Electromagnetic Response of Three-Dimensional Topological Crystalline Insulators

Abstract

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 bµ. bµ can be inferred from the locations of the surface Dirac nodes in energy-momentum space and couples to the surface Dirac nodes like a valley gauge field. From both the effective action and analytical band structure calculations, we show that the vortex core of b or a domain wall of a component of b can trap surface charges.Topological phases of matter have been at the forefront of condensed matter physics for the past decade. One reason for the excitement is that topological phases can exhibit electromagnetic responses that display their topological nature. The integer quantum Hall (IQH) effect was the first such system, and its quantized Hall conductance is characterized by a topological integer [1] multiplying the conductance quantum e 2 /h. In recent years, the ten-fold, periodic table classification of electronic topological insulators and superconductors with time-reversal (TR) T , particle-hole (PH) C, and/or chiral symmetry S was completed in Refs. [2][3][4], and ushered in the concept of a symmetry protected topological (SPT) phase. The electromagnetic (EM) response theories of many of the topological insulator (TI) phases were developed in Ref. [3], and extended what was known about the IQH to all fermionic SPTs. For example, the 3D T -invariant topological insulator has an odd number of Dirac cones on each surface, and harbors a half quantum Hall effect when T is broken on the surface. An odd number of Dirac cones, and the corresponding Hall effect, can never occur in a purely 2D system with the same symmetries without interactions. Indeed, the surface quantum Hall effect is actually a signature of a bulk EM response: the topological magneto-electric effect [3,5] with a response coefficient determined by a Z 2 topological invariant [3].After the periodic table was complete, and after many exciting materials predictions and discoveries [6][7][8][9][10][11][12][13], the classification of topological crystalline phases (TCIs) with point/space-group symmetries, such as reflection and discrete rotation, was initiated and continues to be an active area of research [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]. One highlight of this line of research was the prediction and experimental confirmation of a 3D TCI phase in PbSnTe [31][32][33][34]. The topological properties of this system are protected by mirror symmetry, and it exhibits an insulating bulk with an even number of symmetry-protected Dirac-cone surface states on mirror-symmetric surfaces. The goal of this article is to predict a characteristic electromagnetic response...

Topological Order and Symmetry Anomaly on the Surface of Topological Crystalline Insulators

“…Recently, a new type of TCI, protected jointly by glide reflection and time reversal symmetry, was found in KHgSb [7][8][9]. The richness of crystallography provides a vast opportunity for theoretical and experimental discovery of new classes of TCIs [10][11][12][13][14][15][16][17][18][19][20][21]. Systematic studies of TCIs are expected to provide an organizing principle for electronic structures of solids.…”

Spin-resolved topology and partial axion angles in three-dimensional insulators

“…We have introduced a predictive framework for linking novel low-energy response theories to gauge-invariant quantities obtained from real-material calculations. Despite our progress unraveling the bulk and surface theories of - and -symmetric helical HOTIs, and despite other promising early efforts 88 , 89 , there remain numerous other noninteracting TCI phases—such as SU(2)-doubled magnetic AXIs 24 , 46 and fourfold-rotation-anomaly TCIs like SnTe 19 , 21 —for which the bulk response theories are largely unknown. Additionally, while we focused on resolving band topology through the spin degree of freedom, the methods introduced in this work can straightforwardly be extended to sublattice (pseudospin), orbital, and layer degrees of freedom to predict new valleytronic and layertronic effects, such as valley- and spin-resolved generalizations of the layer Hall response recently observed in the antiferromagnetic AXI MnBi 2 Te 4 90 .…”

Q-switched all-fiber laser with short pulse duration based on tungsten diselenide

“…It can achieve the Q-switched laser output, but it has the disadvantages of high cost, complex manufacturing processes and limited bandwidth [27][28][29]. Therefore, much attention has been paid to two-dimensional (2D) materials such as graphene, topological insulators (TIs), transition metal sulfides (TMDs) and black phosphorus (BPs) [30][31][32][33][34][35][36][37][38][39][40][41][42][43]. These 2D materials have good saturable absorption characteristics, and the SA based on 2D materials can be used to get a stable Q-switched pulse output.…”