO.

Topological semimetals in chiral crystals, which possess both structural handedness and band crossings (or nodes) with topological chiral charge, exhibit many exotic physical properties. Here we demonstrate that the structural and electronic chirality of these systems can endow them with another fascinating phenomenon -- the intrinsic nonlinear planar Hall effect (INPHE), which is prominent around the nodes and reverses sign upon chirality reversal in opposite enantiomers. Taking chiral tellurium as an example, we reveal an intrinsic orbital mechanism, which manifests diverging orbital magnetic moments with hedgehog-like textures around nodes and, therefore, generates a dominant contribution to the INPHE that is proportional to the topological charge. Furthermore, we show that multifold fermions in topological chiral semimetals with B20 structures (e.g., CoSi and PtAl) induce a giant INPHE conductivity reaching the order of $1\sim 10\; \mathrm{A}\cdot\mathrm{V}^{-2}\cdot\mathrm{T}^{-1}$, which is detectable in experiments. Our study not only relates nonlinear transport to band topology and enantiomer recognition but also offers a new way to explore the exotic physical properties associated with unconventional chiral fermions.

Twisted multilayer systems, encompassing materials like twisted bilayer graphene (TBG), twisted trilayer graphene, and twisted bilayer transition metal dichalcogenides, have garnered significant attention in condensed matter physics. Despite this interest, a comprehensive description of their electronic structure, especially in dealing with incommensurate wave functions, poses a persistent challenge. Here, we introduce a unified theoretical framework for efficiently describing the electronic structure covering both spectrum and wave functions in twisted multilayer systems, accommodating both commensurate and incommensurate scenarios. Our analysis reveals that physical observables in these systems can be systematically decomposed into contributions from individual layers and their respective ${k}$ points, even in the presence of intricate interlayer coupling. This decomposition facilitates the computation of wave function-related quantities relevant to response characteristics beyond spectra. We propose a local low-rank approximated Hamiltonian in the truncated Hilbert space that can achieve any desired accuracy, offering numerical efficiency compared to the previous large-scale calculations. The validity of our theory is confirmed through computations of spectra and optical conductivity for moir\'e TBG, and demonstrating its applicability in incommensurate quasicrystalline TBG. Our findings provide a generic approach to studying the electronic structure of twisted multilayer systems and pave the way for future research., Comment: 38 pages, 18 figures

We propose a real-space formalism of the topological Euler class, which characterizes the fragile topology of two-dimensional systems with real wave functions. This real-space description is characterized by local Euler markers whose macroscopic average coincides with the Euler number, and it applies equally well to periodic and open boundary conditions for both crystals and noncrystalline systems. We validate this by diagnosing topological phase transitions in clean and disordered crystalline systems with the reality endowed by the space-time inversion symmetry $\mathcal{I}_{ST}$. Furthermore, we demonstrated the topological Euler phases in quasicrystals and even in amorphous lattices lacking any spatial symmetries. Our work not only provides a local characterization of the fragile topology but also significantly extends its territory beyond $\mathcal{I}_{ST}$-symmetric crystalline materials., Comment: 41 pages,8 figures

We generalize the nested Wilson loop formalism, which has been playing an important role in the study of topological quadrupole insulators, to two-dimensional (2D) and 3D nonsymmorphic materials with higher-order topology. In particular, certain 3D Dirac semimetals exhibit 1D higher-order Fermi arc (HOFA) states localizing on hinges where two surfaces meet and connecting the projection of the bulk Dirac points. We discover that the generalized nested Berry phase (gNBP) derived from this formalism is the bulk topological indicator determining the existence/absence of HOFAs, revealing a direct bulk-hinge correspondence in 3D Dirac semimetals. Finally, we study the Dirac semimetals NaCuSe and KMgBi based on first-principles calculations and explicitly show that the change in gNBP adjacent to the Dirac point corresponds to the termination of HOFAs at the projection of Dirac points on the hinge. Our findings not only improve the understanding of the bulk-hinge correspondence in topological Dirac semimetals but also provide a general formalism for studying the higher-order topology in nonsymmorphic systems.

