Locking of length scales in two-band superconductors

A model of a clean two-band s-wave superconductor with cylindrical Fermi surfaces, different Fermi velocities v1,2, and a general 2×2 coupling matrix Vαβ 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 Δ1 and Δ2 of the two bands for vortices parallel to the Fermi cylinders. For generic values of the interband coupling V12, it is shown that, independently of the couplings Vαβ, of the ratio v1/v2, of the temperature, and the applied field, the length scales of spatial variation of Δ1 and of Δ2 are the same within the accuracy of our calculations. The only exception from this single length-scale behavior is found for V12V11, i.e., for nearly decoupled bands.