拓扑晶体绝缘体代表了一种新的拓扑相的物质，其中的表面状态的保护离散点群对称性的基础晶格。岩盐铅-锡-硒化物合金是该相的一种可能的实现，其在改变铅含量时经历拓扑相变。利用扫描隧道显微镜（STM）和角分辨光电子能谱（ARPES）研究了（001）Pb $_{1-x}$ Sn $_{x}$ Se在拓扑非平凡相（x=0.23）和拓扑平凡相（x=0）的表面态.我们观察到的准粒子干扰STM的拓扑晶体绝缘体的表面上，并证明了测量的干扰可以理解从ARPES研究和一个简单的能带结构模型。此外，我们的研究结果支持了Pb $_{0.77}$ Sn $_{0.23}$ Se和PbSe具有不同拓扑性质的事实.
英文摘要：
Topological crystalline insulators represent a novel topological phase of matter in which the surface states are protected by discrete point group-symmetries of the underlying lattice. Rock-salt lead-tin-selenide alloy is one possible realization of this phase which undergoes a topological phase transition upon changing the lead content. We used scanning tunneling microscopy (STM) and angle resolved photoemission spectroscopy (ARPES) to probe the surface states on (001) Pb$_{1-x}$Sn$_{x}$Se in the topologically non-trivial (x=0.23) and topologically trivial (x=0) phases. We observed quasiparticle interference with STM on the surface of the topological crystalline insulator and demonstrated that the measured interference can be understood from ARPES studies and a simple band structure model. Furthermore, our findings support the fact that Pb$_{0.77}$Sn$_{0.23}$Se and PbSe have different topological nature.
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 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…
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.
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…
We theoretically investigate quasiparticle interference in superconducting topological insulators with the nematic order parameter. This order parameter spontaneously breaks the rotational symmetry of the crystal. Such rotational symmetry breaking is visible in the quasiparticle interference picture both in coordinate and momentum spaces. For a small bias voltages quasiparticle interference incommensurate with the crystal symmetry and shows nematic behavior. If the bias voltage is comparable with the value of the order parameter interference picture is similar to the interference picture of th…
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…
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.
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…
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…
Quasiparticle Interference on the Surface of the Topological Insulator Bi$_2$Te$_3$
利用T矩阵方法研究了大禁带拓扑绝缘体Bi $_2$ Te $_3$表面态的光谱成像扫描隧道显微术的准粒子干涉.考虑了扭曲六边形等能线上的标量势散射和自旋轨道散射。虽然反向散射被禁止的时间反演对称性，其他散射是允许的，并表现出强烈的依赖于自旋配置的本征函数在k点的等能轮廓。我们的分析中发现的特征散射波矢符合最近的实验结果。
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…
Topological crystalline insulators (TCI) are unique systems where a band inversion that is protected by crystalline mirror symmetry leads to a multiplicity of topological surface states. Binary SnTe is an attractive lead-free TCI compound; the present work on high-quality thin films provides a route for increasing the mobility and reducing the carrier density of SnTe without chemical doping. Results of quantum coherent magnetotransport measurements reveal a multiplicity of Dirac surface states that are unique to TCI. Modeling of the weak antilocalization shows variations in the extracted numbe…
We discuss recent advances in the study of topological insulators protected by spatial symmetries by reviewing three representative, theoretical examples. In three dimensions, these states of matter are generally characterized by the presence of gapless boundary states at surfaces that respect the protecting spatial symmetry. We discuss the appearance of these topological states both in crystals with negligible spin-orbit coupling and a fourfold rotational symmetry, as well as in mirror-symmetric crystals with sizable spin-orbit interaction characterized by the so-called mirror Chern number. F…
The topological crystalline insulator tin telluride is known to host superconductivity when doped with indium (Sn$_{1-x}$In$_{x}$Te), and for low indium contents ($x=0.04$) it is known that the topological surface states are preserved. Here we present the growth, characterization and angle resolved photoemission spectroscopy analysis of samples with much heavier In doping (up to $x\approx0.4$), a regime where the superconducting temperature is increased nearly fourfold. We demonstrate that despite strong p-type doping, Dirac-like surface states persist.
