Three-dimensional topological insulators and topological crystalline insulators represent new quantum states of matter, which are predicted to have insulating bulk states and spin-momentum-locked gapless surface states. Experimentally, it has proven difficult to achieve the high bulk resistivity that would allow surface states to dominate the transport properties over a substantial temperature range. Here we report a series of indium-doped Pb$_{1-x}$Sn$_x$Te compounds that manifest huge bulk resistivities together with strong evidence of topological surface states, based on thickness-dependent transport studies and magnetoresistance measurements. For these bulk-insulating materials, the surface states determine the resistivity for temperatures approaching 30 K.
The conducting states, recently discovered at the surface of two special class of insulators -- topological insulators and topological crystalline insulators - are distinguished by their insensitivity to local and non-magnetic surface defects at a level of disorder, sufficiently small to be described within the perturbation theory. However, the behavior of the surface states in case of non local macroscopic imperfections is not clear. Here, we propose a systematic study of the topological surface states on vicinal planes (deviations from perfect surface cleavage) in a topological crystalline i…
The recent discovery of topological insulators has revived interest in the topological properties of insulating band structures. In this work, we extend the topological classification of insulating band structures to include certain point group symmetry of crystals. We find a class of three-dimensional "topological crystalline insulators" which have metallic surface states on certain high symmetry crystal surfaces. These topological crystalline insulators can be viewed as the counterpart of topological insulators in materials without spin-orbit coupling. Their surface states have quadratic ban…
Topological insulators are a novel class of quantum materials in which time-reversal symmetry, relativistic (spin-orbit) effects and an inverted band structure result in electronic metallic states on the surfaces of bulk crystals. These helical states exhibit a Dirac-like energy dispersion across the bulk bandgap, and they are topologically protected. Recent theoretical proposals have suggested the existence of topological crystalline insulators, a novel class of topological insulators in which crystalline symmetry replaces the role of time-reversal symmetry in topological protection [1,2]. In…
Based on the conventional energy band theory, an approach is presented to describe the electronic structure of crystalline insulators in the presence of a finite homogeneous electric field. The expression of polarization is derived which extends the ``Berry-phase'' theory of polarization to nonzero fields. The characteristics of the solutions are studied in details and the associations with the existing perturbation theories and computational schemes are discussed.
Crystalline Si substrates are doped by laser annealing of solution processed Si. For this experiment, dispersions of highly B-doped Si nanoparticles (NPs) are deposited onto intrinsic Si and laser processed using an 807.5nm cw-laser. During laser processing the particles as well as a surface-near substrate layer are melted to subsequently crystallize in the same orientation as the substrate. The doping profile is investigated by secondary ion mass spectroscopy revealing a constant B concentration of 2x10^18 cm^-3 throughout the entire analyzed depth of 5μm. Four-point probe measurements demons…
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, …
The introduction of magnetism in SnTe-class topological crystalline insulators is a challenging subject with great importance in the quantum device applications. Based on the first-principles calculations, we have studied the defect energetics and magnetic properties of 3d transition-metal (TM)-doped SnTe. We find that the doped TM atoms prefer to stay in the neutral states and have comparatively high formation energies, suggesting that the uniform TM doping in SnTe with a higher concentration will be difficult unless clustering. In the dilute doping regime, all the magnetic TM atoms are in th…
Co40Fe40B20 layers were grown on the Pb0.71Sn0.29Te topological insulator substrates by laser molecular beam epitaxy (LMBE) method, and the growth conditions were studied. The possibility of growing epitaxial layers of a ferromagnet on the surface of a topological insulator was demonstrated for the first time. The Co40Fe40B20 layers obtained have a bcc crystal structure with a crystalline (111) plane parallel to the (111) PbSnTe plane. The use of three-dimensional mapping in the reciprocal space of reflection high electron diffraction (RHEED) patterns made it possible to determine the epitaxia…
Topological phase transition in a single material usually refers to transitions between a trivial band insulator and a topological Dirac phase, but the transition may also occur between different classes of topological Dirac phases. However, it is a fundamental challenge to realize quantum transition between Z2 nontrivial topological insulator (TI) and topological crystalline insulator (TCI) in one material because Z2 TI and TCI are hardly both co-exist in a single material due to their contradictory requirement on the number of band inversions. The Z2 TIs must have an odd number of band inver…
In this paper we present an approach aimed at performing many-body calculations of Born-effective charges of crystalline insulators, by including the electron-correlation effects. The scheme is implemented entirely in the real space, using Wannier-functions as single-particle orbitals. Correlation effects are computed by including virtual excitations from the Hartree-Fock mean field, and the excitations are organized as per a Bethe-Goldstone-like many-body hierarchy. The results of our calculations suggest that the approach presented here is promising.
