Spontaneous breaking of time-reversal symmetry in topological insulators

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.

10 pages, 3 figures

References in corpus (7)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• On the $Z_2$ classification of Quantum Spin Hall Models
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Cited by in corpus (9)

• Spontaneous breaking of time-reversal symmetry in topological superconductors
• Mott transition in two-band fermion model with on-site Coulomb repulsion
• Topological states in the Hofstadter model on a honeycomb lattice
• Electron liquid state in the symmetric Anderson lattice
• Chern insulator with large Chern numbers. Chiral Majorana fermion liquid
• Edge modes in the Hofstadter model of interacting electrons
• The quantum Hall effect at a weak magnetic field
• Persistent current in 2D topological superconductors
• Electron pairing in the Hubbard model as a result of on-site repulsion fluctuations