Chern insulator with large Chern numbers. Chiral Majorana fermion liquid

TL;DR

This paper explores the realization of Chern insulators with large Chern numbers using Hofstadter's approach, revealing a new state called the chiral Majorana fermion liquid characterized by a sharp increase in edge states.

Contribution

It provides a detailed analysis of topological states with large Chern numbers and introduces the concept of a chiral Majorana fermion liquid in this context.

Findings

Large Chern number states occur near half filling in weak magnetic fields.

Hall conductance exhibits abnormal behavior inversely proportional to magnetic field.

Sharp increase in chiral Majorana fermion edge states at half-filling.

Abstract

In the framework of Hofstadter`s approach we provide a detailed analysis of a realization of exotic topological states such as the Chern insulator with large Chern numbers. In a transverse homogeneous magnetic field a one-particle spectrum of fermions transforms to an intricate spectrum with a fine topological structure of the subbands. In a weak magnetic field $H$ for a rational magnetic flux, a topological phase with a large Chern number is realized near the half filling. There is an abnormal behavior of the Hall conductance ${\sigma_{xy}\simeq \frac{e}{2 H}}$. At half-filling, the number of chiral Majorana fermion edge states increases sharply forming a new state, called the chiral Majorana fermion liquid.