Surface Theory of a Family of Topological Kondo Insulators

TL;DR

This paper develops a low-energy surface state theory for cubic topological Kondo insulators, especially SmB6, capturing Dirac surface states and their dependence on parameters, with implications for experimental observations.

Contribution

It introduces a detailed low-energy surface theory for topological Kondo insulators derived from an eight-band bulk model, applicable to SmB6 and similar compounds.

Findings

Helical Dirac states occur near specific points in the surface Brillouin zone.

Dirac point energies show offsets relative to each other.

Band bending can significantly alter surface Dirac states.

Abstract

A low-energy theory for the helical metallic states, residing on the surface of cubic topological Kondo insulators, is derived. Despite our analysis being primarily focused on a prototype topological Kondo insulator, Samarium hexaboride (SmB$_6$), the surface theory derived here can also capture key properties of other heavy fermion topological compounds with a similar underlying crystal structure. Starting from an effective mean-field eight-band model in the bulk, we arrive at a low-energy description of the surface states, pursuing both analytical and numerical approaches. In particular, we show that helical Dirac excitations occur near the $\bar{\Gamma}$ point and the two $\bar{X}$-points of the surface Brillouin zone and generally the energies of the Dirac points display {\it offset} relative to each other. We calculate the dependence of several observables (such as bulk insulating gap, energies of the surface Dirac fermions, their relative position to the bulk gap, etc.) on various parameters in the theory. We also investigate the effect of a spatial modulation of the chemical potential on the surface spectrum and show that this band bending generally results in "dragging down" of the Dirac points deep into the valence band and strong enhancement of Fermi velocity of surface electrons. Comparisons with recent ARPES and quantum oscillation experiments are drawn.