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

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 = 1 2 (Q 2 eff /h)(Φ/Φ0)V between two normal metal contacts at voltage difference V , with Φ the magnetic flux through the system, Φ0 the superconducting flux quantum, and Q 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.

Chiral charge transfer along magnetic field lines in a Weyl superconductor

“…As shown in the same Fig. 3, in that case the conductance at μ = 0 follows the predicted κ 2 = 1 − 2 0 /β 2 parabolic profile [13]. The agreement is better for B perpendicular to β than it is for B parallel to β.…”

“…At μ = 0 this was calculated in Ref. [13], with the result e * = Q 0 . We wish to generalize this to nonzero μ.…”

“…Following Ref. [13] we probe the Landau band by electrical conduction: A voltage V 1 is applied to contact N 1 while contact N 2 and the bulk superconductor are kept at ground potential. In this three-terminal circuit, most of the current injected into the superconductor by contact N 1 is absorbed by the superconducting condensate, a small fraction I 2 = GV 1 is carried by the Weyl fermions to the distant contact N 2 .…”

“…The chemical potential μ N in the normal-metal contacts is assumed to be large compared to the value μ in the superconductor. When the chemical potential is at the Weyl point (μ = 0) the conductance is determined by the renormalized charge and B only enters via the Landau band degeneracy [13],…”

“…The key quantity to calculate is the charge e * transferred by the quasiparticles across the normal-superconductor interface. At μ = 0 this is simply given by the renormalized charge κe of the Weyl fermions [13], but that no longer holds at nonzero μ. In Secs.…”