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Author(s): Multer, D; Yin, JX; Zhang, SS; Zheng, H; Chang, TR; Bian, G; Sankar, R; Hasan, MZ | Abstract: Magnetic impurities deposited on topological superconductor candidate PbTaSe2 can introduce a nonsplitting zero-energy state inside the superconducting gap, which has been proposed as a field-free platform for topological zero modes. However, it is still unclear how robust the topological state in PbTaSe2 is against magnetic impurities, which is related to the topological nature of the zero-energy state as well as its potential for quantum computation. In this paper, we use scanning tunneling microscopy to study the topological surface state in the normal state of PbTaSe2 under the perturbation of magnetic impurities. We visualize the quasiparticle interference (QPI) arising from the topological surface state. We then deposit Fe impurities on the surface to form atomic Fe adatoms. We find that each Fe adatom sits at a unique interstitial position on the surface and features a local state at high energies, both of which are consistent with our first-principles calculation that further reveals its large magnetic moment. Our systematic Fe deposition and subsequent measurements show that the arclike QPI pattern at the Fermi energy is robust with up to 3% Fe coverage where the atomic nature of Fe adatoms still holds. Our results provide evidence that the topological surface state at the Fermi energy in PbTaSe2 is robust against dilute magnetic impurities.

Author(s): Wang, Z; Jiang, YX; Yin, JX; Li, Y; Wang, GY; Huang, HL; Shao, S; Liu, J; Zhu, P; Shumiya, N; Hossain, MS; Liu, H; Shi, Y; Duan, J; Li, X; Chang, G; Dai, P; Ye, Z; Xu, G; Wang, Y; Zheng, H; Jia, J; Hasan, MZ; Yao, Y | Abstract: Kagome superconductors with TC up to 7 K have been discovered for over 40 y. Recently, unconventional chiral charge order has been reported in kagome superconductor KV3Sb5, with an ordering temperature of one order of magnitude higher than the TC. However, the chirality of the charge order has not been reported in the cousin kagome superconductor CsV3Sb5, and the electronic nature of the chirality remains elusive. In this paper, we report the observation of electronic chiral charge order in CsV3Sb5 via scanning tunneling microscopy (STM). We observe a 2 × 2 charge modulation and a 1 × 4 superlattice in both topographic data and tunneling spectroscopy. 2 × 2 charge modulation is highly anticipated as a charge order by fundamental kagome lattice models at van Hove filling, and is shown to exhibit intrinsic chirality. We find that the 1 × 4 superlattices form various small domain walls, and can be a surface effect as supported by our first-principles calculations. Crucially, we find that the amplitude of the energy gap opened by the charge order exhibits real-space modulations, and features 2 × 2 wave vectors with chirality, highlighting the electronic nature of the chiral charge order. STM study at 0.4 K reveals a superconducting energy gap with a gap size 2Δ=0.85meV, which estimates a moderate superconductivity coupling strength with 2Δ/kBTC=3.9. When further applying a c-axis magnetic field, vortex core bound states are observed within this gap, indicative of clean-limit superconductivity.

Author(s): Zhang, SS; Yin, JX; Dai, G; Zhao, L; Chang, TR; Shumiya, N; Jiang, K; Zheng, H; Bian, G; Multer, D; Litskevich, M; Chang, G; Belopolski, I; Cochran, TA; Wu, X; Wu, D; Luo, J; Chen, G; Lin, H; Chou, FC; Wang, X; Jin, C; Sankar, R; Wang, Z; Hasan, MZ | Abstract: Superconducting materials exhibiting topological properties are emerging as an exciting platform to realize fundamentally new excitations from topological quantum states of matter. In this letter, we explore the possibility of a field-free platform for generating Majorana zero energy excitations by depositing magnetic Fe impurities on the surface of candidate topological superconductors, LiFeAs and PbTaSe2. We use scanning tunneling microscopy to probe localized states induced at the Fe adatoms on the atomic scale and at sub-Kelvin temperatures. We find that each Fe adatom generates a striking zero-energy bound state inside the superconducting gap, which do not split in magnetic fields up to 8 T, underlining a nontrivial topological origin. Our findings point to magnetic Fe adatoms evaporated on bulk superconductors with topological surface states for exploring Majorana zero modes and quantum information science under field-free conditions.

