Analytical solutions of topological surface states in a series of lattice models

TL;DR

This paper derives analytical solutions for surface states in a series of 3D topological insulator lattice models, providing a tractable approach to understanding their unique surface phenomena.

Contribution

It introduces a new ansatz-based method for analytically solving surface states in topological lattice models, highlighting a specific restriction that enables solvability.

Findings

Analytical solutions for surface states are obtained for various lattice models.

The method reveals how surface states depend on model parameters.

The approach can describe diverse surface phenomena in topological insulators.

Abstract

We derive the analytical solutions of surface states in a series of lattice models for three-dimensional topological insulators and their nontopological counterparts based on an ansatz. A restriction on the spin-flip matrices in nearest-neighbor hopping characterizes the series. This restriction affords the ansatz and favors analytical solvability of surface-state eigenvectors. Despite the restriction, the series retains sufficient designability to describe various types of surface states. We also describe how it can serve as a tractable tool for elucidating unique phenomena on topological surfaces.