Krakovna et al. (2020)

[2002.02969] Higher-order topological insulators in antiperovskites 
 
 
 
 
 
 
 
 
 
 
 

 
 
 

 
 
 
 
 
 
 Higher-order topological insulators in antiperovskites

 
 
 Yuan Fang
 
 Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11974, USA
 
    
 Jennifer Cano
 
 Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11974, USA
 
 Center for Computational Quantum Physics, The Flatiron Institute, New York, New York 10010, USA
 
 

 
 Abstract

 We predict that a family of antiperovskite materials realize a higher order topological insulator phase, characterized by a previously introduced ℤ 4 subscript ℤ 4 \mathbb{Z}_{4} index. A tight binding model and a k ⋅ p ⋅ 𝑘 𝑝 k\cdot p model are used to capture the physics of the bulk, surface and hinge states of these materials. A phase diagram of the higher order and weak topological invariants is obtained for the tight binding model. The mirror Chern number is also discussed. In order to reveal the gapless hinge states in the presence of mirror Chern surface states, several ways of opening the surface gap are proposed and confirmed by calculation, including cleaving the crystal to reveal a low-symmetry surface, building a heterostructure, and applying strain. Upon opening the surface gap, we are able to study the hinge states by computing the momentum space band structure and real space distribution of mid-gap states.

 
 
 
 I Introduction

 
 The recent classification [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ] of topological insulators with crystal symmetry has led to the discovery of a new type of topological phase, the higher order topological insulator (HOTI) [ 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ] .
HOTIs in three dimensions (3D) are gapped in the bulk and on all surfaces, but have one dimensional gapless modes along “hinges” where two surfaces meet.
Here, we are concerned with HOTIs in 3D protected by time reversal and inversion symmetry: for these HOTIs, the one dimensional gapless hinge mode is a helical mode. Hence, when combined with superconductivity, HOTIs present a new route to engineering Majorana fermions from topological insulator heterostructures [ 23 , 24 , 25 , 26 , 27 , 28 , 29 ] .

 
 
 Realizing such a heterostructure requires a 3D HOTI material.
So far, Bismuth, which has a continuous direct band gap, is topologically equivalent to a HOTI [ 14 ] and strained SnTe has also been predicted [ 13 ] .
In addition, several weak TIs are predicted to be nontrivial HOTIs when their surfaces are gapped by breaking translation symmetry [ 13 , 30 ] .

 
 
 In this manuscript, we propose a family of HOTIs in the antiperovskites as a promising material class.
The antiperovskites are familiar to the topological community as mirror Chern insulators [ 31 ] .
Many antiperovskites exhibit a “double band inversion,” caused by the inversion of two J = 3 / 2 𝐽 3 2 J=3/2 quartets [ 32 , 33 , 34 ] , which results 

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