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Chiral superconductors spontaneously break time-reversal and mirror-reflection symmetries through the polarized orbital angular momentum of Cooper pairs. In three dimensions, chiral superconducting order can realize a Weyl superconducting phase, while in two dimensions it can realize a time-reversal-symmetry-broken topological superconducting phase[1]. These broken symmetries allow zero-field transverse responses, offering powerful probes of chiral superconducting order. In this presentation, we discuss two recent theoretical studies on anomalous thermal and magneto-optical responses in chiral superconductors.

In the first part, we focus on the anomalous (zero-field) thermal Hall effect in Weyl superconductors. The thermal Hall response has two contributions: an intrinsic contribution arising from the Berry curvature of Weyl quasiparticles and an extrinsic contribution induced by impurity scattering [2]. Using quasiclassical Eilenberger theory combined with the self-consistent T-matrix approximation, we clarify how impurity scattering and impurity-band formation control the extrinsic anomalous thermal Hall conductivity[3]. We show that when impurity bands form near the Fermi level, the extrinsic contribution can be strongly enhanced and may dominate over the intrinsic topological contribution even at low temperatures.

In the second part, we discuss the polar Kerr effect in two-dimensional multiband chiral superconductors. In two dimensions, chiral superconductors are fully gapped and provide a platform for time-reversal-symmetry-broken topological superconductivity. We show that clapping modes—the collective oscillations of the relative phase and amplitude between the two chiral components of the superconducting order parameter—remain stable inside the quasiparticle excitation gap in multiband systems [4]. These collective modes dominate the magneto-optical response in the microwave regime. When the light frequency matches the clapping-mode energy, the Kerr rotation angle exhibits resonant enhancement accompanied by sign reversals. Therefore, the microwave Kerr effect can serve not only as a probe of time-reversal-symmetry breaking, but also as a spectroscopic probe of collective excitations characteristic of chiral superconductivity.

Together, these results show that transverse thermal and optical responses provide complementary routes to identifying chiral superconductivity: the anomalous thermal Hall effect probes the interplay of topology, quasiparticles, and disorder in three-dimensional Weyl superconductors, while microwave Kerr resonances can simultaneously detect broken time-reversal symmetry and resolve clapping modes in two-dimensional chiral topological superconductors.

[1] M. Sato and S. Fujimoto, J. Phys. Soc. Jpn. 85, 072001 (2016).
[2] H. Sumiyoshi and S. Fujimoto, J. Phys. Soc. Jpn. 82, 023602 (2013).
[3] T. Matsushita, N. Kimura, T. Mizushima, I. Vekhter, and S. Fujimoto, Phys. Rev. B 110, 214511 (2024).
[4] T. Matsushita, J. Ieda, Y. Araki, T. Morimoto, I. Vekhter, and Y. Yanase, arXiv:2601.10151 (2026).

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