The low energy, local density of states of an isolated vortex in an extreme Type II superconductor

The local density of states of low energy electronic excitations in a vortex is investigated. Starting from the Bogoliubov Hamiltonian, the authors make the approximation of replacing the quadratic momentum dependence of the free particle kinetic energy by a linear dependence. They then work with a linearized order parameter profile of the vortex Δ(r); Δ(r)∼Δ'(0), where r is the distance from the vortex axis. The resulting theory has a simple operator structure and is exactly diagonalizable. It leads to a sequence of open-quotes oscillator-likeclose quotes excitations in the core of the vortex. The low energy behaviour is contained in the zeroth oscillator level and when the excitation energy E and vortex profile obey Δ(r)2-E2 much-lt vf Δ'(0). where vf is the Fermi velocity, it is found that the leading behaviour in the local density of states is of the form (Δ(r)2-E2-1/2 ΘΔ(r)2-E2) with Θ(x) a Heaviside step function. This open-quotes edgeclose quotes behaviour is clearly discernible in numerical calculations of the local density of states