“Soft” modes of the excitation spectrum constructed on perturbations of the Abrikosov lattice with a single flux quantum in the unit cell

Abstract

We have analyzed the spectrum of gapless excitations emerging upon the perturbation of the Abrikosov lattice with a single flux quantum in the unit cell. Superconductors with Ginzburg–Landau parameter κ close to unity are of special interest. We have determined the spectrum of gapless excitations close to zeroth shear modes for an arbitrary angle ϕ between the unit cell vectors. Analysis of the excitation spectra of triangular and square lattices with a single flux quantum in the unit cell has shown that solutions with a number of flux quanta greater than one exist at least in the range of parameters κ close to unity (κ > 1) and give smaller values of the free energy as compared to its values for a triangular lattice with a single flux quantum. For small values of momentum k (in the k² approximation), the excitation spectrum of the “transverse” mode in the triangular lattice is independent of the direction of the momentum lying in the plane perpendicular to the magnetic field. For the square lattice (ϕ = π/2), the transverse mode is anisotropic in the k² approximation also.