Visualised predictions of gap anisotropy to test new electron pairing scheme

Abstract

The rich and fertile but not yet adequately exploited ground of superconductor anisotropy is proposed as a test bed for a new empirical scheme of electron pairing. The scheme is directed to resolving a numerical and conceptual difficulty in the BCS theory. The original theoretical formulation of the anisotropy problem by Bennett is adopted and its outcomes extensively explored. Here the Bennett conclusion that in metallic superconductors phonon anisotropy is the principal source of gap anisotropy is accepted. Values of the energy gap are visualised globally in k-space with unprecedented detail and accuracy. Comparison is made between the anisotropy pattern from the new and the usual BCS pairing schemes. Differences are revealed for future experimental resolution.

Avoiding umklapp dilemma in BCS superconductor theory

“…For some time we have been investigating why it has been so difficult to find consistent values of ρ(T) and α 2 F(ν) [5][6][7][8][9][10][11][12][13][14] and confirmed that the strength of the interactions has been overestimated in the superconducting state [7]. Starting from experimental values of ρ(T), we found from inversion the effective Coulomb potential, or pseudopotential, that determines the values of the matrix element in the normal state.…”

“…In short, we have calibrated values of the matrix element, g ℓ (ν) in equation (13), for the electron-phonon interactions. We understand that, when a metal is in the normal state, these interactions manifest themselves as electrical resistivity.…”

“…Following BCS [1] we assume superconductivity arises from the electron-phonon interactions which, in the normal state, lead to electrical resistivity. We substitute the values of equation (13), evaluated for electrical resistivity in the normal state, into equation (15) without change.…”

“…) and = r 1.0 nm max ( a 3.48 ) for the initial values of V n . With the help of the method of pattern search and move [34] we adjust V n to find through equations (10)-( 13) optimum values of r ( ) T , with an average deviation ∼0.31% from the Webb values [41] relative to niobium resistivity at 295 K. We substitute the matrix element in equation (13), found for ρ(T) in the normal state, into equation (15) to evaluate α 2 F(ν). We then adjust the values of S n in equation ( 16), again with the help of the pattern search and move method, to minimize differences between the numerical and experimental values of tunneling conductance [44], and find the optimum numerical α 2 F(ν) (histogram in figure 9) and S(q) (curve in figure 10).…”

“…We adjust the values of V n , with the help of the method of pattern search and move [34], to optimize ρ(T) from equations (10)- (13). On average the optimum values of ρ(T) deviate ∼0.35% from the data in [46] compared with tantalum resistivity at 295 K. Values of the matrix element in equation (13), found for ρ(T) in the normal state, are substituted into equation (15) and kept unchanged when we optimize the values of S n in equation ( 16) using the method of pattern search and move, with tunneling conductance data from [48] that lead to the silhouette in figure 11 for the experimental α 2 F(ν) (evaluated in house). Consequently we find the numerical α 2 F(ν) (histogram in figure 11) and S(q) (curve in figure 12).…”