Topological phase transitions in strained Lieb-Kagome lattices

TL;DR

This paper explores how shear and uniaxial strains can induce topological phase transitions in Lieb and Kagome lattices by affecting their electronic properties and topological invariants, revealing strain as a control parameter.

Contribution

It introduces a comprehensive analysis of strain effects on topological phases in Lieb-Kagome lattices using a parameterized tight-binding model and confirms phase transitions through Berry curvature and Chern number evolution.

Findings

Strain can induce topological phase transitions in Lieb-Kagome lattices.

Structural lattice angle and ISO coupling influence topological states.

Strain effects are linked to changes in hopping and ISO parameters.

Abstract

Lieb and Kagome lattices exhibit two-dimensional topological insulator behavior with $\mathbb{Z}_2$ topological classification when considering spin-orbit coupling. In this study, we used a general tight-binding Hamiltonian with a morphological control parameter $\theta$ to describe the Lieb ($\theta=\pi/2$), Kagome ($\theta=2\pi/3$), and transition lattices ($\pi/2<\theta<2\pi/3$) while considering intrinsic spin-orbit (ISO) coupling. We systematically investigated the effects of shear and uniaxial strains, applied along different crystallographic directions, on the electronic spectrum of these structures. Our findings reveal that these deformations can induce topological phase transitions by modifying the structural lattice angle associated with the interconversibility process between Lieb and Kagome, the amplitude of the strain, and the magnitude of the ISO coupling. These transitions are confirmed by the evolution of Berry curvature and by changes in the Chern number when the gap closes. Additionally, by analyzing hypothetical strain scenarios in which the hopping and ISO coupling parameters remain intentionally unchanged, our results demonstrated that the strain-induced phase transitions arise from changes in the hopping and ISO coupling parameters.