We study the anomalous Hall effect (AHE) of single-crystalline ${\mathrm{Co}}_{3}{\mathrm{Sn}}_{2\ensuremath{-}x}{\mathrm{In}}_{x}{\mathrm{S}}_{2}$ over a large range of indium concentration $x$ from 0 to 1. Their magnetization reduces progressively with increasing $x$ while their ground state evolves from a ferromagnetic Weyl semimetal into a nonmagnetic insulator. Remarkably, after systematically scaling the AHE, we find that their intrinsic anomalous Hall conductivity (AHC) features an unexpected maximum at around $x=0.15$. The change of the intrinsic AHC corresponds with the doping evolution of Berry curvature and the maximum arises from the magnetic topological nodal-ring gap. Our experimental results show a larger AHC in a fundamental nodal-ring gap than that of Weyl nodes.

We utilize a combination of vector magnetic field and scanning tunneling microscopy to elucidate the three-dimensional field based electronic phase diagram of a correlated iron-based superconductor, LiFeAs. We observe, under a zero-field-cooled method, an ordered hexagonal vortex lattice ground state in contrast to the disordered lattice observed under a field-cooled method. It transforms to a fourfold-symmetric state by increasing the c-axis field and distorts elliptically upon tilting the field in-plane. The vortex lattice transformations correlate with the field-dependent superconducting gap that characterizes the Cooper pairing strength. The anisotropy of the vortex lattice agrees with the field-enhanced Bogoliubov quasiparticle scattering channel that is determined by the pairing symmetry in respect to its Fermi surface structure. Our systematic tuning of the vortex lattice symmetry and study of its correlation with Cooper pairing demonstrates the many-body interplay between the superconducting order parameter and emergent vortex matter.

The experimental discovery of the topological Dirac semimetal establishes a platform to search for various exotic quantum phases in real materials. ZrSiS-type materials have recently emerged as topological nodal-line semimetals where gapped Dirac-like surface states are observed. Here, we present a systematic angle-resolved photoemission spectroscopy (ARPES) study of ZrGeTe, a nonsymmorphic symmetry protected Dirac semimetal. We observe two Dirac-like gapless surface states at the same $\bar X$ point of the Brillouin zone. Our theoretical analysis and first-principles calculations reveal that these are protected by crystalline symmetry. Hence, ZrGeTe appears as a rare example of a naturally fine tuned system where the interplay between symmorphic and non-symmorphic symmetry leads to rich phenomenology, and thus opens for opportunities to investigate the physics of Dirac semimetallic and topological insulating phases realized in a single material., Comment: 20 pages, 7 figures

Weyl semimetals are novel topological conductors that host Weyl fermions as emergent quasiparticles. In this Rapid Communication, we propose a new type of Weyl semimetal state that breaks both time-reversal symmetry and inversion symmetry in the $R\mathrm{AlGe}$ ($R=\mathrm{rare}\ensuremath{-}\mathrm{earth}$) family. Compared to previous predictions of magnetic Weyl semimetal candidates, the prediction of Weyl nodes in $R\mathrm{AlGe}$ is more robust and less dependent on the details of the magnetism because the Weyl nodes are generated already by the inversion breaking and the ferromagnetism acts as a simple Zeeman coupling that shifts the Weyl nodes in $k$ space. Moreover, $R\mathrm{AlGe}$ offers remarkable tunability, which covers all varieties of Weyl semimetals including type I, type II, inversion breaking, and time-reversal breaking, depending on a suitable choice of the rare-earth elements. Furthermore, the unique noncentrosymmetric and ferromagnetic Weyl semimetal state in $R\mathrm{AlGe}$ enables the generation of spin currents.