Topological crystalline insulators are topological insulators whose surface states are protected by the crystalline symmetry, instead of the time reversal symmetry. Similar to the first generation of three-dimensional topological insulators such as Bi2Se3 and Bi2Te3, topological crystalline insulators also possess surface states with exotic electronic properties such as spin-momentum locking and Dirac dispersion. Experimentally verified topological crystalline insulators to date are SnTe, Pb1-xSnxSe, and Pb1-xSnxTe. Because topological protection comes from the crystal symmetry, magnetic impur…
Topological crystalline insulator (TCI) is one of the symmetry-protected topological states. Any TCI can be deformed into a simple product state of several decoupled two-dimensional (2D) topologically nontrivial layers in its lattice respecting its crystalline symmetries called the layer construction (LC) limit. In this work, based on first-principles calculations we have revealed that both tetragonal LaSbTe (t-LaSbTe) and orthorhombic LaSbTe (o-LaSbTe) can be interpreted as stacking of 2D topological insulators in each lattice space. The structural phase transition from t-LaSbTe to o-LaSbTe d…
We study the nature of (001) surface states in Pb_{0.73}Sn_{0.27}Se in the newly discovered topological-crystalline-insulator (TCI) phase as well as the corresponding topologically trivial state above the band-gap-inversion temperature. Our calculations predict not only metallic surface states with a nontrivial chiral spin structure for the TCI case, but also nonmetallic (gapped) surface states with nonzero spin polarization when the system is a normal insulator. For both phases, angle- and spin-resolved photoelectron spectroscopy measurements provide conclusive evidence for the formation of t…
The electronic and magnetic properties of iron-doped topological insulator Bi1.84-xFe0.16CaxSe3 single crystals were studied. By co-doping Fe and Ca atoms, ferromagnetic bulk states with different carrier density (from n-type to p-type) were obtained. Effective magnetic moments for each Fe atom was estimated as small as about 0.07$μ$B. Magnetic and non-magnetic phases separation was observed in all samples. Our results suggest that the bulk ferromagnetism in Fe-doped Bi2Se3 is not intrinsic and regardless of carrier density.
Magnetic interaction with the gapless surface states in topological insulator (TI) has been predicted to give rise to a few exotic quantum phenomena. However, the effective magnetic doping of TI is still challenging in experiment. Using first-principles calculations, the magnetic doping properties (V, Cr, Mn and Fe) in three strong TIs (Bi$_{2}$Se$_{3}$, Bi$_{2}$Te$_{3}$ and Sb$_{2}$Te$_{3}$) are investigated. We find that for all three TIs the cation-site substitutional doping is most energetically favorable with anion-rich environment as the optimal growth condition. Further our results show…
Using a tight-binding approach we study theoretically the nature of surface states in Pb0.4Sn0.6Te - the newly discovered topological-crystalline-insulator. Apart from the studied before (001) surface states, two other surface families, {011} and {111}, in which the mirror symmetry of the crystal's rock-salt structure plays the same role in topological protection, are considered. Our calculations show that while in (111) surface states of (Pb,Sn)Te four single topologically protected Dirac-cones should appear, for the (110) surface states the protection is lifted for two L points. In this case…
Using microwave-assisted plasma chemical vapour deposition (CVD) a layer of Nitrogen doped ultra-nano-crystalline diamond (N-UNCD) is deposited on top of a non-conducting diamond layer, which itself is situated on a Silicon wafer. This structure is then shaped into Hall-bar devices of various dimensions using optical lithography and dry-etching techniques. The devices' electrical properties are investigated at various temperatures using a cryogen-free dilution refrigerator.
