Interacting surface states of three-dimensional topological insulators

TL;DR

This paper numerically explores the surface states of a three-dimensional topological insulator under strong electron interactions, revealing various phases and boundary modes using a spherical geometry model.

Contribution

It introduces a finite size spherical model to analyze topological insulator surface states with strong interactions, identifying new phases and boundary modes.

Findings

Superconducting phases for attractive interactions

Quantum Hall phases for repulsive interactions

Presence of chiral fermion and Majorana boundary modes

Abstract

We numerically investigate the surface states of a strong topological insulator in the presence of strong electron-electron interactions. We choose a spherical topological insulator geometry to make the surface amenable to a finite size analysis. The single-particle problem maps to that of Landau orbitals on the sphere with a magnetic monopole at the center that has unit strength and opposite sign for electrons with opposite spin. Assuming density-density contact interactions, we find superconducting and anomalous (quantum) Hall phases for attractive and repulsive interactions, respectively, as well as chiral fermion and chiral Majorana fermion boundary modes between different phases. Our setup is preeminently adapted to the search for topologically ordered surface terminations that could be microscopically stabilized by tailored surface interaction profiles.