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

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.

16 Pages, 8 Figures, published in PRR

References in corpus (8)

• Absence of a Spin Liquid Phase in the Hubbard Model on the Honeycomb Lattice
• The Berry curvature dipole in Weyl semimetal materials: an ab initio study
• Band signatures for strong nonlinear Hall effect in bilayer WTe${}_2$
• Fermionic quantum criticality in honeycomb and $\pi$-flux Hubbard models: Finite-size scaling of renormalization-group-invariant observables from quantum Monte Carlo
• Emergent space-time supersymmetry in 3D Weyl and 2D Dirac semimetals
• Quantum superconducting criticality in graphene and topological insulators
• The $8Pmmn$ borophene sheet: A solid-state platform for space-time engineering
• Optical conductivity of an interacting Weyl liquid in the collisionless regime