Self-consistent surface superconductivity in time-reversal symmetric Weyl semimetals

Abstract

Weyl semimetals host topologically protected surface states, the so-called Fermi arcs, that have a penetration depth into the bulk that depends on surface-momentum, and diverges at the Weyl points. It has recently been observed in PtBi${}_2$ that such Fermi arc states can become superconducting, with a critical temperature larger than that of the bulk. Here we introduce a general variational method that captures the interplay between surface and bulk superconductivity, for any bulk Hamiltonian that harbors (topological) surface states with varying penetration depth. From the self-consistent solutions we establish that the surface state localization length of Weyl semimetals leads to characteristic features in the surface superconductivity, with a gap depending on surface momentum and a penetration length for the order parameter that is temperature-dependent due to competition with the bulk superconductivity.

10 pages, 7 figures

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• Surface states in topological semimetal slab geometries
• Fermi arcs dominating the electronic surface properties of trigonal PtBi${}_2$
• The role of the chemical potential in the BCS theory
• Enhanced weak superconductivity in trigonal $\gamma$-PtBi${}_2$
• Berry curvature associated to Fermi arcs in continuum and lattice Weyl systems

Cited by in corpus (6)

• Phonon-mediated intrinsic topological superconductivity in Fermi arcs
• Ginzburg-Landau theory for unconventional surface superconductivity in PtBi${}_2$
• Interplay between inversion and translation symmetries in trigonal PtBi${}_2$
• Higher-order topological superconductivity in type-II time-reversal-symmetric Weyl semimetals with a hybrid pairing
• Fermi surface and topology of multiband superconductor BeAu
• Mechanism for Nodal Topological Superconductivity on PtBi${}_2$ Surface