Super-weakly coupled superconductivity in ultrathin superconductor–normal-metal bilayers

Abstract

Tunneling measurements of the temperature dependence of the electronic density of states (DOS) of ultrathin bilayers of Pb and Ag reveal that their superconducting energy gap, ∆(T ), evolves similarly to BCS predictions despite the presence of a large anomalous DOS at the Fermi energy that persists as T → 0. The gap ratio,k B Tc , systematically decreases more than 20% below the BCS universal value of 3.52 in bilayers with the lowest superconducting transition temperatures, T c ; a behavior we deem super weakly coupled. A semi-quantitative model suggests that the reduced gap ratios result from a systematic depletion of the DOS available for pairing that occurs with the growth of the anomalous DOS at the Fermi energy.

Effect of inhomogeneous coupling on BCS superconductors

“…48,49 A straightforward realization of inhomogeneous coupling is in disordered superconductor-normalmetal ͑SN͒ bilayer thin films. In a homogeneous bilayer SN with thickness smaller than the coherence length , meanfield analysis yields that T c and the energy gap E g of the system are determined by the averaged coupling constant [50][51][52] …”

“…41,48,49 Interestingly, these studies found a broadening of the BCS peak and also a subgap density of states. 6,23,25,26,28,48 Of particular interest to us is the work in Ref.…”

“…6,23,25,26,28,48 Of particular interest to us is the work in Ref. 49, which studied a thin SN bilayer system, and found a surprisingly low value of the ratio of the energy gap to T c , in contradiction to standard BCS theory, and the theory of proximity [50][51][52] where it is claimed that the energy gap-T c ratio should be bounded from below by ϳ3. 52.…”

“…, which is relevant to the experiments of Long et al 48,49 Note that while Anderson theorem states that the critical temperature and gap of a homogeneous superconductor do not depend on disorder, 1 in an inhomogeneous system, the theorem does not hold. Indeed, we find that the results of Ref.…”

Field-dependent nonlinear surface resistance and its optimization by surface nanostructuring in superconductors

“…Numerous STM experiments have shown that the DOS broadening can be significant, particularly in thin films and bilayers [37][38][39] . The subgap states have been attributed to inelastic scattering of quasiparticles on phonons 9,40 , Coulomb correlations 41 , anisotropy of the Fermi surface 42 , inhomogeneities of the BCS pairing constant 43 , magnetic impurities 31 , spatial correlations in impurity scattering 31,44 , or diffusive surface scattering.…”