The respective unique merit of antiferromagnets and two-dimensional (2D) materials in spintronic applications inspire us to exploit 2D antiferromagnetic spintronics. However, the detection of the N\'eel vector in 2D antiferromagnets remains a great challenge because the measured signals usually decrease significantly in the 2D limit. Here we propose that the N\'eel vector of 2D antiferromagnets can be efficiently detected by the intrinsic nonlinear Hall (INH) effect which exhibits unexpected significant signals. As a specific example, we show that the INH conductivity of the monolayer manganese chalcogenides Mn$X$ ($X$=S, Se, Te) can reach the order of nm$\cdot$mA/V$^2$, which is orders of magnitude larger than experimental values of paradigmatic antiferromagnetic spintronic materials. The INH effect can be accurately controlled by shifting the chemical potential around the band edge, which is experimentally feasible via electric gating or charge doping. Moreover, we explicitly demonstrate its $2\pi$-periodic dependence on the N\'eel vector orientation based on an effective $k.p$ model. Our findings enable flexible design schemes and promising material platforms for spintronic memory device applications based on 2D antiferromagnets.

We investigate the effect of disorder on topologically nontrivial states in a two dimension (2D) mechanical system. We first propose a quantum spin Hall (QSH) insulator based on an out-of-plane spring-mass model and analytically study the interplay between the disorder and topology in both topologically trivial and nontrivial systems. We adopt the spin Bott index to characterize the topological property in disordered mechanical systems. By tracking the evolution of the spin Bott index with the increase of disorders, we quantitatively demonstrate the disorder induced transition from a topologically nontrivial QSH insulator to a trivial insulator. We then validate the topological phase transition through transient analysis in discrete lattices. Finally, we design a phononic crystal based on the discrete spring-mass model and numerically verify the topologically protected states along the boundary between the trivial insulator and disordered topological QSH insulator in a continuous system. This work puts a step forward in understanding the role of disorder in a 2D topological classical system.

Two-dimensional (2D) Stiefel-Whitney (SW) insulator is a fragile topological state characterized by the second SW class in the presence of space-time inversion symmetry. So far, SWIs have been proposed in several electronic materials but seldom in phononic systems. Here we recognize that a large class of 2D buckled honeycomb crystals termed Xenes and their ligand-functionalized derivatives realize the nontrivial phononic SW topology. The phononic SWIs are identified by a nonzero second SW number $w_2=1$, associated with gaped edge states and robust topological corner modes. Despite the versatility of electronic topological properties in these materials, the nontrivial phononic SW topology is mainly attributed to the double band inversion between in-plane acoustic and out-of-plane optical bands with opposite parities due to the structural buckling of the honeycomb lattice. Our findings not only reveal an overlooked phononic topological property of 2D Xene-related materials, but also afford abundant readily synthesizable material candidates with simple phononic spectra for further experimental studies of phononic SW topology physics., Comment: Phys. Rev. B (in press)

The calculation of response functions in correlated electronic systems is one of the most important problems in the condensed matter physics. To obtain a physical response function, preserving both the Ward-Takahashi identity and the fluctuation-dissipation theorem are crucial. Here we propose a self-consistent many body method within the GW framework to calculate the response functions based on the fluctuation-dissipation theorem, which also satisfies the Ward-Takahashi identity. The validity of this methodology is demonstrated on the two-dimensional one-band Hubbard model, where both the Ward-Takahashi identity and fluctuation-dissipation theorem are verified numerically. Moreover, comparing to the accurate spin susceptibility of the determinantal Monte Carlo approach, the results obtained from our method are quite satisfactory and the computational cost are greatly reduced., Comment: 12 pages, 4 figures, supplemental material 15 pages

High-order topological insulators (HOTIs), as generalized from topological crystalline insulators (TCIs), are characterized with lower-dimensional metallic boundary states protected by spatial symmetries of a crystal, whose theoretical framework based on band inversion at special $k$-points cannot be readily extended to quasicrystals because quasicrystals contain rotational symmetries that are not compatible with crystals, and momentum is no longer a good quantum number. Here, we develop a low-energy effective model underlying HOTI states in 2D quasicrystals for all possible rotational symmetries. By implementing a novel Fourier transform developed recently for quasicrystals and approximating the long-wavelength behavior by their large-scale average, we construct an effective $k \cdot p$ Hamiltonian to capture the band inversion at the center of a pseudo-Brillouin zone (PBZ). We show that an in-plane Zeeman field can induce mass-kinks at the intersection of adjacent edges of a 2D quasicrystal TI and generate corner modes (CMs) with fractional charge, protected by rotational symmetries. Our model predictions are confirmed by numerical tight-binding calculations. Furthermore, when the quasicrystal is proximitized by an \textit{s}-wave superconductor, Majorana CMs can also be created by tuning the field strength and chemical potential. Our work affords a generic approach to studying the low-energy physics of quasicrystals, in association with topological excitations and fractional statistics., Comment: 14 pages,4 figures

