Fluctuational Anomalous Hall and Nernst Effects in Superconductors

Abstract

In this work we develop microscopic kinetic theory of the anomalous Hall and Nernst effects in superconductors induced by fluctuations in the vicinity of the critical transition temperature. The technical analysis is carried out within the Matsubara diagrammatic technique and linear response Kubo formula with disorder averaging and an analytical continuation. It is shown that asymmetric skew-scattering due to spin-orbit interaction gives rise to a new anomalous Hall conductance promoted by Maki-Thompson interference and density of states fluctuational effects. The side-jump mechanism of the anomalous Hall effect is present only in the density of states contributions. The anomalous Nernst effect is found due to a special nonlinear Aslamazov-Larkin term from the quantum-crossing of interacting fluctuations in a Hikami box with the skew-scattering process. In addition to calculations in the weak-coupling BCS model we also sketch an approach for the account of fluctuational transport effects in the strong-coupling limit. In particular we explore an example of how Keldysh version of the Eliashberg theory can in principle be constructed and estimate fluctuation-induced conductivity within conventional electron-phonon coupling scenario. These ideas may pave the way for further developments of strong coupling theories in applications to fluctuations in unconventional superconductors and anomalous transport responses in particular.

Preprint submitted to Annals of Physics special issue "Eliashberg theory at 60" [23 pages, 6 figures, 1 table]

References in corpus (27)

• Anomalous Hall effect
• Electron pockets in the Fermi surface of hole-doped high-Tc superconductors
• Vortex motion and the Hall effect in type II superconductors: a time dependent Ginzburg-Landau theory approach
• Observation of broken time-reversal symmetry in the heavy fermion superconductor UPt${}_3$
• Gaussian superconducting fluctuations, thermal transport, and the Nernst effect
• Nernst effect in metals and superconductors: a review of concepts and experiments
• Evidence for broken time-reversal symmetry in the superconducting phase of URu${}_2$Si${}_2$
• Intrinsic Hall effect in a multiband chiral superconductor in the absence of an external magnetic field
• Giant Nernst Effect due to Fluctuating Cooper Pairs in Superconductors
• Frequency and temperature dependence of the anomalous Hall conductivity in a chiral px+ipy superconductor with impurities
• Nernst effect and diamagnetism in phase fluctuating superconductors
• Impurity Induced Polar Kerr Effect in A Chiral p-wave Superconductor
• Fluctuations of the superconducting order parameter as an origin of the Nernst effect
• Superconductivity in disordered thin films: giant mesoscopic fluctuations
• Evidence of Chiral Order in the Charge-Ordered Phase of Superconducting La1.875Ba0.125Cuo4 Single Crystals Using Polar Kerr-Effect Measurements
• The Kerr rotation in the unconventional superconductor Sr${}_2$RuO${}_4$
• Superconducting fluctuations and the Nernst effect: A diagrammatic approach
• Anomalous Hall effect in ferromagnetic disordered metals
• The Hall Effect in Superconducting Films
• Keldysh Ginzburg-Landau action of fluctuating superconductors
• Anomalous flux-flow dynamics in layered type-II superconductors at low temperatures
• Time Reversal Symmetry Breaking in the B Phase of the Heavy Fermion Superconductor PrOs${}_4$Sb${}_{12}$
• Theory of Tunneling Anomaly in Superconductor above Paramagnetic Limit
• Giant Nernst and Hall Effects in Chiral Superconductors due to Berry Phase Fluctuations
• Anomalous mesoscopic fluctuations of transport coefficients above the critical temperature
• Josephson current noise above Tc in superconducting tunnel junctions
• Anomalous mesoscopic kinetics in disordered superconductors

Cited by in corpus (6)

• The functional-integral approach to Gaussian fluctuations in Eliashberg theory
• Anomalous thermodynamic properties of quantum critical superconductors
• Coherent photogalvanic effect in fluctuating superconductors
• Renormalization of the valley Hall conductivity due to interparticle interaction
• Fluctuation contribution to Spin Hall Effect in Superconductors
• Phenomenological model for the third-harmonic magnetic response of superconductors: application to Sr${}_2$RuO${}_4$