Quasiparticle spectrum of a type-II superconductor in a high magnetic field with randomly pinned vortices

Abstract

We show that gapless superconductivity of a strongly type-II superconductor in a high magnetic field prevails in the presence of disorder, suggesting a topological nature. We calculate the density of states of the Bogoliubov-de Gennes quasi-particles for a two-dimensional inhomogeneous system in both cases of weak and strong disorder. In the limit of very weak disorder, the effect is very small and the density of states is not appreciably changed. As the disorder increases, the density of states at low energies increases and the ratio of the low energy density of states to its maximum increases significantly.The interplay between superconductivity and a magnetic field has attracted interest for a long time. For sufficiently strong fields the Meissner phase is destroyed and a mixed state appears in the form of a quantized vortex lattice 1 . The superconductor order parameter has zeros at the vortex locations, through which the external magnetic field penetrates in the sample. Contrarily to previous understanding, the increase of the magnetic field intensity, and its associated diamagnetic pair breaking, is counteracted at high magnetic fields by the Landau level structure of the electrons 2 . This leads to interesting properties such as enhancement of the superconducting transition temperature at very high magnetic fields where the electrons are confined to the lowest Landau level 2 . Associated with the zeros of the order parameter in real space are gapless points in the magnetic Brillouin zone 3 , which lead to qualitatively different behavior at low temperatures and high magnetic fields 4 .It has been argued that the gapless behavior is restricted to high fields very close to the upper critical line where the so-called diagonal approximation (where the coupling between Landau levels is neglected) is valid. It has been shown, however, that the presence of offdiagonal terms does not destroy this behavior 4 and that a perturbation scheme on the off-diagonal terms is possible, as long as there are no band-crossings 5 . It was shown analytically to all orders in the perturbation theory on the off-diagonal terms that there is always a discrete set of points which are gapless that are associated with coherent propagation of the quasiparticles (so-called Eilenberger points). These nodes are associated with the center of mass coordinates of the Cooper pairs and not to some internal structure like in d-wave superconductors. Lowering the magnetic field, a quantum levelcrossing transition has been found that eventually leads to a gapped regime and to states localized in the vortex cores 6,7 .On the other hand, the effect of disorder on superconductivity has also attracted interest for a long time. In the case of non-magnetic impurities and s-wave pairing Anderson's theorem states that, at least for low concentrations, they have little effect since the impurities are not pair-breaking 8 . In d-wave superconductors however, non-magnetic impurities cause a strong pair breaking effect 9 . In the limit of strong scattering it ...

Interplay of disorder and magnetic field in the superconducting vortex state

“…In the gapped s-wave case, however, the disorder introduces states in the gap thereby changing qualitatively the low-energy density of states, as in the high-field limit. 10 We found a power-law behavior with an exponent that scales with the magnetic length. rϭ(3,14), (4,15), (5,16), (6,17), (7,18), (8,19) around a vortex position r v ϭ(5.5,16.5) belonging to a disordered vortex lattice.…”

“…In the same regime of high magnetic fields, but with randomly pinned vortices and no impurities, the density of states at low energies increases significantly with respect to the lattice case suggesting a finite value at zero energy. 10 References 11 and 12 considered the effects of random and statistically independent scalar and vector potentials on d-wave quasiparticles and it was predicted 12 that at low energies (⑀)ϳ 0 ϩa⑀ 2 , where 0 ϳB 1/2 . The effect of randomly pinned discrete vortices on the spectrum of a d-wave superconductor was considered recently and a preliminary report was presented in Ref.…”

Vortex spectroscopy in the vortex glass: A real-space numerical approach

“…In this section, we build on the results of the previous section to study how the spectra in the 0 • and 45 • vortex-lattice orientations progressively become identical as disorder is increased. Unlike previous studies, 17,20 we consider positional disorder with respect to a perfect lattice rather than completely random vortex positions, and we focus on the vortex-core spectrum rather than the average DOS. Starting from the ideal lattices, we introduce a disorder δR = dρ(cos τ, sin τ) in the vortex positions, where d is the initial distance between vortices, ρ is a random number with Gaussian distribution of variance η, and τ is a uniform random number between 0 and 2π.…”

Low-temperature specific heat of an extreme type-II superconductor at high magnetic fields

“…10 Furthermore, it was shown that the high-field gapless character of the excitation spectrum is not destroyed by a moderate level of nonmagnetic impurities present in either dirty homogeneous superconductor 11 or dirty inhomogeneous superconducting systems. 12 The strongest evidence for Landau level quantization within the superconducting state comes from the experimental observation of de Haas-van Alphen ͑dHvA͒ oscillations in various A-15 and borocarbide superconductors. 3 The persistence of the dHvA signal deep within the mixed state of these three-dimensional extreme type-II systems can be attributed to the presence of a small portion of the Fermi surface containing gapless quasiparticle excitations, surrounded by regions where the gap is large.…”

“…However, a marked difference appears at lower fields H ≪ 0.5H c2 , where an swave superconductor is clearly in the regime of localized, bound vortex core states while a d-wave system still exhibits the extended nature of low-lying quasiparticle excitations as predicted by Franz and Tešanović 10 . Furthermore, it was shown that the high-field gapless character of the excitation spectrum is not destroyed by a moderate level of nonmagnetic impurities present in either dirty homogeneous superconductor 11 or dirty inhomogeneous superconducting systems 12 .…”