Quantized Born Effective charges as probes for the topological phase transition in the Haldane and Kane-Mele models

TL;DR

This paper introduces a novel method using quantized Born effective charges to detect topological phase transitions in the Haldane and Kane-Mele models, linking vibrational spectra to topological properties.

Contribution

It demonstrates that Born effective charges nearly quantize and exhibit discontinuous jumps at topological transitions, providing a new probe for topological phases.

Findings

Born effective charges are nearly quantized in topological models.

Discontinuous jumps in Born effective charges occur at phase transitions.

Chiral splitting of phonon frequencies also shows quantized jumps at the transition.

Abstract

We propose a new approach to study the transition between different topological states, based on the assessment of the vibrational resonances in infrared spectra. We consider the Haldane and Kane-Mele models finding that Born effective charges are nearly quantized, with a discontinuous jump concomitant with the topological phase transition. In particular, Born effective charges display a finite value in the trivial phase and a null one in the nontrivial one. This is rooted in the connection between Born effective charges and electronic Berry curvature at the band edges. Finally, at the topological phase transition of the Haldane model, we also observe a nearly quantized jump of the chiral splitting of the zone-center phonon frequencies, induced by time-reversal symmetry breaking.