The performance and radiation tolerance of the proton detector based on MAPbBr3 perovskite single crystal are investigated here with 3MeV protons. The detector can monitor fluence rate and dose quantificationally at a low applied bias electric field(0.01$V/{\mu}m$) within a dose range of 45 kGy. The detector can also be worked at zero bias due to the Dember effect. The dark current of the detector reduced to 20% of the initial value after being irradiated with protons to a total fluence of $7.3\times 10^{13} p/cm^2$ (1 MGy), however, it can be recovered at room temperature within hours. These results suggest that this kind of detector has a promising application in proton therapy and proton imaging etc., Comment: 19 pages, 7 figures

Two-dimensional (2D) Stiefel-Whitney insulator (SWI), which is characterized by the second Stiefel-Whitney class, is a new class of topological phases with zero Berry curvature. As a novel topological state, it has been well studied in theory but seldom realized in realistic materials. Here we propose that a large class of liganded Xenes, i.e., hydrogenated and halogenated 2D group-IV honeycomb lattices, are 2D SWIs. The nontrivial topology of liganded Xenes is identified by the bulk topological invariant and the existence of protected corner states. Moreover, the large and tunable band gap (up to 3.5 eV) of liganded Xenes will facilitate the experimental characterization of the 2D SWI phase. Our findings not only provide abundant realistic material candidates that are experimentally feasible, but also draw more fundamental research interest towards the topological physics associated with Stiefel-Whitney class in the absence of Berry curvature., Comment: 6 pages 3figures

With the rapid development of topological states in crystals, the study of topological states has been extended to quasicrystals in recent years. In this review, we summarize the recent progress of topological states in quasicrystals, particularly focusing on one-dimensional (1D) and 2D systems. We first give a brief introduction to quasicrystalline structures. Then, we discuss topological phases in 1D quasicrystals where the topological nature is attributed to the synthetic dimensions associated with the quasiperiodic order of quasicrystals. We further present the generalization of various types of crystalline topological states to 2D quasicrystals, where real-space expressions of corresponding topological invariants are introduced due to the lack of translational symmetry in quasicrystals. Finally, since quasicrystals possess forbidden symmetries in crystals such as five-fold and eight-fold rotation, we provide an overview of unique quasicrystalline symmetry-protected topological states without crystalline counterpart., Comment: 26 pages, 17 figures, to be published in Front. Phys. 17(1), 13203 (2022)

Diamond-structure materials have been extensively studied for decades, which form the foundation for most semiconductors and their modern day electronic devices. Here, we discover a e$_g$-orbital ($d_{z^2}$,$d_{x^2-y^2}$ ) model within the diamond lattice (e$_g$-diamond model) that hosts novel topological states. Specifically, the e$_g$-diamond model yields a 3D nodal cage (3D-NC), which is characterized by a $d$-$d$ band inversion protected by two types of degenerate states (i.e., e$_g$-orbital and diamond-sublattice degeneracies). We demonstrate materials realization of this model in the well-known spinel compounds (AB$_2$X$_4$), where the tetrahedron-site cations (A) form the diamond sub-lattice. An ideal half metal with one metallic spin channel formed by well-isolated and half-filled e$_g$-diamond bands, accompanied by a large spin gap (4.36 eV) is discovered in one 4-2 spinel compound (VMg$_2$O$_4$), which becomes a magnetic Weyl semimetal when spin-orbit coupling effect is further considered. Our discovery greatly enriches the physics of diamond structure and spinel compounds, opening a door to their application in spintronics.

