Modeling tunneling for the unconventional superconducting proximity effect

Abstract

Recently there has been reinvigorated interest in the superconducting proximity effect, driven by predictions of the emergence of Majorana fermions. To help guide this search, we have developed a phenomenological model for the tunneling spectra in anisotropic superconductor-normal metal proximity devices. We combine successful approaches used in s-wave proximity and standard d-wave tunneling to reproduce tunneling spectra in d-wave proximity devices, and clarify the origin of various features. Different variations of the pair potential are considered, resulting from the proximity-induced superconductivity. Furthermore, the effective pair potential felt by the quasiparticles is momentum-dependent in contrast to s-wave superconductors. The probabilities of reflection and transmission are calculated by solving the Bogoliubov equations. Our results are consistent with experimental observations of the unconventional proximity effect and provide important experimental parameters such as the size and length scale of the proximity induced gap, as well as the conditions needed to observe the reduced and full superconducting gaps.

Superconducting Proximity Effect in d‐Wave Cuprate/Graphene Heterostructures

“…Using topological insulators grown on a d-wave superconductor and ARPES the groups of T. Valla and Z. Hasan [143,163] concluded that the proximity effect is prohibited in these structures due to Fermi surface mismatch. Burch's group, based on exfoliated dwave/TI devices, transport experiments [164] and theory [14] showed the opposite. To our knowledge, no other topological insulator in proximity with d-wave superconductors has been studied so far, which might be due to the growth conditions making it difficult to combine both class of materials.…”

Andreev reflection without Fermi surface alignment in high-Tcvan der Waals heterostructures

“…It should be noted that in a real system, one must also account for the evolution of the wavefunctions and potential multiple reflections. Numerical calculations in s-wave [63] and in d-wave [64] proximity junctions confirmthis picture. Thus the induced and reduced gaps produce Andreev features in the dI/dV that are tell-tale signs of the proximity effect [18,19,29,[58][59][60][61][62].…”

“…The observed features are reproduced by modifying a standard approach to tunneling into d-wave superconductors [30,60,63,64]. Specifically, the differential conductance below T c [dI/dV] S , divided by the normal state conductance [dI/dV] N is given by the half-sphere integration over the solid angle Ω:…”

Localization and oscillations of Majorana fermions in a two-dimensional electron gas coupled with d -wave superconductors

“…The momentum parallel to the interface is conserved and therefore, the induced pairing for d-superconductors takes the form given in Eq. ( 11) [34,[43][44][45][46]. Note that for an s-wave parent superconductor where ∆(k) = ∆ s is constant, the above condition, |V | ∆(k), is more restrictive than for a d-wave parent superconductor, where |V | ∆(k) is automatically satisfied for k ∼ 0, unlike the s-wave case.…”