Probing quantum criticality using nonlinear Hall effect in a metallic Dirac system

TL;DR

This paper proposes using the nonlinear Hall effect as a direct method to detect quantum criticality and symmetry breaking in metallic Dirac systems, revealing unique spectral and phase transition features.

Contribution

It introduces the nonlinear Hall effect as a novel probe for interaction-driven quantum phase transitions in tilted Dirac materials, highlighting the transformation of spectral features and critical behavior.

Findings

Transformation of inter-band resonance peak into non-Lorentzian form

Identification of a tilt-dependent line of critical points

Suppression of nonlinear Hall conductivity near criticality

Abstract

Interaction driven symmetry breaking in a metallic (doped) Dirac system can manifest in the spontaneous gap generation at the nodal point buried below the Fermi level. Across this transition linear conductivity remains finite making its direct observation difficult in linear transport. We propose the nonlinear Hall effect as a direct probe of this transition when inversion symmetry is broken. Specifically, for a two-dimensional Dirac material with a tilted low-energy dispersion, we first predict a transformation of the characteristic inter-band resonance peak into a non-Lorentzian form in the collisionless regime. Furthermore, we show that inversion-symmetry breaking quantum phase transition is controlled by an exotic tilt-dependent line of critical points. As this line is approached from the ordered side, the nonlinear Hall conductivity is suppressed owing to the scattering between the strongly coupled incoherent fermionic and bosonic excitations. Our results should motivate further studies of nonlinear responses in strongly interacting Dirac materials.