Topological materials are derived from the interplay between symmetry and topology. Advances in topological band theories have led to the prediction that the antiperovskite oxide Sr$_3$SnO is a topological crystalline insulator, a new electronic phase of matter where the conductivity in its (001) crystallographic planes is protected by crystallographic point group symmetries. Realization of this material, however, is challenging. Guided by thermodynamic calculations we design and implement a deposition approach to achieve the adsorption-controlled growth of epitaxial Sr$_3$SnO single-crystal f…
Heterostructures between topological insulators (TI) and magnetic insulators represent a pathway to realize the quantum anomalous Hall effect (QAHE). Using density functional theory based systematic screening and investigation of thermodynamic, magnetic and topological properties of heterostructures, we demonstrate that forming a type-I heterostructure between a wide gap antiferromagnetic insulator Cr$_2$O$_3$ and a TI-film, such as Sb$_2$Te$_3$, can lead to pinning of the Fermi-level at the center of the gap, even when magnetically doped. Cr-doping in the heterostructure increases the gap to …
We present a study of the structural and electronic properties of highly doped topological insulator Bi2Se3 single crystals synthesized by the Bridgman method. Lattice structural characterizations by X-ray diffraction, scanning tunneling microscopy, and Raman spectroscopy confirmed the high quality of the as-grown single crystals. The topological surface states in the electronic band structure were directly re- vealed by angle-resolved photoemission spectroscopy. Transport measurements showed that the conduction was dominated by the bulk carriers and confirmed a previously observed bulk quantu…
We study what kind of topological crystalline insulator phase emerges from nodal line semimetal phases in the face-centered cubic system which is not indicated by topological indices when spin-orbit coupling (SOC) is introduced. We construct an effective model which hosts two different nodal lines phases, and calculated mirror Chern numbers in it by introducing SOC. As a result, we find that the two nodal line phases with different nodal line configurations are mapped to different topological crystalline insulator phases. This result shows that turning off SOC and checking the nodal line confi…
Based on $k\cdot p$ analysis and realistic tight-binding calculations, we find that time-reversal-breaking Weyl semimetals can be realized in magnetically-doped (Mn, Eu, Cr etc.) Sn$_{1-x}$Pb$_x$(Te,Se) class of topological crystalline insulators. All the Weyl points are well separated in momentum space and possess nearly the same energy due to high crystalline symmetry. Moreover, both the Weyl points and Fermi arcs are highly tunable by varying Pb/Sn composition, pressure, magnetization, temperature, surface potential etc., opening up the possibility of manipulating Weyl points and rewiring t…
SmB6 was recently proposed to be both a strong topological insulator and a topological crystalline insulator. For this and related cubic topological Kondo insulators, we prove the existence of four different topological phases, distinguished by the sign of mirror Chern numbers. We characterize these phases in terms of simple observables, and we provide concrete tight-binding models for each phase. Based on theoretical and experimental results for SmB6 we conclude that it realizes the phase with C^+_{k_z=0}=+2, C^+_{k_z=pi}=+1, C^+_{k_x=k_y}=-1, and we propose a corresponding minimal model.
Cr2Ge2Te6 (CGT), a layered ferromagnetic insulator, has attracted a great deal of interest recently owing to its potential for integration with Dirac materials to realize the quantum anomalous Hall effect (QAHE) and to develop novel spintronics devices. Here, we study the uniaxial magnetic anisotropy energy of single-crystalline CGT and determine that the magnetic easy axis is directed along the c-axis in its ferromagnetic phase. In addition, CGT is an insulator below the Curie temperature. These properties make CGT a potentially promising candidate substrate for integration with topological i…
We predict a new class of topological crystalline insulators (TCI) in the anti-perovskite material family with the chemical formula A$_3$BX. Here the nontrivial topology arises from band inversion between two $J=3/2$ quartets, which is described by a generalized Dirac equation for a "Dirac octet". Our work suggests that anti-perovskites are a promising new venue for exploring the cooperative interplay between band topology, crystal symmetry and electron correlation.
The chirality associated with broken time reversal symmetry in magnetically doped topological insulators has important implications to the quantum transport phenomena. Here we report the anomalous Hall effect studies in Mn- and Cr-doped Bi$_2$Te$_3$ topological insulators with varied thickness and doping content. By tracing the chirality of the Hall loops, we find that the Mn-type anomalous Hall effect with clockwise chirality is strengthened by the reduction of film thickness, which is opposite to that of the Cr-type anomalous Hall effect with counterclockwise chirality. We provide a phenomen…
We study the magnetic properties of topological insulators doped with isoelectronic magnetic impurities. We obtain that at zero temperature the impurities order ferromagnetically, but when raising the temperature the topological insulator undergoes a first order phase transition to a spin density wave phase before the system reaches the paramagnetic phase. The origin of this phase is the non-trivial dependence of the topological insulator spin susceptibility on the momentum. We analyze the coupling of the non-uniform magnetic phase with the Dirac electronic system that occurs at the surfaces o…
The paper examines weak localization (WL) of surface states with a quadratic band crossing in topological crystalline insulators. It is shown that the topology of the quadratic band crossing point dictates the negative sign of the WL conductivity correction. For the surface states with broken time-reversal symmetry, an explicit dependence of the WL conductivity on the band Berry flux is obtained and analyzed for different carrier-density regimes and types of the band structure (normal or inverted). These results suggest a way to detect the band Berry flux through WL measurements.