Hawking radiation, a manifestation of quantum field theory in curved spacetime, has stimulated extensive theoretical and experimental studies of various black-hole (BH) analogs. However, an undisputed confirmation of Hawking radiation remains elusive. One challenge is BH analog structures with long-lived horizons are difficult to achieve. Here, we theoretically demonstrate a new type of optical BH analog based on light cone evolution associated with topological phase transition of Dirac cones. The transition from a type-II to type-I Dirac/Weyl cone creates an analogous curved spacetime that crosses a type-III Dirac/Weyl cone, which affords a stationary configuration of long-lived event horizon. Photons tunneling through the horizon emit a spectrum of Hawking radiation. As an example, we design a laboratory version in an inhomogeneous two-dimensional graphyne-like topological photonic lattice with a Hawking temperature of 0.14 mK. Understanding Hawking-like radiation in this unique topological BH is not only of fundamental interest in its own right but may also provide new hints to gravitational physics.

We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Re-evaluating the band evolution from an "atomic crystal" [a normal insulator (NI)] to a solid crystal, such as a semiconductor, we demonstrate that there exists ubiquitously an intermediate phase of topological insulator (TI), whose critical transition point displays a linear scaling between electron hopping potential and average bond length, underlined by deformation-potential theory. The validity of the scaling relation is verified in various two-dimensional (2D) lattices regardless of lattice symmetry, periodicity, and form of electron hoppings, based on a generic tight-binding model. Significantly, this linear scaling is shown to set an upper bound for the degree of structural disorder to destroy the topological order in a crystalline solid, as exemplified by formation of vacancies and thermal disorder. Our work formulates a simple framework for understanding the physical nature of TPTs with significant implications in practical applications of topological materials., Comment: 13 pages, 4 figures

Based on first-principles calculations, we propose that a layered electride Mg2O can serve as an effective substrate, in place of metal substrate, to grow honeycomb borophene (h-borophene). We first confirm the thermodynamic stability of h-B@Mg2O heterostructure by energetics analysis and dynamic stability by absence of imaginary frequency in phonon spectra. Then, kinetically, we identify the atomistic pathways for a preferred 2D growth mode over 3D growth, and reveal a growth transition from 2D compact islands to h-borophene at ~13-atom cluster size, indicating the feasibility of epitaxial growth of h-borophene on Mg2O. The h-borophene is found to be stabilized by nearly one electron transfer from Mg2O to h-borophene based on the Bader charge analysis. Moreover, the intrinsic band structure of the free-standing h-borophene is only weakly perturbed by the Mg2O substrate, a significant advantage over metal substrate. We envision that layered electrides provide an attractive family of substrates for epitaxial growth of a range of 2D materials that can otherwise only be grown on undesirable metal substrates., Comment: 10 pages, 4 figures

Following the discovery of topological insulators (TIs), topological Dirac/Weyl semimetal has attracted much recent interest. A prevailing mechanism for the formation of Weyl points is by breaking time-reversal symmetry (TRS) or spatial inversion symmetry of a Dirac point. Here we demonstrate a generic formation mechanism for Weyl points by breaking TRS of a three-dimensional (3D) TI featured with highly degenerate 3D flat bands (FBs). It is in direct contrast to the conventional view that breaking TRS of a 2D/3D TI leads to a Chern insulator exhibiting quantum anomalous Hall effect. Based on a tight-binding model of pyrochlore lattice, we show that this unusual 3D-FB-enabled Weyl state may contain only a minimum of two Weyl points. Furthermore, using first-principles calculations, we identify this Weyl state in a real material Sn$_2$Nb$_2$O$_7$. The main features of the resulting Weyl points are analyzed with respect to symmetry, topological invariant and surface state. Our finding sheds new light on our fundamental understanding of topological physics and significantly extends the scope of Weyl semimetals to attract immediate experimental interest.

This is a joint publication with the Letter by H. Huang and F. Liu [Phys. Rev. Lett. 121, 126401 (2018)]. In this work, we propose the spin Bott index to identify the quantum spin Hall (QSH) state in both crystalline and non-periodic systems. The applicability of the spin Bott index is confirmed by analyzing the periodic and disorder Kane-Mele models. As an example of non-periodic systems, we systematically investigate the QSH effect in a Penrose-type quasicrystal lattice (QL). We characterized the nontrivial electronic topology of the QL by directly calculating the spin Bott index. In addition, the topological edge states, the localization of wavefunctions and quantized transport signatures are also studied in detail., Comment: 14 pages, 14 figures

