Universal scaling in Bardeen-Cooper-Schrieffer superconductivity in two dimensions in non-s waves

Abstract

The solutions of a renormalized BCS model are studied in two space dimensions in s, p and d waves for finite-range separable potentials. The gap parameter, the critical temperature T c , the coherence length ξ and the jump in specific heat at T c as a function of zero-temperature condensation energy exhibit universal scalings. In the weak-coupling limit, the present model yields a small ξ and large T c appropriate to those for high-T c cuprates. The specific heat, penetration depth and thermal conductivity as a function of temperature show universal scaling in p and d waves.

Phase transition from a dx2−y2 to dx2−y2+idxy superconductor

“…The detailed nature of anisotropy was thought to be typical to that of an extended s-wave, a pure d-wave, or a mixed (s + exp(iθ)d)-wave type. Some high-T c materials have singlet d-wave Cooper pairs and the order parameter has d x 2 −y 2 symmetry in two dimensions [2,3], which has been supported by recent studies of temperature dependence of some superconducting observables [4][5][6][7][8][9][10][11][12][13]. In some cases there is the signature of an extended sor d-wave symmetry.…”

Mixing of dx2−y2 and dxy superconducting states for different filling and temperature

“…This procedure had the advantage of reproducing the experimentally observed isotope effect. It can also be handled by using the technique of renormalization [12][13][14]. Here we introduce a cut off in the momentum sums of the gap equation.…”

“…From both experimental observations [2][3][4][5][6] and related theoretical analyses [7][8][9][10][11][12][13][14] there is a consensus that immediately below T c , the symmetry of the order parameter is of the d x 2 −y 2 type. However, many experiments [15][16][17][18][19][20][21][22][23][24] and theoretical analyses [25,26,[28][29][30][31][32][33][34][35][36][37][38][39][40] suggest that at lower temperatures the order parameter has a mixed symmetry of the d x 2 −y 2 + exp(iθ)χ type, where χ represents a minor-component state with a distinct symmetry superposed on the major component d x 2 −y 2 .…”

The solvable three-dimensional rank-two separable potential model: partial-wave scattering

“…Ghirardi and Rimini [19] have examined general properties of separable potentials. Moreover, such potentials have been studied as models for a variety of physical problems [20][21][22][23][24][25][26][27][28][29][30].…”