Topological crystalline Kondo insulators and universal topological surface states of SmB$_6$

TL;DR

This paper theoretically demonstrates that SmB$_6$ is a topological crystalline Kondo insulator with universal surface states protected by both time-reversal and crystal symmetries, revealing new surface Dirac points on certain crystal surfaces.

Contribution

It provides a theoretical proof that SmB$_6$ hosts topological surface states protected by crystal symmetries, with universal properties independent of microscopic details.

Findings

SmB$_6$ has a nontrivial Z$_2$ topological index and mirror Chern numbers.

On the (100) surface, no additional surface states beyond Z$_2$ prediction.

On the (110) surface, two additional Dirac points are predicted.

Abstract

We prove theoretically that certain strongly correlated Kondo insulators are topological crystalline insulators with nontrivial topology protected by crystal symmetries. In particular, we find that SmB$_6$ is such a material. In addition to a nontrivial Z$_2$ topological index protected by time reversal symmetry, SmB$_6$ also has nontrival mirror Chern numbers protected by mirror symmetries. On the $(100)$ surface of SmB$_6$, the nontrivial mirror Chern numbers do not generate additional surface states beyond those predicted by the Z$_2$ topological index. However, on the $(110)$ surface, two more surface Dirac points are predicted. Remarkably, we find that for SmB$_6$ both the Z$_2$ topological index and the mirror Chern numbers are independent of microscopic details, which enables us to obtain surface state properties that are universal.