Landau levels and optical conductivity in the mixed state of a generic Weyl superconductor

TL;DR

This paper explores the Landau level structure and optical conductivity in the mixed state of Weyl superconductors, revealing how tilt affects quantization and optical transitions, and proposing signatures to distinguish cone types.

Contribution

It introduces a heterostructure model to analyze Landau levels and optical responses in tilted Weyl superconductor cones, highlighting differences between type-I and type-II cones.

Findings

Tilted type-I cones show squeezed Landau levels with reduced spacing.

Type-II cones exhibit angle-dependent Landau level quantization.

Optical conductivity peaks follow a $ oot{n}+ oot{n+1}$ pattern in the untilted case.

Abstract

The low-energy quasiparticle states in the mixed state of most superconductors remain Bloch waves due to the presence of supercurrent around vortex cores. In contrast, the Weyl superconductor (WSC) may display Dirac-Landau levels in the presence of a vortex lattice. Here, we investigate the Landau level (LL) structure and optical conductivity in the mixed state of a generic WSC using a heterostructure model, where the tilt of the Bogoliubov-Weyl (BW) cones can be tuned, yielding either type-I (undertilted) or type-II (overtilted) cones. We find that, in a magnetic field, the tilted type-I BW cone in the mixed state may exhibit squeezed LLs with reduced spacings. On the other hand, the spectrum of type-II cones shows a dependence on the angle between the magnetic field and the tilt direction; LL quantization is only possible if the angle is below a critical value. For zero tilt, the optical conductivity in the mixed state of the WSC shows peaks only at photon frequencies $\omega_n \propto \sqrt{n}+\sqrt{n+1}$, with a linear background. However, the tilt of BW cones results in the emergence of optical transitions beyond the usual dipolar ones. For type-II BW cones, unique intraband transition conductivity peaks emerge at low frequency, which can serve as an indicator to distinguish between type-I and type-II BW cones in WSCs.