Disorder driven superconductor to insulator transition via intermediate metallic regime is reported in nano-crystalline thin films of molybdenum. The nano-structured thin films have been deposited at room temperature using DC magnetron sputtering at different argon pressures. The grain size has been tuned using deposition pressure as the sole control parameter. A variation of particle sizes, room temperature resistivity and superconducting transition has been studied as a function of deposition pressure. The nano-crystalline molybdenum thin films are found to have large carrier concentration b…
Topological crystalline insulators are new states of matter in which the topological nature of electronic structures arises from crystal symmetries. Here we predict the first material realization of topological crystalline insulator in the semiconductor SnTe, by identifying its nonzero topological index. We predict that as a manifestation of this nontrivial topology, SnTe has metallic surface states with an even number of Dirac cones on high-symmetry crystal surfaces such as {001}, {110} and {111}. These surface states form a new type of high-mobility chiral electron gas, which is robust again…
In this review, we discuss recent progress in the explorations of topological materials beyond topological insulators; specifically, we focus on topological crystalline insulators and bulk topological superconductors. The basic concepts, model Hamiltonians, and novel electronic properties of these new topological materials are explained. The key role of symmetries that underlie their topological properties is elucidated. Key issues in their materials realizations are also discussed.
Topological crystalline insulators (TCIs) are insulating materials whose topological property relies on generic crystalline symmetries. Based on first-principles calculations, we study a three-dimensional (3D) crystal constructed by stacking two-dimensional TCI layers. Depending on the inter-layer interaction, the layered crystal can realize diverse 3D topological phases characterized by two mirror Chern numbers (MCNs) ($μ_1,μ_2$) defined on inequivalent mirror-invariant planes in the Brillouin zone. As an example, we demonstrate that new TCI phases can be realized in layered materials such as…
Possible high-Tc superconductivity at 45 K in the Ge-doped cluster Mott insulator GaNb4Se8
Institute of Physics and Beijing National Laboratory for Condensed Matter Physics, Chinese Academy of Sciences（中国科学院物理研究所与北京凝聚态物理国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）
We investigate electromagnetic properties of a topological crystalline insulator (TCI) thin film under external electromagnetic fields. The TCI thin film is a topological insulator indexed by the mirror-Chern number. It is demonstrated that the gap closes together with the emergence of a pair of gapless cones carrying opposite chirarities by applying in-plane magnetic field. A pair of gapless points have opposite vortex numbers. This is a reminiscence of a pair of Weyl cones in 3D Weyl semimetal. We thus present an a magnetic-field induced semimetal-semiconductor transition in 2D material. Thi…
We investigate the electrical conductivity and thermoelectric effects in topological crystalline insulators in the presence of short- and long-range impurity interactions. We employ the generalized Boltzmann formalism for anisotropic Fermi surface systems. The conductivity exhibits a local minimum as doping varies owing to the Van Hove singularity in the density of states originated from the saddle point in the surface states band structure. Suppression of the interband scattering of the charge carriers at high-energy Dirac points results in a maximum in the electrical conductivity. Whenever t…
In this paper we present an approach aimed at calculating the optical dielectric constant of crystalline insulators both at the Hartree-Fock, and correlated levels. Our scheme employs a real-space methodology, employing Wannier functions as the basic building blocks. The scheme has been applied to compute the optical dielectric constants of LiF, LiCl, MgO, and Li2O. In all the cases, results of correlated calculations, based upon systematic many-body corrections beyond Hartree-Fock, exhibit excellent agreement with the experiments. To the best of our knowledge, the calculations presented here …
Based on a combination of $k \cdot p$ theory, band topology analysis and electronic structure calculations, we predict the (111) thin films of the SnTe class of three-dimensional (3D) topological crystalline insulators realize the quantum spin Hall phase in a wide range of thickness. The nontrivial topology originates from the inter-surface coupling of the topological surface states of TCI in the 3D limit. The inter-surface coupling changes sign and gives rise to topological phase transitions as a function of film thickness. Furthermore, this coupling can be strongly affected by an external el…
A theory of self-excitation in the metal-insulator-metal structure doped with metal nanowires is developed for the case where the power is provided by an external source of radio waves. Both the transient stage of self-excitation and the steady-state regime of self-oscillation are analyzed in a fully analytical form. The numerical estimates demonstrate that this effect can be used for diverse practical purposes, in particular, for radio frequency power harvesting. These findings extend the approach developed in nano-optics to the field of electrical engineering.