The topological semimetal $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ag}}_{2}\mathrm{Se}$ features a Kramers-Weyl node at the origin in momentum space and a quadruplet of spinless Weyl nodes, which are annihilated by spin-orbit coupling. We show that single-crystalline $\ensuremath{\beta}\text{\ensuremath{-}}{\mathrm{Ag}}_{2}\mathrm{Se}$ manifests giant Shubnikov--de Haas oscillations in the longitudinal magnetoresistance, which stem from a small electron pocket that can be driven beyond the quantum limit by a field less than 9 T. This small electron pocket is a remainder of the spin-orbit annihilated Weyl nodes and thus encloses a Berry-phase structure. Moreover, we observed a negative longitudinal magnetoresistance when the magnetic field is beyond the quantum limit. Our experimental findings are complemented by thorough theoretical band-structure analyses of this Kramers-Weyl semimetal candidate, including first-principles calculations and an effective $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ model.

The discovery of a topological nodal-line (TNL) semimetal phase in ZrSiS has invigorated the study of other members of this family. Here, we present a comparative electronic structure study of $\mathrm{ZrSi}X$ (where $X=\text{S}$, Se, Te) using angle-resolved photoemission spectroscopy (ARPES) and first-principles calculations. Our ARPES studies show that the overall electronic structure of $\mathrm{ZrSi}X$ materials comprises the diamond-shaped Fermi pocket, the nearly elliptical-shaped Fermi pocket, and a small electron pocket encircling the zone center ($\mathrm{\ensuremath{\Gamma}}$) point, the $M$ point, and the $X$ point of the Brillouin zone, respectively. We also observe a small Fermi surface pocket along the $M\ensuremath{-}\mathrm{\ensuremath{\Gamma}}\ensuremath{-}M$ direction in ZrSiTe, which is absent in both ZrSiS and ZrSiSe. Furthermore, our theoretical studies show a transition from nodal-line to nodeless gapped phase by tuning the chalcogenide from S to Te in these material systems. Our findings provide direct evidence for the tunability of the TNL phase in $\mathrm{ZrSi}X$ material systems by adjusting the spin-orbit coupling strength via the $X$ anion.

Members of the Mo${}_{x}$W${}_{1-x}$Te${}_{2}$ series are predicted to be Weyl semimetals, hosting type-II Weyl fermions, which have yet to be experimentally realized and which are unusual because they strongly violate Lorentz invariance. Crucially, the Weyl points in this system are predicted to sit above the Fermi level. Here, the authors show that for a type-II Weyl cone, although not for a type-I Weyl cone, if the Weyl point is above the Fermi level, then it's necessary to see the band structure above the Fermi level to observe a topological Fermi arc. The authors also discover that pump-probe angle-resolved photoemission beautifully displays the unoccupied band structure in Mo${}_{x}$W${}_{1-x}$Te${}_{2}$. Their work sets the stage for demonstrating that this system is the first type-II Weyl semimetal, as well as the first tunable Weyl semimetal.

We report high-resolution angle-resolved photoemission spectroscopy measurements on the honeycomb iridate ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$. Our measurements reveal the existence of a metallic surface band feature crossing the Fermi level with nearly linear dispersion and an estimated surface carrier density of $3.2\ifmmode\times\else\texttimes\fi{}{10}^{13}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$, which has not been theoretically predicted or experimentally observed, and provides the first evidence for metallic behavior on the boundary of this material, whereas the bulk bands exhibit a robust insulating gap. We further show the lack of theoretically predicted Dirac cones at the $\overline{M}$ points of the surface Brillouin zone, which confirms the absence of a stacked quantum spin Hall phase in this material. Our data indicates that the surface ground state of this material is exotic and metallic, unlike as predicted in theory, and establishes ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ as a rare example of a strongly correlated spin-orbit insulator with surface metallicity.

