Locking of length scales in two-band superconductors

TL;DR

This study demonstrates that in two-band s-wave superconductors, the spatial variation of the order parameters in vortex lattices occurs at a single length scale for most interband couplings, except when the bands are nearly decoupled.

Contribution

The paper provides a numerical analysis showing the locking of length scales in two-band superconductors across various parameters, except in the nearly decoupled limit.

Findings

Length scales of order parameters are the same for most interband couplings.

The single length-scale behavior persists regardless of temperature and applied field.

Nearly decoupled bands exhibit different length scales.

Abstract

A model of a clean two-band s-wave superconductor with cylindrical Fermi surfaces, different Fermi velocities v_{1,2}, and a general 2x2 coupling matrix V_{alpha beta} is used to study the order parameter distribution in vortex lattices. The Eilenberger weak coupling formalism is used to calculate numerically the spatial distributions of the pairing amplitudes Delta_1_ and Delta_2_ of the two bands for vortices parallel to the Fermi cylinders. For generic values of the interband coupling V_{12}, it is shown that, independently of the couplings V_{alpha beta}, of the ratio v_1 /v_2, of the temperature, and the applied field, the length scales of spatial variation of Delta_1 and of Delta_2 are the same within the accuracy of our calculations. The only exception from this single length-scale behavior is found for V_{12} --> 0, i.e., for nearly decoupled bands.