# Thermal Hall conductivity in the spin-triplet superconductor with broken time-reversal symmetry

## TL;DR

This paper investigates the thermal Hall conductivity in spin-triplet superconductors with broken time-reversal symmetry, analyzing different pairing symmetries to identify signatures that distinguish chiral p-wave from f-wave states.

## Contribution

It provides a theoretical analysis of thermal Hall conductivity behaviors for various pairing symmetries in Sr2RuO4, highlighting signatures to differentiate between chiral p-wave and f-wave states.

## Key findings

- Chiral p-wave phase shows linear and exponential temperature dependence of thermal Hall conductivity.
- f-wave states exhibit quadratic temperature dependence due to linear quasiparticle dispersions.
- Results suggest thermal Hall measurements can distinguish pairing symmetries in Sr2RuO4.

## Abstract

Motivated by the spin-triplet superconductor Sr2RuO4, the thermal Hall conductivity is investigated for several pairing symmetries with broken time-reversal symmetry. In the chiral p-wave phase with a fully opened quasiparticle excitation gap, the temperature dependence of the thermal Hall conductivity has a temperature linear term associated with the topological property directly, and an exponential term, which shows a drastic change around the Lifshitz transition. Examining f-wave states as alternative candidates with $\bm d=\Delta_0\hat{z}(k_x^2-k_y^2)(k_x\pm ik_y)$ and $\bm d=\Delta_0\hat{z}k_xk_y(k_x\pm ik_y)$ with gapless quasiparticle excitations, we study the temperature dependence of the thermal Hall conductivity, where for the former state the thermal Hall conductivity has a quadratic dependence on temperature, originating from the linear dispersions, in addition to linear and exponential behavior. The obtained result may enable us to distinguish between the chiral p-wave and f-wave states in Sr2RuO4.