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.
Highlights
Nonlinear response functions are extremely sensitive to the structural symmetry of crystalline systems
In this work we show that the nonlinear Hall effect can be used as a powerful tool to probe the electron-interactiondriven inversion-symmetry breaking in a metallic phase that emerges from a generic nodal band structure
We find that the dynamical nonlinear Hall conductivity (NLHC) is suppressed in the ordered phase close to this line of quantum-critical points (QCPs) as compared to the noninteracting massive tilted Dirac fermions (TDFs) and can be used to probe such a symmetry breaking in a TDF metal
Summary
Nonlinear response functions are extremely sensitive to the structural symmetry of crystalline systems. In this work we show that the nonlinear Hall effect can be used as a powerful tool to probe the electron-interactiondriven inversion-symmetry breaking in a metallic phase that emerges from a generic nodal band structure In this case, the chemical potential is outside the gap region (see Fig. 1) and the usual linear conductivity is finite in both symmetric and symmetry-broken phases. We find that the dynamical nonlinear Hall conductivity (NLHC) is suppressed in the ordered (symmetry-broken) phase close to this line of QCPs as compared to the noninteracting massive TDFs and can be used to probe such a symmetry breaking in a TDF metal This effect can be traced back to the scattering of the strongly interacting soup of incoherent fermionic and bosonic excitations close to this line of QCPs. This effect can be traced back to the scattering of the strongly interacting soup of incoherent fermionic and bosonic excitations close to this line of QCPs This suppression increases with the tilt parameter, consistent with the expectation based on the scaling of the density of states (DOS). We note that the strong tilt dependence of the linear optical properties of TDFs was previously discussed [34,35]
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