Superconductivity in topological band structures is a platform for realizing Majorana bound states and other exotic physical phenomena such as emergent supersymmetry. This potential nourishes the search for topological materials with intrinsic superconducting instabilities, in which Cooper pairing is introduced to electrons with helical spin texture such as the Dirac surface states of topological insulators, forming a time-reversal symmetric topological superconductor on the surface. We employ first-principles calculations and angle-resolved photoemission spectroscopy experiments to reveal that ${\mathrm{PbTaSe}}_{2}$, a noncentrosymmetric superconductor, possesses a nonzero ${\mathbb{Z}}_{2}$ topological invariant and fully spin-polarized Dirac surface states. Moreover, we analyze the phonon spectrum of ${\mathrm{PbTaSe}}_{2}$ to show how superconductivity emerges in this compound due to a stiffening of phonons by the Pb intercalation, which diminishes a competing charge-density-wave instability. By combining our findings on the topological band structure and the superconducting electron pairing, our work establishes ${\mathrm{PbTaSe}}_{2}$ as a stoichiometric superconductor with topological Dirac surface states. This type of intrinsic topological Dirac superconductors holds great promise for studying aspects of topological superconductors such as Majorana zero modes.

A topological nodal-line semimetal is a new condensed matter state with one-dimensional bulk nodal lines and two-dimensional drumhead surface bands. Based on first-principles calculations and our effective k . p model, we propose the existence of topological nodal-line fermions in the ternary transition- metal chalcogenide TlTaSe2. The noncentrosymmetric structure and strong spin-orbit coupling give rise to spinful nodal-line bulk states which are protected by a mirror reflection symmetry of this compound. This is remarkably distinguished from other proposed nodal-line semimetals such as Cu3NPb(Zn) in which nodal lines exist only in the limit of vanishing spin-orbit coupling. We show that the drumhead surface states in TlTaSe2, which are associated with the topological nodal lines, exhibit an unconventional chiral spin texture and an exotic Lifshitz transition as a consequence of the linkage among multiple drumhead surface-state pockets., Related papers at http://physics.princeton.edu/zahidhasangroup/index.html

We report electronic properties of superconductivity in single crystals of topological nodal-line semimetal ${\mathrm{PbTaSe}}_{2}$. Resistivity, magnetic susceptibility, and specific heat measurements were performed on high-quality single crystals. We observed large, temperature-dependent anisotropy in its upper critical field (${H}_{c2}$). The upper critical field measured for $H\ensuremath{\parallel}\phantom{\rule{0.28em}{0ex}}\mathbf{ab}$ plane shows a sudden upward feature instead of saturation at low temperatures. The specific heat measurements in magnetic fields reveal a full superconducting gap with no gapless nodes.

Atomically uniform Sb(111) films are fabricated by the method of molecular beam epitaxy on an optimized Si(111) surface. Two dimensional quantum well states and topological surface states in these films are well resolved as measured by angle-resolved photoemission spectroscopy. We observe an evolution of direct transition resonances by varying the excitation photon energy (and thus the perpendicular crystal momentum). The experimental results are reproduced in a comprehensive model calculation taking into account first-principles calculated initial states and time-reversed low-energy-electron-diffraction final states in the photoexcitation process. The resonant behavior illustrates that the topological surface states and the quantum well states are analytically connected in momentum space in all three dimensions.

The family of binary compounds including TaAs, TaP, NbAs, and NbP was recently discovered as the first realization of Weyl semimetals. In order to develop a comprehensive description of the charge carriers in these Weyl semimetals, we performed detailed and systematic electronic band structure calculations which reveal the nature of Fermi surfaces and their complex interconnectivity in TaAs, TaP, NbAs, and NbP. Our work reports a comparative and comprehensive study of Fermi surface topology and band structure details of all known members of the Weyl semimetal family and hence provides the fundamental knowledge for realizing the many predicted exotic topological quantum physics of Weyl semimetals based on the TaAs class of materials.

