Spontaneous breaking of time-reversal symmetry in topological insulators

TL;DR

This paper investigates a novel mechanism for topological insulators where spontaneous breaking of time-reversal symmetry occurs due to phase-dependent hopping in a hexagonal lattice, leading to nontrivial topological states.

Contribution

It introduces a new realization of topological insulators through spontaneous symmetry breaking driven by phase solutions in a spinless fermion model on a hexagonal lattice.

Findings

Identified stable phase solutions leading to topological insulator states.

Calculated the band structure and Chern numbers for the system.

Mapped the ground-state phase diagram in parameter space.

Abstract

The system of spinless fermions on a hexagonal lattice is studied . We have considered tight-binding model with the hopping integrals between the nearest-neighbor and next-nearest-neighbor lattice sites, that depend on the direction of the link. The links are divided on three types depending on the direction, the hopping integrals are defined by different phases along the links. The energy of the system depends on the phase differences, the solutions for the phases, that correspond to the minimums of the energy, lead to a topological insulator state with the nontrivial Chern numbers. We have analyzed distinct topological states and phase transitions, the behavior of the chiral gapless edge modes, have defined the Chern numbers. The band structure of topological insulator (TI) is calculated, the ground-state phase diagram in the parameter space is obtained. We propose a novel mechanism of realization of TI, when the TI state is result of spontaneous breaking of time-reversal symmetry due to nontrivial stable solutions for the phases that determine the hopping integrals along the links and show that the Haldane model can be implemented in real compounds of the condensed matter physics.