Effective field theories of topological crystalline insulators and topological crystals
@article{Huang2022EffectiveFT, title={Effective field theories of topological crystalline insulators and topological crystals}, author={Sheng-Jie Huang and Chang-Tse Hsieh and Jiabin Yu}, journal={Physical Review B}, year={2022} }
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…
Figures and Tables from this paper
2 Citations
Higher Berry Phase of Fermions and Index Theorem
- Physics, Mathematics
- 2022
When a quantum field theory is trivially gapped, its infrared fixed point is an invertible field theory. The partition function of the invertible field theory records the response to various background…
The K-homology of 2-dimensional Crystallographic Groups
- Mathematics
- 2021
In this paper we compute the topological K-homology of 2-dimensional crystal groups. Our method focuses on the fixed points of group action and simplifies the calculation of the K-homology of…
References
SHOWING 1-10 OF 84 REFERENCES
Topological crystalline insulators.
- PhysicsPhysical review letters
- 2011
A class of three-dimensional "topological crystalline insulators" which have metallic surface states with quadratic band degeneracy on high symmetry crystal surfaces is found.
Theory of interacting topological crystalline insulators
- Physics
- 2015
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…
Intrinsically interacting topological crystalline insulators and superconductors
- Physics
- 2018
Motivated by recent progress in crystalline symmetry protected topological (SPT) phases of interacting bosons, we study topological crystalline insulators/superconductors (TCIs) of strongly…
The classification of surface states of topological insulators and superconductors with magnetic point group symmetry
- PhysicsProgress of Theoretical and Experimental Physics
- 2022
We present the exhaustive classification of surface states of topological insulators and superconductors protected by crystallographic magnetic point group symmetry in three spatial dimensions.…
Topological states from topological crystals
- Mathematics, PhysicsScience Advances
- 2019
This work explicitly enumerates all inequivalent topological crystals for noninteracting time-reversal symmetric electronic insulators with spin-orbit coupling and any one of the 230 space groups, which gives topological crystalline insulators a full classification.
Topology of crystalline insulators and superconductors
- Physics
- 2014
We complete a classification of topological phases and their topological defects in crystalline insulators and superconductors. We consider topological phases and defects described by noninteracting…
Topological crystalline materials: General formulation, module structure, and wallpaper groups
- Physics
- 2017
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…
Topological Classification of Crystalline Insulators through Band Structure Combinatorics
- Materials Science
- 2016
We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure in all physically relevant dimensions. The algorithm…
Periodic table for topological insulators and superconductors
- Physics, Mathematics
- 2009
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a…
Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
- Physics
- 2015
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…