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 topological phases with anomalous surface states of crystalline topological insulators and superconductors for key space-groups, layer-groups, and rod-groups. This is done in a unified manner for the full tenfold-way of Altland-Zirnbauer non-spatial symmetry classes. We establish a comprehensive paradigm that harnesses the modern mathematical framework of equivariant spectra; it allows us to obtain results applicable to generic topological classification problems. In particular, this paradigm provides efficient computational tools that enable an inherently unified treatment of the full tenfold-way.
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…
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…
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…
We introduce a coupled-layer construction to describe three-dimensional topological crystalline insulators protected by reflection symmetry. Our approach uses stacks of weakly-coupled two-dimensional Chern insulators to produce topological crystalline insulators in one higher dimension, with tunable number and location of surface Dirac cones. As an application of our formalism, we turn to a simplified model of topological crystalline insulator SnTe, showing that its protected surface states can be described using the coupled layer construction.
In this work, we identify a new class of Z2 topological insulator protected by non-symmorphic crystalline symmetry, dubbed a "topological non-symmorphic crystalline insulator". We construct a concrete tight-binding model with the non-symmorphic space group pmg and confirm the topological nature of this model by calculating topological surface states and defining a Z2 topological invariant. Based on the projective representation theory, we extend our discussion to other non-symmorphic space groups that allows to host topological non-symmorphic crystalline insulators.
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…
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…
In this Book Chapter (invited) we briefly review the basic concepts defining topological insulators and focus on elaborating on the key experimental results that revealed and established their symmetry protected (SPT) topological nature. We then present key experimental results that demonstrate magnetism, Kondo insulation, mirror chirality or topological crystalline order and superconductivity in spin-orbit topological insulator settings and how these new (bulk insulating) phases of matter arise through topological quantum phase transitions from Bloch band insulators via topological or Dirac s…
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…
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.
We propose magnonic analogs of topological crystalline insulators which possess Dirac surface states protected by the combined symmetry of time-reversal and half translation. Constructing models of the topological magnon systems, we demonstrate that the energy current flows through the systems in response to an electric field, owing to the Dirac surface states with the spin-momentum locking. We also propose a realization of the magnonic analogs of topological crystalline insulators in a magnetic compound CrI$_{3}$ with a monoclinic structure.
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…
Topological crystalline insulators define a new class of topological insulator phases with gapless surface states protected by crystalline symmetries. In this work, we present a general theory to classify topological crystalline insulator phases based on the representation theory of space groups. Our approach is to directly identify possible nontrivial surface states in a semi-infinite system with a specific surface, of which the symmetry property can be described by 17 two-dimensional space groups. We reproduce the existing results of topological crystalline insulators, such as mirror Chern i…
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…
Gapless surface states of time reversal invariant topological insulators are protected by the anti-unitary nature of the time reversal operation. Very recently, this idea was generalized to magnetic structures, in which time reversal symmetry is explicitly broken, but there is still an anti-unitary symmetry operation combining time reversal symmetry and crystalline symmetry. These topological phases in magnetic structures are dubbed "topological magnetic crystalline insulators". In this work, we present a general theory of topological magnetic crystalline insulators in different types of magne…
We present a general approach to obtain effective field theories for topological crystalline insulators whose low-energy theories are described by massive Dirac fermions. We show that these phases are characterized by the responses to spatially dependent mass parameters with interfaces. These mass interfaces implement the dimensional reduction procedure such that the state of interest is smoothly deformed into a topological crystal, which serves as a representative state of a phase in the general classification. Effective field theories are obtained by integrating out the massive Dirac fermion…
We propose a phenomenological theory for topological crystalline insulators with time reversal and $C_4$ symmetries. First, we introduce a fictitious space and transformation of electromagnetic field operators. This transformation leaves the speed of light unchanged but changes the elementary charge to $\sqrt{2}e$. Then we formulate the theory of topological crystalline insulators in terms of transformed fields in this fictitious space as 3D BF theory containing $π$-flux excitations. It is known that a 3D BF theory with half flux quantum excitations describes low energy properties of time reve…
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.
