# Drastic enhancement of the thermal Hall angle in a $d$-wave superconductor

## TL;DR

This paper provides a microscopic calculation of the thermal Hall angle in $d$-wave superconductors, confirming its drastic enhancement at low temperatures and weak magnetic fields due to quasiparticle behavior near gap nodes.

## Contribution

It derives the thermal Hall coefficient microscopically using augmented quasiclassical equations, explaining the enhancement without impurity scattering.

## Key findings

- Thermal Hall angle is significantly enhanced at low temperatures.
- Quasiparticle relaxation time increases near gap nodes.
- Enhancement may occur in other nodal superconductors.

## Abstract

A drastic enhancement of the thermal Hall angle in $d$-wave superconductors was observed experimentally in a cuprate superconductor and in CeCoIn$_5$ at low temperatures and very weak magnetic field [Phys. Rev. Lett. $\bf 86$, 890 (2001); Phys. Rev. B $\bf 72$, 214515 (2005)]. However, to the best of our knowledge, its microscopic calculation has not been performed yet. To study this microscopically, we derive the thermal Hall coefficient in extreme type-II superconductors with an isolated pinned vortex based on the augmented quasiclassical equations of superconductivity with the Lorentz force. Using it, we can confirm that the quasiparticle relaxation time and the thermal Hall angle are enhanced in $d$-wave superconductors without impurities of the resonant scattering because quasiparticles around the gap nodes which become dominant near zero temperature are restricted to the momentum in a specific orientation. This enhancement of the thermal Hall angle may also be observed in other nodal superconductors with large magnetic-penetration depth.