# Effect of charge renormalization on electric and thermo-electric transport along the vortex lattice of a Weyl superconductor

## TL;DR

This paper explores how charge renormalization affects electric and thermo-electric transport in a Weyl superconductor's vortex lattice, revealing a flux-dependent current and a nonzero thermo-electric effect due to energy-dependent charge renormalization.

## Contribution

It demonstrates the impact of charge renormalization on transport properties and introduces a flux-dependent current formula in Weyl superconductors.

## Key findings

- Vortex lattice supports a flux-dependent electric current.
- Charge renormalization leads to a nonzero thermo-electric coefficient.
- Transport properties are influenced by energy-dependent charge renormalization.

## Abstract

Building on the discovery that a Weyl superconductor in a magnetic field supports chiral Landau level motion along the vortex lines, we investigate its transport properties out of equilibrium. We show that the vortex lattice carries an electric current $I=\tfrac{1}{2}(Q_{\rm eff}^2/h)(\Phi/\Phi_0) V$ between two normal metal contacts at voltage difference $V$, with $\Phi$ the magnetic flux through the system, $\Phi_0$ the superconducting flux quantum, and $Q_{\rm eff}<e$ the renormalized charge of the Weyl fermions in the superconducting Landau level. Because the charge renormalization is energy dependent, a nonzero thermo-electric coefficient appears even in the absence of energy-dependent scattering processes.