Topologically Protected Landau Level in the Vortex Lattice of a Weyl Superconductor

Abstract

The question whether the mixed phase of a gapless superconductor can support a Landau level is a celebrated problem in the context of 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=1/2g_{0}Φ/Φ_{0}, with Φ as the magnetic flux through the system, Φ_{0} as the superconducting flux quantum, and g_{0} as the thermal conductance quantum.

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

“…The spatial density profile f χ (x, y) is peaked at the vortex cores, with a power law decay |f χ | 2 ∝ δr −1+|Qχ|/e at a distance δr from the core [7]. The renormalization of the quasiparticle charge does not affect the degeneracy of the zeroth Landau level: each of the four chiral modes in Fig.…”

“…In the next section II we summarize the effective lowenergy theory of the superconducting vortex lattice [7], on which we base our scattering theory in Sec. III, followed by a calculation of electrical and thermo-electric transport properties in Sec.…”

Universal chiral magnetic effect in the vortex lattice of a Weyl superconductor

“…We have calculated the eigenvalues and eigenfunctions of the tight-binding Hamiltonian (2.1) using the Kwant code [28] as described in Ref. 13. We take parameters β = t 0 , ∆ 0 = 0.5 t 0 , µ = 0.…”

“…The numerical calculation was performed on a square lattice with two h/2e vortices in a magnetic unit cell, using the discretization described in Ref. 13. We calculate separately the total induced current response…”

“…The second topic, the search for Landau levels in an Abrikosov vortex lattice, goes back to the discovery of massless Dirac fermions in d -wave superconductors [19,20]. In that context scattering by the vortex lattice obscures the Landau level quantization [21][22][23], however, as discovered recently [13], the chirality of Weyl fermions protects the zeroth Landau level by means of a topological index theorem. The same index theorem enforces the (e/h)Φ degeneracy of the Landau level, even though the charge of the quasiparticles is renormalized to e * < e. Does this topological protection extend to the equilibrium chiral magnetic effect, so that we can realize Eq.…”