Superconducting proximity effect and order parameter fluctuations in disordered and quasiperiodic systems

Abstract

We study the superconducting proximity effect in inhomogeneous systems in which a disordered or quasicrystalline normal-state wire is connected to a BCS superconductor. We self-consistently compute the local superconducting order parameters in the real-space Bogoliubov-de Gennes framework for three cases, namely, when states are (i) extended, (ii) localized, or (iii) critical. The results show that the spatial decay of the superconducting order parameter as one moves away from the normal-superconductor interface is power law in cases (i) and (iii), stretched exponential in case (ii). In the quasicrystalline case, we observe self-similarity in the spatial modulation of the proximity-induced superconducting order parameter. To characterize fluctuations, which are large in these systems, we study the distribution functions of the order parameter at the center of the normal region. These are Gaussian functions of the variable [case (i)] or of its logarithm [cases (ii) and (iii)]. We give arguments to explain the characteristics of the distributions and their scaling with system size for each of the three cases.

Proximity effect and spatial Kibble-Zurek mechanism in atomic Fermi gases with inhomogeneous pairing interactions

“…The scaling behavior was obtained by solving the Gor'kov equation in Refs. [12,15] and verified in SC-NM hybrid rings [18], superconducting thin films [19], niobium-gold layers [25], and normal metal on top of a superconducting slab [20]. The reason for the slower power-law decay of F (x) into the normal metal at zero temperature is because thermal excitations are absent in restricting the penetration of Cooper pairs.…”

“…The proximity effect results from a sudden change of the pairing interaction across the SC-NM interface, so it may be thought of as a phase transition in space. The proximity effect in other heterostructures have been extensively studied, including a superconductor-quasicrystal hybrid ring [17], disordered and quasi-periodic systems [18], superconducting thin films [19] and normal metal-superconducting slab [20]. Experimental [21,22] and theoretical [20,[23][24][25] studies of niobium-gold layers suggest that the proximity effect may create topological superconductivity.…”

The Fibonacci quasicrystal: case study of hidden dimensions and multifractality

“…One sees here the characteristic multifractal properties reflected in the variations of the order parameter. Fitting the average curve obtained by changing the phason angle parameter φ, one sees that the OP decays as a power law in the distance from the N-S interface (Rai et al, 2020). The power, which varies with t A /t B , is expected to depend both on the exponent of the density of states at the Fermi level and the averaged fractal dimensions of the wavefunctions near E = 0.…”

Effects of disorder in the Fibonacci quasicrystal

“…Nowadays, new insights are still being provided. These range from the topological character of the system to superconductivity [15][16][17][18][19][20][21].…”