Despite the rapid progresses in the field of quantum spin Hall (QSH) effect, most of the QSH systems studied up to now are based on crystalline materials. Here we propose that the QSH effect can be realized in quasicrystal lattices (QLs). We show that the electronic topology of aperiodic and amorphous insulators can be characterized by a spin Bott index $B_s$. The nontrivial QSH state in a QL is identified by a nonzero spin Bott index $B_s=1$, associated with robust edge states and quantized conductance. We also map out a topological phase diagram in which the QSH state lies in between a normal insulator and a weak metal phase due to the unique wavefunctions of QLs. Our findings not only provide a better understanding of electronic properties of quasicrystals but also extend the search of QSH phase to aperiodic and amorphous materials that are experimentally feasible., Comment: 6 pages 3 figures

Measurement of gravitational Hawking radiation of black hole (BH) is prohibitive because of an extremely low Hawking temperature (TH). Here we demonstrate a fermionic analog of BH with a super high TH ~ 3 K, which is several orders of magnitude higher than previous works. We propose that Floquet-Dirac states, formed in a periodically laser driven two-dimensional black phosphorous thin film, can be designed with a spatial gradient to mimic the "gravity" felt by fermionic quasiparticles as that for a Schwarzschild BH (SBH). Quantum tunneling of electrons from a type-II Dirac cone (inside BH) to a type-I Dirac cone (outside) emits a SBH-like Hawking radiation spectrum.

The hunt for the benchmark topological superconductor (TSc) has been an extremely active research subject in condensed matter research, with quite a few candidates identified or proposed. However, low transition temperatures (Tc) and/or strong sensitivity to disorder and dopant levels in known TSc candidates have greatly hampered progress in this field. Here, we use Angle-resolved Photoemission Spectroscopy (ARPES) to show the presence of Dirac Nodal Lines (DNLs) and the corresponding topological surface states (TSS's) on the [010] faces of the Tc=39K s-wave BCS superconductor MgB2. Not only is this nearly triple the current record of superconducting Tc among all candidate TSc's, but the nature of these DNL states should make them highly tolerant against disorder and inadvertent doping variations. This makes MgB2 a promising high temperature platform for the study of topological superconductivity.

Dirac, triple-point and Weyl fermions represent three topological semimetal phases, characterized with a descending degree of band degeneracy, which have been realized separately in specific crystalline materials with different lattice symmetries. Here we demonstrate an alloy engineering approach to realize all three types of fermions in one single material system of MgTa$_{2-x}$Nb$_x$N$_3$. Based on symmetry analysis and first-principles calculations, we map out a phase diagram of topological order in the parameter space of alloy concentration and crystalline symmetry, where the intrinsic MgTa$_2$N$_3$ with the highest symmetry hosts the Dirac semimetal phase which transforms into the triple-point and then the Weyl semimetal phase with the increasing Nb concentration that lowers the crystalline symmetries. Therefore, alloy engineering affords a unique approach for experimental investigation of topological transitions of semimetallic phases manifesting different fermionic behaviors., Comment: in press, Phys. Rev. Lett. (2018)

We theoretically demonstrate that screw dislocation (SD), a 1D topological defect widely present in semiconductors, exhibits ubiquitously a new form of spin-orbit coupling (SOC) effect. Differing from the widely known conventional 2D Rashba-Dresselhaus (RD) SOC effect that typically exists at surfaces/interfaces, the deep-level nature of SD-SOC states in semiconductors readily makes it an ideal SOC. Remarkably, the spin texture of 1D SD-SOC, pertaining to the inherent symmetry of SD, exhibits a significantly higher degree of spin coherency than the 2D RD-SOC. Moreover, the 1D SD-SOC can be tuned by ionicity in compound semiconductors to ideally suppress spin relaxation, as demonstrated by comparative first-principles calculations of SDs in Si/Ge, GaAs, and SiC. Our findings therefore open a new door to manipulating spin transport in semiconductors by taking advantage of an otherwise detrimental topological defect., Comment: 16 pages, 4 figures

