Shrinking Magnetic Vortices inV3Sidue to Delocalized Quasiparticle Core States: Confirmation of the Microscopic Theory for Interacting Vortices

Abstract

We report muon spin rotation measurements on the conventional type-II superconductor V3Si that provide clear evidence for changes to the inner structure of a vortex due to the delocalization of bound quasiparticle core states. The experimental findings described here confirm a key prediction of recent microscopic theories describing interacting vortices. The effects of vortex-vortex interactions on the magnetic and electronic structure of the vortex state are of crucial importance to the interpretation of experiments on both conventional and exotic superconductors in an applied magnetic field.PACS numbers: 74.20.Fg, 74.25.Qt, 74.70.Ad, 76.75.+i In 1964, a breakthrough paper by Caroli, de Gennes and Matricon [1] showed that in the framework of the microscopic theory, quasiparticles (QPs) bound to an isolated vortex of a conventional s-wave type-II superconductor occupy discrete energy levels. Twenty-five years later, localized vortex core states were observed for the first time in NbSe 2 by scanning tunneling microscopy (STM) [2]. Our understanding of the vortex state in type-II superconductors has accordingly progressed from Abrikosov's initial prediction [3] based on the macroscopic Ginzburg-Landau (GL) theory [4], to current theories describing the electronic structure of magnetic vortices on a microscopic level. However, it is only in recent years that predictions have emerged from the microscopic theory on the effects of vortex-vortex interactions. In analogy with bringing atoms close together to form a conducting solid, increasing the vortex density by applying a stronger magnetic field H enhances the overlap of bound state wave functions of neighboring vortices, resulting in the formation of energy bands that allow the intervortex transfer of QPs [5,6,7,8]. This is expected to strongly influence experiments on conventional superconductors that are sensitive to quasiparticle excitations, such as specific heat and thermal transport, and to have profound effects on the magnetic structure of the vortex state. However, understanding the potential interplay between vortices and quasiparticles is also of crucial importance in the study of high-temperature superconductors. In these and other exotic superconductors, comparatively little is known about the structure of the vortex state and its effect on experiments in large magnetic fields. It is therefore essential to have a solid understanding of the behavior of interacting vortices in conventional superconductors, and to establish the connections with quasiparticle properties.The effect of delocalized QP core states on the spatial variation of the pair potential ∆(r) at a vortex site has been considered in the framework of the quasiclassical Eilenberger theory [7,8,9]. These calculations show that the effect of the intervortex transfer of QPs on ∆(r) leads to a reduction of the size of the vortex cores with increasing H. Such shrinking of the vortex cores has in fact been observed by muon spin rotation (µSR) [10,11,12,13,14,15,16] and STM [17], and proposed as...

Supercurrent on a vortex core in 2H-NbSe2: Current-driven scanning tunneling spectroscopy measurements

“…[68][69][70] The same experiments find a significant increase of the amount of quasiparticle states in between vortices with the magnetic field. 69 It is proposed that different Andreev levels are formed in vortex cores of multiband superconductors, associated to different parts of the Fermi surface with varying gap size. The magnetic-fieldinduced disappearance of the smaller-sized superconducting gaps depletes core states created by smaller gaps.…”

“…This, in turn, gives core states with only large gaps associated Andreev bound states that are confined at a smaller length scale. 69 The definition of the vortex core radius is somewhat arbitrary 70 and depends on the particular experiment. It is found that, generally, the magnetic field produces a slight reduction of the coherence length ξ in conventional superconductors.…”

Muon spin rotation measurements of the vortex state in vanadium: A comparative analysis using iterative and analytical solutions of the Ginzburg-Landau equations

“…ξ is a measure of the vortex core size. Recently, we have demonstrated from µSR and thermal conductivity measurements on BCS superconductors 7,8 that the core size is dependent on the degree of localization of the quasiparticle bound core states. Thermal depopulation of the more spatially extended high-energy core states results in a shrinking of the core size with decreasing temperature.…”

Field dependence of the vortex core size

“…(19) and integrating over s one obtains S in the form (18). Having the quantity S(H, ξ, T, ℓ) for both 3D (Fermi sphere) and 2D (Fermi cylinder), one can solve Eq.…”