Confining two dimensional Dirac fermions on the surface of topological insulators has remained an outstanding conceptual challenge. Here we show that Dirac fermion confinement is achievable in topological crystalline insulators (TCI), which host multiple surface Dirac cones depending on the surface termination and the symmetries it preserves. This confinement is most dramatically reflected in the flux dependence of these Dirac states in the nanowire geometry, where different facets connect to form a closed surface. Using SnTe as a case study, we show how wires with all four facets of the <100>…
We report a numerical analysis of Anderson localization in a model of a doped semiconductor. The model incorporates the disorder arising from the random spatial distribution of the donor impurities and takes account of the electron-electron interactions between the carriers using density functional theory in the local density approximation. Preliminary results suggest that the model exhibits a metal-insulator transition.
We propose that a specific spatial configuration of lattice sites that energetically favor {\it 3+} or {\it 4+} Mn ions in moderately doped manganites constitutes approximately a spatially random two-energy-level system. Such an effect results in a mechanism of metal-insulator transitions that appears to be different from both the Anderson transition and the Mott-Hubbard transition. Correspondingly, a disordered Kondo lattice model is put forward, whose dynamical mean-field solution agrees reasonably with experiments.
We present first principles calculations of the nontrivial surface states and their spin-textures in the topological crystalline insulator SnTe. The surface state dispersion on the [001] surface exhibits four Dirac-cones centered along the intersection of the mirror plane and the surface plane. We propose a simple model of two interacting coaxial Dirac cones to describe both the surface state dispersion and the associated spin-texture. While the out-of-the-plane spin polarization is zero due to the crystalline and time-reversal symmetries, the in-plane spin texture shows helicity with some dis…
Heterointerfaces in complex oxide systems open new arenas in which to test models of strongly correlated material, explore the role of dimensionality in metal-insulator-transitions (MITs) and small polaron formation. Close to the quantum critical point Mott MITs depend on band filling controlled by random disordered substitutional doping. Delta-doped Mott insulators are potentially free of random disorder and introduce a new arena in which to explore the effect of electron correlations and dimensionality. Epitaxial films of the prototypical Mott insulator GdTiO3 are delta-doped by substituting…
Narrow gap semiconductor Pb$_{1-x}$Sn$_{x}$Se was investigated for topologically protected surface states in its rock-salt structural phase for x=0.45, 0.23, 0.15, and 0. Angle-resolved photoelectron spectroscopy of intrinsically p-doped samples showed clear indication of two Dirac cones, eccentric about the time-reversal invariant point X of the surface Brillouin zone for all but the x=0 sample. Adsorption of alkalies gradually filled the surface bands with electrons, driving the x>0 topological crystalline insulator systems through Lifshitz transitions, and from a hole- to electron-like Ferm…
A topological insulator is a new state of matter, possessing gapless spin-locking surface states across the bulk band gap which has created new opportunities from novel electronics to energy conversion. However, the large concentration of bulk residual carriers has been a major challenge for revealing the property of the topological surface state via electron transport measurement. Here we report surface state dominated transport in Sb-doped Bi2Se3 nanoribbons with very low bulk electron concentrations. In the nanoribbons with sub-10nm thickness protected by a ZnO layer, we demonstrate complet…
Quantum spin liquid states, in which spins are quantum-mechanically delocalized in direction, have been so far studied for charge-localized Mott insulators arising from strong repulsive interaction. Recently, however, it was found that the doped Mott insulator with a triangular lattice, $κ$-(ET)$_4$Hg$_{2.89}$Br$_8$, exhibits both spin-liquid-like magnetism and metallic electrical conduction. Thus, it is now possible to experimentally explore how the spin liquidity affects the electrical conduction, an issue that has received a great deal of theoretical attention. Here, with a newly developed …
Superconducting topological crystalline insulators (TCI) are predicted to host new topological phases protected by crystalline symmetries, but available materials are insufficiently suitable for surface studies. To induce superconductivity at the surface of a prototypical TCI SnTe, we use molecular beam epitaxy to grow a heterostructure of SnTe and a high-Tc superconductor Fe(Te,Se), utilizing a 'buffer' layer to bridge the large lattice mismatch between SnTe and Fe(Te,Se). Using low-temperature scanning tunneling microscopy and spectroscopy, we measure a prominent spectral gap on the surface …