We consider an interface between two strong time-reversal invariant topological insulators having surface states with opposite spin chirality, or equivalently, opposite mirror Chern number. We show that such an interface supports gapless modes that are protected by mirror symmetry. The interface states are investigated with a continuum model for the Bi2Se3 class of topological insulators that takes into account terms up to third order in the crystal momentum, which ensures that the model has the correct symmetry. The model parameters are obtained from ab initio calculations. Finally, we consid…
Periodically driven systems can host so called anomalous topological phases, in which protected boundary states coexist with topologically trivial Floquet bulk bands. We introduce an anomalous version of reflection symmetry protected topological crystalline insulators, obtained as a stack of weakly-coupled two-dimensional layers. The system has tunable and robust surface Dirac cones even though the mirror Chern numbers of the Floquet bulk bands vanish. The number of surface Dirac cones is given by a new topological invariant determined from the scattering matrix of the system. Further, we find…
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…
We report on the fabrication of Josephson junctions using the topological crystalline insulator Pb$_{0.5}$Sn$_{0.5}$Te as the weak link. The properties of these junctions are characterized and compared to those fabricated with weak links of PbTe, a similar material yet topologically trivial. Most striking is the difference in the AC Josephson effect: junctions made with Pb$_{0.5}$Sn$_{0.5}$Te exhibit rich subharmonic structure consistent with a skewed current-phase relation. This structure is absent in junctions fabricated from PbTe. A discussion is given on the origin of this effect as an ind…
We investigate a topological switch between second-order topological insulators (SOTIs) and topological crystalline insulators (TCIs). Both the SOTI and the TCI are protected by the mirror and inversion symmetries, for which we define the bulk topological numbers of the same type. We take examples of square nanodisks on the square lattice and hexagonal nanodisks on the triangular lattice. When inplane magnetic field is introduced parallel to one of the helical edges, the system becomes a TCI. The conductance along the edge is 1 in the unit of the conductance quantum $e^2/h$. As the inplane fie…
We study the properties of a family of anti-pervoskite materials, which are topological crystalline insulators with an insulating bulk but a conducting surface. Using ab-initio DFT calculations, we investigate the bulk and surface topology and show that these materials exhibit type-I as well as type-II Dirac surface states protected by reflection symmetry. While type-I Dirac states give rise to closed circular Fermi surfaces, type-II Dirac surface states are characterized by open electron and hole pockets that touch each other. We find that the type-II Dirac states exhibit characteristic van-H…
Large Chern Number Quantum Anomalous Hall Effect In Thin-film Topological Crystalline Insulators
量子反常霍尔绝缘体是一种二维绝缘态，在没有外加磁场的情况下，表现出与量子霍尔态相似的性质。它们具有量子化的霍尔电导$σ^H=Ce^2/h$，其中整数$C$被称为陈数，并且表示无间隙边缘模式的数量。最近的实验表明，掺铬薄膜（Bi，Sb）$_2$ Te $_3$是一种QAH绝缘体，具有陈数$C=\pm1$。在这里，我们从理论上预测，薄膜拓扑晶体绝缘体（TCI）可以托管各种QAH相，当掺杂铁磁有序掺杂剂。$\pm4$之间的任何陈氏数原则上可以作为（a）取决于磁掺杂浓度的感应塞曼场，（b）固有的或由压电材料通过邻近效应感应的结构变形，以及（c）薄膜的厚度之间的相互作用的结果而达到。在TCI中发现的可调陈氏数在超低功耗信息处理应用中具有重要的潜力。
We extend the theory of dipole moments in crystalline insulators to higher multipole moments. In this paper, we expand in great detail the theory presented in Ref. 1, and extend it to cover associated topological pumping phenomena, and a novel class of 3D insulator with chiral hinge states. In quantum-mechanical crystalline insulators, higher multipole bulk moments manifest themselves by the presence of boundary-localized moments of lower dimension, in exact correspondence with the electromagnetic theory of classical continuous dielectrics. In the presence of certain symmetries, these moments …
We theoretically predict two new classes of three-dimensional topological crystalline insulators (TCIs), which have an odd number of unpinned surface Dirac cones protected by crystal symmetries. The first class is protected by a single glide plane symmetry; the second class is protected by a composition of a twofold rotation and time-reversal symmetry. Both classes of TCIs are characterized by a quantized $π$ Berry phase associated with surface states and a $Z_2$ topological invariant associated with the bulk bands. In the presence of disorder, these TCI surface states are protected against lo…
Breaking Hermiticity in topological systems gives rise to intriguing phenomena, such as the exceptional topology and the non-Hermitian skin effect. In this work, we study a non-Hermitian topological crystalline insulator sitting on the Kekulé-modulated honeycomb lattice with balanced gain and loss. We find that the gaplessness of the topological edge states in the non-Hermitian system is insensitive to edge geometries under moderate strength of gain and loss, unlike the cases of Hermitian topological crystalline insulators that depend on edge geometries crucially. We focus on two types of gain…
