Signature of odd-frequency pairing correlations induced by a magnetic interface

Abstract

We investigate the mutual proximity effect in a normal metal contacted to a superconductor through a magnetic interface. Analytical and self-consistent numerical results are presented, and we consider both the diffusive and ballistic regimes. We focus on the density of states in both the normal and superconducting region, and find that the presence of spin-dependent phase-shifts occurring at the interface qualitatively modifies the density of states. In particular, we find that the proximity-induced pairing amplitudes in the normal metal region undergo a conversion at the Fermi level from pure even-frequency to odd-frequency. Above a critical value of the interface spin-polarization (or, equivalently, for fixed interface spin-polarization, above a critical interface resistance), only odd frequency correlations remain. This is accompanied by the replacement of the familiar proximity minigap or pseudogap in the normal layer by an enhancement of the density of states above its normal state value for energies near the chemical potential. The robustness of this effect towards inelastic scattering, impurity scattering, and the depletion of the superconducting order parameter close to the interface is investigated. We also study the inverse proximity effect in the diffusive limit. We find that the above-mentioned conversion persists also for thin superconducting layers comparable in size to the superconducting coherence length ξS, as long as the inverse proximity effect is relatively weak. Concomitantly, we find a shift in the critical interface resistance where the pairing conversion occurs. Our findings suggest a robust and simple method for producing purely odd-frequency superconducting correlations, that can be tested experimentally.

Symmetry protected topological superfluid3He-B

“…Nevertheless, OSO and OTE pair amplitudes can emerge ubiquitously in spatially non-uniform systems accompanied by Andreev bound states and anomalous proximity effect. In particular, anomalous charge and spin transport, electromagnetic responses, proximity effects via Andreev bound states have also been clarified in the light of odd-frequency Cooper pairing [306,307,308,309,310,311,312,313,314,315,316,317,318,319].…”

“…We regard the contribution of the dipole interaction as a small perturbation, which reduces the gap equation (317) to…”

Pair symmetry conversion in driven multiband superconductors

“…While some research has been dedicated to the thermodynamic stability of intrinsically odd-ω phases [3][4][5][6] , a great deal of previous research has been devoted to the identification of heterostructures in which odd-ω pairing could be induced including: ferromagnetic -superconductor heterostructures [7][8][9][10][11][12][13] , topological insulator -superconductor systems [14][15][16][17] , normal metal -superconductor junctions due to broken translation symmetry [18][19][20][21][22] , two-dimensional bilayers coupled to conventional s-wave superconductors 23 , and in generic two-dimensional electron gases coupled to superconductor thin films 24 . In addition to theoretical studies, there are experimental indications of the realization of odd-ω pairing at the interface of Nb thin films and epitaxial Ho 25 .…”

Theory of superconducting and magnetic proximity effect in S/F structures with inhomogeneous magnetization textures and spin-active interfaces

“…In this case, the low-energy LDOS is completely suppressed in the regime G φ /G T < 1, and suddenly reappears for G φ /G T > 1. It is very interesting to note that the same effect was recently discovered for an S|N junction with a magnetically active interface 60 , but in that case the effect was completely independent of the junction thickness. In order to investigate this effect further, we focus on the zero-energy LDOS in the thin junction case in Fig.…”