Tunable phase transitions from semimetals to Chern insulators in two-dimensional quadratic-band-crossing materials

TL;DR

This paper explores how static and dynamic perturbations can induce topological phase transitions in two-dimensional quadratic-band-crossing materials, transforming semimetals into Chern insulators with tunable properties.

Contribution

It provides a systematic analysis of how symmetry-breaking and Floquet light effects can control topological phases in QBCP materials, revealing tunable phase transitions.

Findings

Static perturbations open energy gaps and induce nontrivial Chern numbers.

Circularly or elliptically polarized light creates Chern insulators with quantized Hall conductivity.

Linear polarization results in a topologically trivial insulator.

Abstract

We systematically investigate how static symmetry-breaking perturbations and dynamic Floquet terms via a polarized light manipulate the topological phase transitions in the two-dimensional quadratic-band-crossing-point (QBCP) materials. The Berry curvature shows distinct behavior in such two situations. It is linearly and quadratically proportional to the product of microstructural parameters $t_{x,z}$ for the former and the latter, respectively. The static perturbation eliminates the QBCP and opens an energy gap, which leads to the momentum-inversion symmetry of Berry curvature. This yields a nontrivial Chern number determined by the microstructural parameters. In contrast, we demonstrate that either a circularly or an elliptically polarized light breaks the time-reversal symmetry, transforming the QBCP semimetal into a Chern insulator with a quantized anomalous Hall conductivity $\sigma_{xy} = Ce^2/\hbar$, where the Chern number is governed by the polarization angle. Moreover, the linear polarization preserves the central antisymmetry of the Berry curvature, giving rise to a topological trivial insulator. These results establish a tunable topological phase transition from a QBCP semimetal to Chern insulator in the two-dimensional QBCP materials.