Finite Size Effects of the Surface States in a Lattice Model of Topological Insulator

TL;DR

This paper investigates how the energy gap and wave functions in thin films of topological insulators depend on thickness, revealing damping and oscillation behaviors linked to surface states and electronic properties.

Contribution

It provides a detailed analysis of finite size effects on surface states in topological insulators using a tight-binding model, highlighting the origin of damping and oscillations.

Findings

Energy gap exhibits damping and oscillation with thickness.

Damped behavior is due to gapless surface Dirac cone.

Oscillatory behavior arises from electronic properties in thin films.

Abstract

Energy gap and wave function in thin films of topological insulator is studied, based on tight--binding model. It is revealed that thickness dependence of the magnitude of energy gap is composed of damping and oscillation. The damped behavior originates from the presence of gapless surface Dirac cone in the infinite thickness limit. On the other hand, the oscillatory behavior stems from electronic properties in the thin thickness limit.