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

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.