We study the effect of the long-range Coulomb interaction in $j=3/2$ Dirac electrons in cubic crystals with the $O_h$ symmetry, which serves as an effective model for antiperovskite topological crystalline insulators. The renormalization group analysis reveals three fixed points that are Lorentz invariant, rotationally invariant, and $O_h$ invariant. Among them, the Lorentz- and $O_h$-invariant fixed points are stable in the low-energy limit while the rotationally invariant fixed point is unstable. The existence of a stable $O_h$-invariant fixed point of Dirac fermions with finite velocity ani…
Electronic and magnetic properties of the heavily H-doped LaFeAsO$_{1-x}$H$_x$ $(x\sim0.5 )$ were studied in the framework of the density functional theory combined with the dynamical mean field theory (DFT+DMFT). We found a stripe-like-ordered structure of hydrogen and oxygen atoms, as a ground state, with the same configuration as the antiferromagnetic (AF) order. The new configuration could explain the existing experimental results related to the heavily H-doped LaFeAsO$_{1-x}$H$_x$, such as an in-plane electronic anisotropy and a non-uniform magnetic behavior. A significant anisotropy was …
We report detailed investigations of the properties of a superconductor obtained by substituting In at the Sn site in the topological crystalline insulator (TCI), SnTe. Transport, magnetization and heat capacity measurements have been performed on crystals of Sn0.6In0.4Te, which is shown to be a bulk superconductor with Tc(onset) at ~4.70(5) K and Tc(zero) at ~3.50(5) K. The upper and lower critical fields are estimated to be μ0Hc2(0) = 1.42(3) T and μ0Hc1(0) = 0.90(3) mT respectively, while κ = 56.4(8) indicates this material is a strongly type II superconductor.
In addition to novel surface states, topological insulators can also exhibit robust gapless states at crystalline defects. Step edges constitute a class of common defects on the surface of crystals. In this work we establish the topological nature of one-dimensional (1D) bound states localized at step edges of the [001] surface of a topological crystalline insulator (TCI) Pb$_{0.7}$Sn$_{0.3}$Se, both theoretically and experimentally. We show that the topological stability of the step edge states arises from an emergent particle-hole symmetry of the surface low-energy physics, and demonstrate t…
Three-dimensional, crystalline Hopf insulators are generic members of unitary Wigner-Dyson class, which can break all global discrete symmetries and point group symmetries. In the absence of first Chern number for any two-dimensional plane of Brillouin zone, the Hopf invariant $N_H \in \mathbb{Z}$. But in the presence of Chern number $N_H \in \mathbb{Z}_{2q}$, where $q$ is the greatest common divisor of Chern numbers for $xy$, $yz$, and $xz$ planes of Brillouin zone. How does $N_H$ affect topological quantization of isotropic, magneto-electric coefficient? We answer this question with calculat…
The emergence of superconductivity in doped Mott insulators has been debated for decades. In this paper, we report the theoretical discovery of a time-reversal symmetry breaking superconducting ground state in the doped Mott insulator (described by the well known t-J model) on honeycomb lattice, based on a recently developed variational method: the Grassmann tensor product state approach. As a benchmark, we use exact diagonalization and density-matrix renormalization methods to check our results on small clusters. We find systematic consistency for the ground-state energy as well as other phys…
The celebrated tenfold-way of Altland-Zirnbauer symmetry classes discern any quantum system by its pattern of non-spatial symmetries. It lays at the core of the periodic table of topological insulators and superconductors which provided a complete classification of weakly-interacting electrons' non-crystalline topological phases for all symmetry classes. Over recent years, a plethora of topological phenomena with diverse surface states has been discovered in crystalline materials. In this paper, we obtain an exhaustive classification of topologically distinct groundstates as well as topologica…
Crystalline topological phases have recently attracted a lot of experimental and theoretical attention. Key advances include the complete elementary band representation analyses of crystalline matter by symmetry indicators and the discovery of higher-order hinge and corner states. However, current classification schemes of such phases are either implicit or limited in scope. We present a new scheme for the explicit classification of crystalline topological insulators and superconductors. These phases are protected by crystallographic point group symmetries and are characterized by bulk topolog…