Herbertsmithite and Zn-doped barlowite are two compounds for experimental realization of twodimensional gapped kagome spin liquid. Theoretically, it has been proposed that charge doping a quantum spin liquid gives rise to exotic metallic states, such as high-temperature superconductivity. However, one recent experiment about herbertsmithite with successful Li-doping shows surprisingly the insulating state even under the heavy doped scenario, which can hardly be explained by many-body physics. Using first-principles calculation, we performed a comprehensive study about the Li intercalated doping effect of these two compounds. For the Li-doped herbertsmithite, we identified the optimized Li position at the Cl-(OH)$_3$-Cl pentahedron site instead of previously speculated Cl-(OH)$_3$ tetrahedral site. With the increase of Li doping concentration, the saturation magnetization decreases linearly due to the charge transfer from Li to Cu ions. Moreover, we found that Li forms chemical bonds with the nearby (OH)$^-$ and Cl$^-$ ions, which lowers the surrounding chemical potential and traps the electron, as evidenced by the localized charge distribution, explaining the insulating behavior measured experimentally. Though with different structure from herbertsmithite, Zn-doped Barlowite shows the same features upon Li doping. We conclude that Li doping this family of kagome spin liquid cannot realize exotic metallic states, other methods should be further explored, such as element substitution with different valence electrons., Comment: 6 figures

Recently, realizing new fermions, such as type-I and type-II Dirac/Weyl fermions in condensed matter systems, has attracted considerable attention. Here we show that the transition state from type-I to type-II Dirac fermions can be viewed as a type-III Dirac fermion, which exhibits unique characteristics, including a Dirac-line Fermi surface with nontrivial topological invariant and critical chiral anomaly effect, distinct from previously known Dirac semimetals. Most importantly, we discover Zn$_2$In$_2$S$_5$ is a type-III Dirac semimetal material, characterized with a pair of Dirac points in the bulk and Fermi arcs on the surface. We further propose a solid-state realization of the black-hole-horizon analogue in inhomogeneous Zn$_2$In$_2$S$_5$ to simulate black hole evaporation with high Hawking temperature. We envision that our findings will stimulate researchers to study novel physics of type-III Dirac fermions, as well as astronomical problems in a condensed matter analogue., Comment: 6 page, 4 figures

Topological superconductors are an intriguing and elusive quantum phase, characterized by topologically protected gapless surface/edge states residing in a bulk superconducting gap, which hosts Majorana fermions. Unfortunately, all currently known topological superconductors have a very low transition temperature, limiting experimental measurements of Majorana fermions. Here we discover the existence of a topological Dirac-nodal-line state in a well-known conventional high-temperature superconductor, MgB2. First-principles calculations show that the Dirac-nodal-line structure exhibits a unique one-dimensional dispersive Dirac-nodal line, protected by both spatial-inversion and time-reversal symmetry, which connects the electron and hole Dirac states. Most importantly, we show that the topological superconducting phase can be realized with a conventional s-wave superconducting gap, evidenced by the topological edge mode of the MgB2 thin films showing chiral edge states. Our discovery may enable the experimental measurement of Majorana fermions at high temperature., Comment: 19 pages, 5 figures

Topological semimetals have attracted extensive research interests for realizing condensed matter physics counterparts of three-dimensional Dirac and Weyl fermions, which were originally introduced in high energy physics. Recently it has been proposed that type-II Dirac semimetal can host a new type of Dirac fermions which break Lorentz invariance and therefore does not have counterpart in high energy physics. Here we report the electronic structure of high quality PtSe$_2$ crystals to provide direct evidence for the existence of three-dimensional type-II Dirac fermions. A comparison of the crystal, vibrational and electronic structure to a sister compound PtTe$_2$ is also discussed. Our work provides an important platform for exploring the novel quantum phenomena in the PtSe$_2$ class of type-II Dirac semimetals.

The extremely stringent requirement on material quality has hindered the investigation and potential applications of exotic chiral magnetic effect in Dirac semimetals. Here, we propose that gray tin is a perfect candidate for observing the chiral anomaly effect and Shubnikov-de-Haas (SdH) oscillation at relatively low magnetic field. Based on effective $k.p$ analysis and first-principles calculations, we discover that gray tin becomes a Dirac semimetal under tensile uniaxial strain, in contrast to a topological insulator under compressive uniaxial strain as known before. In this newly found Dirac semimetal state, two Dirac points which are tunable by tensile [001] strains, lie in the $k_z$ axis and Fermi arcs appear in the (100) surface. Duo the low carrier concentration and high mobility of gray tin, a large chiral anomaly induced negative magnetoresistance and a strong SdH oscillation are anticipated in this half of strain spectrum. Comparing to other Dirac semimetals, the proposed Dirac semimetal state in the nontoxic elemental gray tin can be more easily manipulated and accurately controlled. We envision that gray tin provides a perfect platform for strain engineering of chiral magnetic effects by sweeping through the strain spectrum from positive to negative and vice versa.