Topological insulators (TIs) and topological crystal insulators (TCIs) exhibit exotic surface properties. We present optimised growth procedures to obtain high quality bulk crystals of the TCIs Pb_(1-x)Sn_(x)Te and Pb_(1-x)Sn_(x)Se, and nanowires from the bulk crystals using the vapour-liquid-solid (VLS) technique. Nanowires of Pb_(1-x)Sn_(x)Te have been produced with a Sn composition of approx. x = 0.25, at which a transition from trivial to non-trivial insulator is reported. The results obtained on the growth of nanomaterials of Pb_(1-x)Sn_(x)Se are also described. Detailed characterisation …
A higher-order topological insulator (HOTI) in two dimensions is an insulator without metallic edge states but with robust zero-dimensional topological boundary modes localized at its corners. Yet, these corner modes do not carry a clear signature of their topology as they lack the anomalous nature of helical or chiral boundary states. Here, we demonstrate using immunity tests that the corner modes found in the breathing kagome lattice represent a prime example of a mistaken identity. Contrary to previous theoretical and experimental claims, we show that these corner modes are inherently fragi…
Topological crystalline insulators (TCIs) possess metallic surface states protected by crystalline symmetry, which are a versatile platform for exploring topological phenomena and potential applications. However, progress in this field has been hindered by the challenge to probe optical and transport properties of the surface states owing to the presence of bulk carriers. Here we report infrared (IR) reflectance measurements of a TCI, (001) oriented $Pb_{1-x}Sn_{x}Se$ in zero and high magnetic fields. We demonstrate that the far-IR conductivity is unexpectedly dominated by the surface states a…
Inducing magnetism onto a topological crystalline insulator (TCI) has been predicted to result in several novel quantum electromagnetic effects. This is a consequence of the highly strain-sensitive band topology of such symmetry-protected systems. We thus show that placing the TCI surface of SnTe in proximity to EuS, a ferromagnetic insulator, induces magnetism at the interface between SnTe and EuS and thus breaks time-reversal-symmetry in the TCI. Magnetotransport experiments on SnTe-EuS-SnTe trilayer devices reveal a hysteretic lowering of the resistance at the TCI surface that coincides wit…
Dirac fermions in condensed matter physics hold great promise for novel fundamental physics, quantum devices and data storage applications. IV-VI semiconductors, in the inverted regime, have been recently shown to exhibit massless topological surface Dirac fermions protected by crystalline symmetry, as well as massive bulk Dirac fermions. Under a strong magnetic field (B), both surface and bulk states are quantized into Landau levels that disperse as B^1/2, and are thus difficult to distinguish. In this work, magneto-optical absorption is used to probe the Landau levels of high mobility Bi-dop…
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…
In principle the stacking of different two-dimensional (2D) materials allows the construction of 3D systems with entirely new electronic properties. Here we propose to realize topological crystalline insulators (TCI) protected by mirror symmetry in heterostructures consisting of graphene monolayers separated by two-dimensional polar spacers. The polar spacers are arranged such that they can induce an alternating doping and/or spin-orbit coupling in the adjacent graphene sheets. When spin-orbit coupling dominates, the non-trivial phase arises due to the fact that each graphene sheet enters a qu…
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…
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…
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 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…
Here, we analyse two Dirac fermion species in two spatial dimensions in the presence of general quartic contact interactions. By employing functional bosonisation techniques, we demonstrate that depending on the couplings of the fermion interactions the system can be effectively described by a rich variety of topologically massive gauge theories. Among these effective theories, we obtain an extended Chern-Simons theory with higher order derivatives as well as two coupled Chern-Simons theories. Our formalism allows for a general description of interacting fermions emerging, for example, at the …
We show that in the presence of $n$-fold rotation symmetries and time-reversal symmetry, the number of fermion flavors must be a multiple of $2n$ ($n=2,3,4,6$) on two-dimensional lattices, a stronger version of the well-known fermion doubling theorem in the presence of only time-reversal symmetry. The violation of the multiplication theorems indicates anomalies, and may only occur on the surface of new classes of topological crystalline insulators. Put on a cylinder, these states have $n$ Dirac cones on the top and on the bottom surfaces, connected by $n$ helical edge modes on the side surface…
