Topological surface states on Bi(111) based on empirical tight-binding calculations

TL;DR

This study uses empirical tight-binding calculations to analyze the topological surface states of Bi(111), revealing a topological phase transition driven by lattice distortion and the importance of slab thickness in observing bulk topological order.

Contribution

The paper introduces new tight-binding parameters for Bi(111) and systematically investigates surface states, phase transitions, and the effects of slab thickness on topological properties.

Findings

Surface states agree with experimental ARPES results.

A topological phase transition occurs with in-plane expansion.

Thick slabs (>150 layers) are needed to reflect bulk topological order.

Abstract

The topological order of single-crystal Bi and its surface states on the (111) surface are studied in detail based on empirical tight-binding (TB) calculations. New TB parameters are presented that are used to calculate the surface states of semi-infinite single-crystal Bi(111), which agree with the experimental angle-resolved photoelectron spectroscopy results. The influence of the crystal lattice distortion is surveyed and a topological phase transition is found that is driven by in-plane expansion. In contrast with the semi-infinite system, the surface-state dispersions on finite-thickness slabs are non-trivial irrespective of the bulk topological order. The role of the interaction between the top and bottom surfaces in the slab is systematically studied, and it is revealed that a very thick slab is required to properly obtain the bulk topological order of Bi from the (111) surface state: above 150 biatomic layers in this case.