We have performed angle-resolved photoemission spectroscopy (ARPES) on the (111) surface of the topological crystalline insulator SnTe. Distinct from a pair of Dirac-cone surface states across the X_bar point of the surface Brillouin zone on the (001) surface, we revealed two types of Dirac-cone surface states each centered at the G_bar and M_bar points, which originate from the bulk-band inversion at the L points. We also found that the energy location of the Dirac point and the Dirac velocity are different from each other. This ARPES experiment demonstrates the surface states on different cr…
We propose a different route to time-reversal invariant Weyl semimetals employing multilayer heterostructures comprising ordinary "trivial" insulators and nontrivial insulators with \textit{pairs} of protected Dirac cones on the surface. We consider both the case of weak topological insualtors, where surface Dirac cones are pinned to time-reversal invariant momenta, and of topological crystalline insulators with unpinned surface Dirac cones. For both realizations we explain phenomenologically how the proposed construction leads to the emergence of a Weyl semimetal phase. We further formulate e…
Second-order topological insulators and superconductors have a gapped excitation spectrum in bulk and along boundaries, but protected zero modes at corners of a two-dimensional crystal or protected gapless modes at hinges of a three-dimensional crystal. A second-order topological phase can be induced by the presence of a bulk crystalline symmetry. Building on Shiozaki and Sato's complete classification of bulk crystalline phases with an order-two crystalline symmetry [Phys.\ Rev.\ B {\bf 90}, 165114 (2014)], such as mirror reflection, twofold rotation, or inversion symmetry, we classify all co…
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…
Magnetic insulators are a key resource for next-generation spintronic and topological devices. The family of layered metal halides promises ultrathin insulating multiferroics, spin liquids, and ferromagnets, but new characterization methods are required to unlock their potential. Here, we report tunneling through the layered magnetic insulator CrI3 as a function of temperature and applied magnetic field. We electrically detect the magnetic ground state and inter-layer coupling and observe a field-induced metamagnetic transition. The metamagnetic transition results in magnetoresistances of 95%,…
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…
Recently, the topological classification of electronic states has been extended to a new class of matter known as topological crystalline insulators. Similar to topological insulators, topological crystalline insulators also have spin-momentum locked surface states; but they only exist on specific crystal planes that are protected by crystal reflection symmetry. Here, we report an ultra-low temperature scanning tunneling microscopy and spectroscopy study on topological crystalline insulator SnTe nanoplates grown by molecular beam epitaxy. We observed quasiparticle interference patterns on the …
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…
Using a systematic relation between topological gapless phases in three dimensions and topological gapped phases in two dimensions, we identify four types of higher-order topological semimetals or nodal superconductors (HOTS), hosting (i) flat zero-energy "Fermi arcs" at crystal hinges, (ii) flat zero-energy hinge arcs coexisting with surface Dirac cones, (iii) chiral or helical hinge modes, or (iv) flat zero-energy hinge arcs connecting nodes only at finite momentum. Bulk-boundary correspondence relates the hinge states to the bulk topology protecting the nodal point or loop. We classify all …
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…
The gapless surface Dirac cone of time reversal invariant topological insulators is protected by time reversal symmetry due to the Kramers' theorem. Spin degree of freedom is usually required since Kramers' theorem only guarantees double degeneracy for spinful fermions, but not for spinless fermions. In this paper, we present an antiferromagnetic spinless model, which breaks time reversal symmetry. Similar to time reversal invariant topological insulators, this model possesses a topologically non-trivial phase with a single surface Dirac cone, which is protected by the combination of time reve…
We give an introduction to topological crystalline insulators, that is, gapped ground states of quantum matter that are not adiabatically connected to an atomic limit without breaking symmetries that include spatial transformations, like mirror or rotational symmetries. To deduce the topological properties, we use non-Abelian Wilson loops. We also discuss in detail higher-order topological insulators with hinge and corner states, and in particular present interacting bosonic models for the latter class of systems.
