Interface Spin-Orbit Coupling in a Non-centrosymmetric Thin-(3)

We present a detailed study of the effects of interface spin-orbit coupling (ISOC) on the critical field behavior of non-centrosymmetric (NCS), ultra-thin superconducting Be/Au bilayers. Parallel field measurements were made in bilayers with Be thicknesses

ThetransitiontemperatureofthehomogeneouslydisorderedBe/Au lmsusedinthisstudyareplottedasafunctionofBethicknessinFig.2.Filmswithd<2nmareknowntodisplayanon-perturbativezerobiasanomalyintheirtunnelingdensityofstates,whichisassociatedwiththeemergenceoftheCoulombgap[23].AscanbeseeninFig.2,thisisalsothecriticalthicknessbelowwhichthezerotemperaturesuperconductingphaseislostandtheelectrondi usivitygoestozero.InordertomakeuseofEq.(1)itwasnecessaryto tthethicknessdependenceofTcandDwithanempiricalfunctionalform.Inparticular,thesolidlinesinthemainpanelandtheinsetofFig.2arethefunctions:

Tc(d)=Tcotanh[(d 1.35)/1.29)]

D(d)=Dotanh[d2/23.3],(6)(7)

whereTco=0.68KandDo～3 /m.Dowasdeterminedfrom lmswithd>10nmusingtherelation1/R=2e2ν0Dod,whereRisthesheetresistanceandν0isthedensityofstatesperspinofBe.TheBCScoherencelengthforaBe lmwithTc～0.7Kisξo～4µm.Fortherangeofdi usivitiesplottedintheinsetofFig.√2themeanfreepathisalwayslo<1nmandthecorrespondingPippardcoherencelengthsareintherangeξ=0.85