Recently, a new "type-II" Weyl fermion, which exhibits exotic phenomena such as angle-dependent chiral anomaly, was discovered in a new phase of matter where electron and hole pockets contact at isolated Weyl points. [Nature \textbf{527}, 495 (2015)] This raises an interesting question whether its counterpart, i.e., type-II \textit{Dirac} fermion, exists in real materials. Here, we predict the existence of symmetry-protected type-II Dirac fermions in a class of transition metal dichalcogenide materials. Our first-principles calculations on PtSe$_2$ reveal its bulk type-II Dirac fermions which are characterized by strongly tilted Dirac cones, novel surface states, and exotic doping-driven Lifshitz transition. Our results show that the existence of type-II Dirac fermions in PtSe$_2$-type materials is closely related to its structural $P\bar{3}m1$ symmetry, which provides useful guidance for the experimental realization of type-II Dirac fermions and intriguing physical properties distinct from those of the standard Dirac fermions known before., Comment: 12 pages, 3 figures

The rise of topological insulators in recent years has broken new ground both in the conceptual cognition of condensed matter physics and the promising revolution of the electronic devices. It also stimulates the explorations of more topological states of matter. Topological crystalline insulator is a new topological phase, which combines the electronic topology and crystal symmetry together. In this article, we review the recent progress in the studies of SnTe-class topological crystalline insulator materials. Starting from the topological identifications in the aspects of the bulk topology, surface states calculations and experimental observations, we present the electronic properties of topological crystalline insulators under various perturbations, including native defect, chemical doping, strain, and thickness-dependent confinement effects, and then discuss their unique quantum transport properties, such as valley-selective filtering and helicity-resolved functionalities for Dirac fermions. The rich properties and high tunability make SnTe-class materials promising candidates for novel quantum devices., Comment: 15 pages, 15 figures, invited review

Topological semimetals have recently attracted extensive research interests as host materials to condensed matter physics counterparts of Dirac and Weyl fermions originally proposed in high energy physics. These fermions with linear dispersions near the Dirac or Weyl points obey Lorentz invariance, and the chiral anomaly leads to novel quantum phenomena such as negative magnetoresistance. The Lorentz invariance is, however, not necessarily respected in condensed matter physics, and thus Lorentz-violating type-II Dirac fermions with strongly tilted cones can be realized in topological semimetals. Here, we report the first experimental evidence of type-II Dirac fermions in bulk stoichiometric PtTe$_2$ single crystal. Angle-resolved photoemission spectroscopy (ARPES) measurements and first-principles calculations reveal a pair of strongly tilted Dirac cones along the $\Gamma$-A direction under the symmetry protection, confirming PtTe$_2$ as a type-II Dirac semimetal. The realization of type-II Dirac fermions opens a new door for exotic physical properties distinguished from type-I Dirac fermions in condensed matter materials., Comment: 12 pages, 4 figures

Based on first-principles calculations and an effective Hamiltonian analysis, we systematically investigate the electronic and topological properties of alkaline-earth compounds $AX_2$ ($A$=Ca, Sr, Ba; $X$=Si, Ge, Sn). Taking BaSn$_2$ as an example, we find that when spin-orbit coupling is ignored, these materials are three-dimensional topological nodal-line semimetals characterized by a snake-like nodal loop in three-dimensional momentum space. Drumhead-like surface states emerge either inside or outside the loop circle on the (001) surface depending on surface termination, while complicated double-drumhead-like surface states appear on the (010) surface. When spin-orbit coupling is included, the nodal line is gapped and the system becomes a topological insulator with Z$_2$ topological invariants (1;001). Since spin-orbit coupling effects are weak in light elements, the nodal-line semimetal phase is expected to be achievable in some alkaline-earth germanides and silicides., Comment: 13 pages, 5 figures

