Topologically protected Landau level in the vortex lattice of a Weyl superconductor

TL;DR

This paper demonstrates that Weyl superconductors can support a topologically protected zeroth Landau level, leading to universal heat conductance, unlike in d-wave superconductors where vortex scattering obscures Landau levels.

Contribution

It reveals that the chirality of Weyl fermions protects the zeroth Landau level via a topological index theorem, enabling Landau level formation in the vortex lattice of Weyl superconductors.

Findings

Weyl superconductors support a topologically protected zeroth Landau level.

The heat conductance along the magnetic field is universally quantized.

Vortex lattice scattering does not obscure Landau levels in Weyl superconductors.

Abstract

The question whether the mixed phase of a gapless superconductor can support a Landau level is a celebrated problem in the context of \textit{d}-wave superconductivity, with a negative answer: The scattering of the subgap excitations (massless Dirac fermions) by the vortex lattice obscures the Landau level quantization. Here we show that the same question has a positive answer for a Weyl superconductor: The chirality of the Weyl fermions protects the zeroth Landau level by means of a topological index theorem. As a result, the heat conductance parallel to the magnetic field has the universal value $G=\tfrac{1}{2}g_0 \Phi/\Phi_0$, with $\Phi$ the magnetic flux through the system, $\Phi_0$ the superconducting flux quantum, and $g_0$ the thermal conductance quantum.