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 …
Topological crystalline insulators are materials in which the crystalline symmetry leads to topologically protected surface states with a chiral spin texture, rendering them potential candidates for spintronics applications. Using scanning tunneling spectroscopy, we uncover the existence of one-dimensional (1D) midgap states at odd-atomic surface step edges of the three- dimensional topological crystalline insulator (Pb,Sn)Se. A minimal toy model and realistic tight- binding calculations identify them as spin-polarized flat bands connecting two Dirac points. This non-trivial origin provides th…
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…
Topological crystalline insulators (TCI) are a new class of materials which have metallic surface states on select surfaces due to point group crystalline symmetries. In this letter, we consider a model for a three-dimensional (3D) topological crystalline insulator with Dirac nodes occurring on a surface that are protected by the mirror and time reversal symmetry. We demonstrate that the electromagnetic response for such a system is characterized by a $1$-form $b_μ$. $b_μ$ can be inferred from the locations of the surface Dirac nodes in energy-momentum space and couples to the surface Dirac no…
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>…
In the recently discovered topological crystalline insulators (TCIs), topology and crystal symmetry intertwine to create surface states with a unique set of characteristics. Among the theoretical predictions for TCIs is the possibility of imparting mass to the massless Dirac fermions by breaking crystal symmetry, as well as a Lifshitz transition with a change of Fermi surface topology. Here we report high resolution scanning tunneling microscopy studies of a TCI, Pb1-xSnxSe. We demonstrate the formation of zero mass Dirac fermions protected by crystal symmetry and the mechanism of mass generat…
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…
We formulate topological crystalline materials on the basis of the twisted equivariant $K$-theory. Basic ideas of the twisted equivariant $K$-theory is explained with application to topological phases protected by crystalline symmetries in mind, and systematic methods of topological classification for crystalline materials are presented. Our formulation is applicable to bulk gapful topological crystalline insulators/superconductors and their gapless boundary and defect states, as well as bulk gapless topological materials such as Weyl and Dirac semimetals, and nodal superconductors. As an appl…
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…
The surface of a three-dimensional topological electron system often hosts symmetry-protected gapless surface states. With the effect of electron interactions, these surface states can be gapped out without symmetry breaking by a surface topological order, in which the anyon excitations carry anomalous symmetry fractionalization that cannot be realized in a genuine two-dimensional system. We show that for a mirror-symmetry-protected topological crystalline insulator with mirror Chern number $n=4$, its surface can be gapped out by an anomalous $\mathbb Z_2$ topological order, where all anyons c…
We propose a minimal tight-binding model for thin films made of topological crystalline insulator (TCI) on the basis of the mirror and discrete rotational symmetries. The basic term consists of the spin-orbit interaction describing a Weyl semimetal, where gapless Dirac cones emerge at all the high symmetry points in the momentum space. We then introduce the mass term providing gaps to Dirac cones at our disposal. They simulate the thin films made of the [001], [111] and [110] TCI surfaces. TCI thin films are topological insulators protected by the mirror symmetry. We analyze the mirror-Chern n…
We study the effect of electron interactions in topological crystalline insulators (TCIs) protected by mirror symmetry, which are realized in the SnTe material class and host multi-valley Dirac fermion surface states. We find that interactions reduce the integer classification of noninteracting TCIs in three dimensions, indexed by the mirror Chern number, to a finite group $Z_8$. In particular, we explicitly construct a microscopic interaction Hamiltonian to gap 8 flavors of Dirac fermions on the TCI surface, while preserving the mirror symmetry. Our construction builds on interacting edge sta…
The rich variety of crystalline symmetries in solids leads to a plethora of topological crystalline insulators (TCIs) featuring distinct physical properties, which are conventionally understood in terms of bulk invariants specialized to the symmetries at hand. While isolated examples of TCI have been identified and studied, the same variety demands a unified theoretical framework. In this work, we show how the surfaces of TCIs can be analyzed within a general surface theory with multiple flavors of Dirac fermions, whose mass terms transform in specific ways under crystalline symmetries. We ide…
Topological crystalline insulators represent a new state of matter, in which the electronic transport is governed by mirror-symmetry protected Dirac surface states. Due to the helical spin-polarization of these surface states, the proximity of topological crystalline matter to a nearby superconductor is predicted to induce unconventional superconductivity and thus to host Majorana physics. We report on the preparation and characterization of Nb-based superconducting quantum interference devices patterned on top of topological crystalline insulator SnTe thin films. The SnTe films show weak anti…
