Topological phase transitions driven by next-nearest-neighbor hopping in two-dimensional lattices

TL;DR

This paper investigates how real next-nearest-neighbor hopping influences topological phase transitions in various two-dimensional lattice models, revealing new transition mechanisms and potential experimental realizations.

Contribution

It demonstrates that real next-nearest-neighbor hopping induces topological phase transitions in several Dirac systems, expanding understanding of topological phases beyond complex spin-orbit coupling effects.

Findings

Topological phase transitions occur in Lieb, kagome, and T3 lattices due to real next-nearest-neighbor hopping.

In honeycomb lattices, such transitions require an external magnetic field.

Transitions can be realized experimentally in optical lattices with tunable hopping parameters.

Abstract

For two-dimensional lattices in a tight-binding description, the intrinsic spin-orbit coupling, acting as a complex next-nearest-neighbor hopping, opens gaps that exhibit the quantum spin Hall effect. In this paper, we study the effect of a real next-nearest-neighbor hopping term on the band structure of several Dirac systems. In our model, the spin is conserved, which allows us to analyze the spin Chern numbers. We show that in the Lieb, kagome, and T_3 lattices, variation of the amplitude of the real next-nearest-neighbor hopping term drives interesting topological phase transitions. These transitions may be experimentally realized in optical lattices under shaking, when the ratio between the nearest- and next-nearest-neighbor hopping parameters can be tuned to any possible value. Finally, we show that in the honeycomb lattice, next-nearest-neighbor hopping only drives topological phase transitions in the presence of a magnetic field, leading to the conjecture that these transitions can only occur in multigap systems.