We show with systematic photoemission spectroscopy and scanning tunneling spectroscopy data that a spin helical surface state appears on the (110) surface of noncentrosymmetric, three-dimensional HgTe. The topological surface state in HgTe exhibits sharp, linear dispersion without ${k}_{z}$ variation, as well as clear, left-right imbalanced spin polarization and circular dichroism. Chemical gating by alkali metal deposition on the surface causes the unexpected opening and/or increase of a surface insulating gap without changing its topological property. Such an unusual behavior we uncover in three-dimensional HgTe sheds light on a convenient control of the Fermi surface and quantum transport in a topological insulator.

We present high-resolution angle-resolved photoemission spectroscopy studies of trivalent CeB6 and divalent BaB6 rare-earth hexaborides. We find that the Fermi surface electronic structure of CeB6 consists of large oval-shape pockets around the X points of the Brillouin zone, while the states around the zone centre 'Gamma' point are strongly renormalized. Our first-principles calculations agree with data around the X points, but not at the 'Gamma' points, indicating areas of strong renormalization located around 'Gamma'. The Ce quasi-particle states participate in formation of hotspots at the Fermi surface, while the incoherent f states hybridize and lead to the emergence of dispersive features absent in non-f counterpart BaB6. These experimental and theoretical results provide a new understanding of rare-earth hexaboride materials., 21 pages, 9 figures

We discuss the evolution of topological states and their orbital textures in the mixed-valence compounds ${\text{SmB}}_{6}$ and ${\text{YbB}}_{6}$ within the framework of the generalized gradient approximation plus onsite Coulomb interaction $(\mathrm{GGA} + U)$ scheme for a wide range of values of $U$. In ${\text{SmB}}_{6}$, the topological Kondo insulator (TKI) gap is found to be insensitive to the value of $U$, but in sharp contrast, Kondo physics in isostructural ${\text{YbB}}_{6}$ displays a surprising sensitivity to $U$. In particular, as $U$ is increased in ${\text{YbB}}_{6}$, the correlated TKI state in the weak-coupling regime transforms into a $d\ensuremath{-}p$-type topological insulator phase with a band inversion between $\text{Yb-5}d$ and $\text{B-2}p$ orbitals in the intermediate coupling range, without closing the insulating energy gap throughout this process. Our theoretical predictions related to the TKI and non-TKI phases in ${\text{SmB}}_{6}$ and ${\text{YbB}}_{6}$ are in substantial accord with recent angle-resolved photoemission spectroscopy experiments.

We use angle-resolved photoemission spectroscopy to show that the near-surface electronic structure of a bulk insulating iridate Sr3Ir2O7 lying near a metal-Mott insulator transition exhibits weak metallicity signified by finite electronic spectral weight at the Fermi level. The surface electrons exhibit a spin structure resulting from an interplay of spin-orbit, Coulomb interaction and surface quantum magnetism. Our results shed light on understanding the exotic quantum entanglement and transport phenomena in iridate-based oxide devices.

We study symmetry-protected features in the quasiparticle interference (QPI) pattern of two-dimensional (2D) systems with mirror symmetries and time-reversal symmetry, around a single static point impurity. We show that, in the Fourier-transformed local density of states (FT-LDOS) $\ensuremath{\rho}(\mathbf{q},\ensuremath{\omega})$, while the position of high-intensity peaks generically depends on the geometric features of the iso-energy contour at energy $\ensuremath{\omega}$, the absence of certain peaks is guaranteed by the opposite mirror eigenvalues of the two Bloch states that are (i) on the mirror-symmetric lines in the Brillouin zone (BZ) and (ii) separated by scattering vector $\mathbf{q}$. We apply the general result to the QPI on the $\ensuremath{\langle}001\ensuremath{\rangle}$ surface of the topological crystalline insulator Pb${}_{1\ensuremath{-}x}$Sn${}_{x}$Te and predict all vanishing peaks in $\ensuremath{\rho}(\mathbf{q},\ensuremath{\omega})$. The model-independent analysis is supported by numerical calculations using an effective four-band model derived from symmetry analysis.