We study electronic states and topological invariants of (001)-films of topological crystalline insulator (TCI) Pb_{x}Sn_{1-x}Te. Gapless surface Dirac cones on bulk TCIs become gapped in thin films due to finite-size effect, which is hybridization between those on the top and bottom surfaces. We clarify that the TCI film has the strong finite-size effect as compared to three-dimensional topological insulators such as Bi2Se3. Moreover, the energy gap oscillates with the thickness of film. The oscillation stems from topological phase transitions in two dimensions. The obtained data of the topol…
The orbital motion of electrons in a three-dimensional solid can generate a pseudoscalar magnetoelectric coupling $θ$, a fact we derive for the single-particle case using a recent theory of polarization in weakly inhomogeneous materials. This polarizability $θ$ is the same parameter that appears in the "axion electrodynamics" Lagrangian $Δ{\cal L}_{EM} = (θe^2 / 2 πh) {\bf E} \cdot {\bf B}$, which is known to describe the unusual magnetoelectric properties of the three-dimensional topological insulator ($θ=π$). We compute $θ$ for a simple model that accesses the topological insulator and discu…
We envision that quantum spin Hall effect should be observed in $(111)$-oriented thin films of SnSe and SnTe topological crystalline insulators. Using a tight-binding approach supported by first-principles calculations of the band structures we demonstrate that in these films the energy gaps in the two-dimensional band spectrum depend in an oscillatory fashion on the layer thickness. These results as well as the calculated topological invariant indexes and edge state spin polarizations show that for films ~20-40 monolayers thick a two-dimensional topological insulator phase appears. In this ra…
Based on first-principles calculations and symmetry analysis, we predict atomically thin ($1-N$ layers) 2H group-VIB TMDs $MX_2$ ($M$ = Mo, W; $X$ = S, Se, Te) are large-gap higher-order topological crystalline insulators protected by $C_3$ rotation symmetry. We explicitly demonstrate the nontrivial topological indices and existence of the hallmark corner states with quantized fractional charge for these familiar TMDs with large bulk optical band gaps ($1.64-1.95$ eV for the monolayers), which would facilitate the experimental detection by STM. We find that the well-defined corner states exist…
A new class of materials, Topological Crystalline Insulators (TCIs) have been shown to possess exotic surface state properties that are protected by mirror symmetry. These surface features can be enhanced if the surface-area-to-volume ratio of the material increases, or the signal arising from the bulk of the material can be suppressed. We report the experimental procedures to obtain high quality crystal boules of the TCI, SnTe, from which nanowires and microcrystals can be produced by the vapour-liquid-solid (VLS) technique. Detailed characterisation measurements of the bulk crystals as well …
Being Wannierizable is not the end of the story for topological insulators. We introduce a family of topological insulators that would be considered trivial in the paradigm set by the tenfold way, topological quantum chemistry, and the method of symmetry-based indicators. Despite having a symmetric, exponentially-localized Wannier representation, each Wannier function cannot be completely localized to a single primitive unit cell in the bulk. Such multicellular topology is shown to be neither stable, nor fragile, but delicate, i.e., the topology can be nullified by adding trivial bands to eith…
Three-dimensional topological crystalline insulators were recently predicted and observed in the SnTe class of IV-VI semiconductors, which host metallic surface states protected by crystal symmetries. In this work, we study thin films of these materials and expose their potential for device applications. We demonstrate that thin films of SnTe and Pb(1-x)Sn(x)Se(Te) grown along the (001) direction are topologically nontrivial in a wide range of film thickness and carry conducting spin-filtered edge states that are protected by the (001) mirror symmetry via a topological invariant. Application o…
Topological crystalline insulators (TCIs) are nontrivial quantum phases of matter protected by crystalline (and other) symmetries. They are originally predicted by band theories, so an important question is their stability under interactions. In this paper, by directly studying the physical bulk properties of several band-theory-based nontrivial TCIs that are conceptually interesting and/or experimentally feasible, we show they are stable under interactions. These TCIs include (1) a weak topological insulator, (2) a TCI with a mirror symmetry and its time-reversal symmetric generalizations, (3…
Different from the two-dimensional (2D) topological insulator, the 2D topological crystalline insulator (TCI) phase disappears when the mirror symmetry is broken, e.g., upon placing on a substrate. Here, based on a new family of 2D TCIs - SnTe and PbTe monolayers - we theoretically predict the realization of the quantum anomalous Hall effect with Chern number C = 2 even when the mirror symmetry is broken. Remarkably, we also demonstrate that the considered materials retain their large-gap topological properties in quantum well structures obtained by sandwiching the monolayers between NaCl laye…
Bismuth telluride is a low energy bulk band-gap topological system with conducting surface states. Besides its very good thermoelectric properties, it also makes a very good candidate for broadband photodetectors. Here, we report temperature-dependent photo-Seebeck effect in a bulk single crystalline bismuth telluride. On light illumination, an electrically biased sample shows distinguishable contributions in the measured current due to both the Seebeck effect and the normal photo-generated carriers within a narrow layer of the sample. Detailed experiments are performed to elucidate the distin…
