Anomalous gap ratio in anisotropic superconductors: Aluminum under pressure

Abstract

Pressure dependence of the thermodynamic critical field B c in elemental aluminum was studied by means of the muon-spin rotation-relaxation technique. Pressure enhances the deviation of B c (T ) from parabolic behavior, expected for a typical type-I superconductor, thus suggesting the weakening of the gap ratio α = /k B T c ( is the average value of the superconducting energy gap, T c is the transition temperature, and k B is the Boltzmann constant). With the pressure increase from 0.0 to 1.6 GPa, α decreases almost linearly from 1.73(1) to 1.67(1). Our results imply, therefore, that in elemental aluminum, the gap ratio α is smaller than the weak-coupled BCS prediction α BCS 1.764, and it is even further reduced under pressure.

Anomalously small superconducting gap in the strong spin-orbit coupled superconductor: $ β- $Tungsten

“…In a clean system, the coupling strength of superconductivity can be defined relative to α BCS , with α α BCS for a weakly coupled superconductor and α somewhat greater than α BCS for a strongly coupled superconductor. In disordered systems, pair breaking tends to decrease T c faster than it does the ∆, which increases the ratio above α BCS 13 . Thus, in general we expect α ≥ α BCS 13 , which is in contrast to observations in β−W 2 .…”

“…In disordered systems, pair breaking tends to decrease T c faster than it does the ∆, which increases the ratio above α BCS 13 . Thus, in general we expect α ≥ α BCS 13 , which is in contrast to observations in β−W 2 . However, in such considerations, there is an implicit assumption that the order parameter is uniform both in space and in momentum.…”

Isotropic single-gap superconductivity of elemental Pb

“…[B c (0) = B c (T = 0), N F (0) is the density of states at the Fermi level, and is the zero-temperature value of the superconducting energy gap], becomes a direct probe of multiple superconducting energy gaps [16][17][18][19], as well as allows one to probe the superconducting gap anisotropy [20][21][22]. As the temperature dependence of B c normalized to its zerotemperature value follows very closely a nearly quadratic * rustem.khasanov@psi.ch behavior, the deviation function D(T ) is normally considered:…”

“…The transverse-field muon-spin rotation/relaxation (TF-μSR) experiments were conducted using the Dolly spectrometer (π E1 beam line) at the Paul Scherrer Institute, Switzerland. Measurements were performed in the intermediate state of superconducting Pb, i.e., when the sample volume is separated into the normal-state and the superconductingstate (Meissner) domains [15,18,22,[26][27][28][29][30][31][32]. Two sets of experiments were performed.…”

“…The magnetic-field distribution in a type-I superconductor in the intermediate state, which is probed directly by means of TF-μSR, consists of two sharp peaks corresponding to the response of the domains remaining in the Meissner state (B = 0) and in the normal-state (B ≡ B c > B ex ). Consequently, the value of B c could be directly and very precisely determined by measuring the position of the B > B ex peak [18,22,[26][27][28][29][30][31][32][35][36][37][38][39][40]. The details of the TF-μSR experiments on elemental Pb and the data analysis procedure are discussed in the Supplemental Material [41]. )…”