Theory of the supercyclotron resonance and Hall response in anomalous two-dimensional metals

Abstract

Weakly disordered superconducting films can be driven into an anomalous low temperature resistive state upon applying a magnetic field. Recent experiments on weakly disordered amorphous InOx have established that both the Hall resistivity and the frequency of a cyclotron-like resonance in the anomalous metal are highly suppressed relative to the values expected for a conventional metal. We show that both of these observations can be understood from the flux flow dynamics of vortices in a superconductor with significant vortex pinning. Results for flux flow transport are obtained using a systematic hydrodynamic expansion, controlled by the diluteness of mobile vortices at low temperatures. Hydrodynamic transport coefficients are related to microscopics through Kubo formulae for the longitudinal and Hall vortex conductivities, as well as a 'vorto-electric' conductivity.Introduction.-In conventional metals, the Hall resistivity and the cyclotron frequency are key observables that can often be used as proxies for the density and mass of charge carriers, respectively. Recent measurements have probed these quantities in the anomalous metallic state of weakly disordered amorphous InO x films. The low temperature superconducting state in this material becomes metallic upon applying a magnetic field greater than H c ≈ 2T. In the metallic phase at a field of 5T the measured Hall resistivity is three orders of magnitude smaller than in the more conventional high temperature state [1], and falls below experimental sensitivity at a lower field H M2 > H c . Furthermore, the maximum of the frequency-dependent conductivity is at zero frequency to within experimental resolution [2]; for a conventional Drude peak this fact would require a cyclotron frequency at least four orders of magnitude smaller than expected based on normal state properties [3].

Magnetic field reveals vanishing Hall response in the normal state of stripe-ordered cuprates

“…Previous studies have identified 3 , 4 the H < H peak regime as the vortex liquid. The Hall resistivity due to mobile vortex cores is expected 32 , 33 to obey the relation , which is indeed observed in this regime in our samples (Supplementary Fig. 6 ), thus confirming its identification as the vortex liquid.…”

Theory of Diffusive Fluctuations

“…They do however enter in the transverse part of current correlators, see e.g. the appendix of [42]. The same statement also applies to interactions, suggesting that the Hall sector does not get renormalized at one loop to leading order in derivatives.…”

Theory of collective magnetophonon resonance and melting of a field-induced Wigner solid

“…However, in the cores of dislocations the symmetry is restored and the phase is not well-defined. In this case, the arguments developed in [36,44,45] show thatφ…”

“…This expression is closely related to the final term in (3.7), but the factor of 2 is a little subtle and is due to the fact that the integral is over all mobile dislocation cores, that have time-dependent locations [45]. The first terms in (3.7) do not contribute since the phase decays rapidly in the normal state.…”