Weyl semimetal is a new quantum state of matter [1-12] hosting the condensed matter physics counterpart of relativisticWeyl fermion [13] originally introduced in high energy physics. The Weyl semimetal realized in the TaAs class features multiple Fermi arcs arising from topological surface states [10, 11, 14-16] and exhibits novel quantum phenomena, e.g., chiral anomaly induced negative mag-netoresistance [17-19] and possibly emergent supersymmetry [20]. Recently it was proposed theoretically that a new type (type-II) of Weyl fermion [21], which does not have counterpart in high energy physics due to the breaking of Lorentz invariance, can emerge as topologically-protected touching between electron and hole pockets. Here, we report direct spectroscopic evidence of topological Fermi arcs in the predicted type-II Weyl semimetal MoTe2 [22-24]. The topological surface states are confirmed by directly observing the surface states using bulk-and surface-sensitive angle-resolved photoemission spectroscopy (ARPES), and the quasi-particle interference (QPI) pattern between the two putative Fermi arcs in scanning tunneling microscopy (STM). Our work establishes MoTe2 as the first experimental realization of type-II Weyl semimetal, and opens up new opportunities for probing novel phenomena such as exotic magneto-transport [21] in type-II Weyl semimetals., Comment: submitted on 01/29/2016. Nature Physics, in press. Spectroscopic evidence of the Fermi arcs from two complementary surface sensitive probes - ARPES and STS. A comparison of the calculated band structure for T_d and 1T' phase to identify the topological Fermi arcs in the T_d phase is also included in the supplementary information

The generally accepted view that spin polarization is induced by the asymmetry of the global crystal space group has limited the search for spintronics [1] materials to non-centrosymmetric materials. Recently it has been suggested that spin polarization originates fundamentally from local atomic site asymmetries [2], and therefore centrosymmetric materials may exhibit previously overlooked spin polarizations. Here by using spin- and angle-resolved photoemission spectroscopy (spin-ARPES), we report helical spin texture induced by local Rashba effect (R-2) in centrosymmetric monolayer PtSe$_2$ film. First-principles calculations and effective analytical model support the spin-layer locking picture: in contrast to the spin splitting in conventional Rashba effect (R-1), the opposite spin polarizations induced by R-2 are degenerate in energy while spatially separated in the top and bottom Se layers. These results not only enrich our understanding of spin polarization physics, but also may find applications in electrically tunable spintronics.

The prospect of a Dirac half metal, a material which is characterized by a bandstructure with a gap in one spin channel but a Dirac cone in the other, is of both fundamental interest and a natural candidate for use in spin-polarized current applications. However, while the possibility of such a material has been reported based on model calculations[H. Ishizuka and Y. Motome, Phys. Rev. Lett. 109, 237207 (2012)], it remains unclear what material system might realize such an exotic state. Using first-principles calculations, we show that the experimentally accessible Mn intercalated epitaxial graphene on SiC(0001) transits to a Dirac half metal when the coverage is > 1/3 monolayer. This transition results from an orbital-selective breaking of quasi-2D inversion symmetry, leading to symmetry breaking in a single spin channel which is robust against randomness in the distribution of Mn intercalates. Furthermore, the inclusion of spin-orbit interaction naturally drives the system into the quantum anomalous Hall (QAH) state. Our results thus not only demonstrate the practicality of realizing the Dirac half metal beyond a toy model but also open up a new avenue to the realization of the QAH effect., Comment: 6 pages, 4 figures

A Chern insulator (quantum anomalous Hall insulator) phase is demonstrated to exist in a typical semi-Dirac system, the TiO2/VO2 heterostructure. By combining first-principles calculations with Wannier-based tight-binding model, we calculate the Berry curvature distribution, finding a Chern number of -2 for the valence bands, and demonstrate the existence of gapless chiral edge states, ensuring quantization of the Hall conductivity to 2e^2/h. A new semi-Dirac model, where each semi-Dirac cone is formed by merging three conventional Dirac points, is proposed to reveal how the nontrivial topology with finite Chern number is compatible with a semi-Dirac electronic spectrum., Comment: 12 pages, 3 figures

We predict from first-principles calculations a novel structure of stanene with dumbbell units (DB), and show that it is a two-dimensional topological insulator with inverted band gap which can be tuned by compressive strain. Furthermore, we propose that the boron nitride sheet and reconstructed ($2\times2$) InSb(111) surfaces are ideal substrates for the experimental realization of DB stanene, maintaining its non-trivial topology. Combined with standard semiconductor technologies, such as magnetic doping and electrical gating, the quantum anomalous Hall effect, Chern half metallicity and topological superconductivity can be realized in DB stanene on those substrates. These properties make the two-dimensional supported stanene a good platform for the study of new quantum spin Hall insulator as well as other exotic quantum states of matter., Comment: 4 figures