Abstract
Bogolyubov quasiparticles move in a practically uniform magnetic field in the vortex state of high-temperature cuprate superconductors. When set in motion by an externally applied heat current, the quasiparticles' trajectories may bend, causing a temperature gradient perpendicular to the heat current and the applied magnetic field, resulting in the thermal Hall effect. Here we relate this effect to the Berry curvature of quasiparticle magnetic sub-bands, and calculate the dependence of the intrinsic thermal Hall conductivity on superconductor's temperature, magnetic field and the amplitude of the d-wave pairing. The intrinsic contribution to thermal Hall conductivity displays a rapid onset with increasing temperature, which compares favourably with existing experiments at high magnetic field on the highest purity samples. Because such temperature onset is related to the pairing amplitude, our finding may help to settle a much-debated question of the bulk value of the pairing strength in cuprate superconductors in magnetic field.
Highlights
Bogolyubov quasiparticles move in a practically uniform magnetic field in the vortex state of high-temperature cuprate superconductors
If the resulting net flow velocity of QPs is deflected preferentially to one side, their energy is deposited at the corresponding edge of the sample, causing a transverse gradient of superconductor’s temperature T, that is, a non-zero off-diagonal component of the Fourier law jEm 1⁄4 À kmnrnT or, equivalently, the thermal Hall effect
Volovikp’s ffiffisffiffiemiclassical approximation successfully captures the overall H increase of the QP density of states, a full quantum mechanical solution is needed to calculate the QPs’ contribution to the thermal Hall conductivity, kxy, because, as discussed below, this quantity is related to the non-trivial topological structure of the QP wavefunctions
Summary
Bogolyubov quasiparticles move in a practically uniform magnetic field in the vortex state of high-temperature cuprate superconductors. Based on the same linearized continuum model, it was argued[5] that the QP Dirac spectrum in the vortex state acquires a mini-gap, which grows linearly with H, and that limT!0 kxy=T 1⁄4 npk2B=ð6‘ Þ with n 1⁄4 0 or ±2.
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