Electronic structure of multiquantum giant vortex states in mesoscopic superconducting disks

Abstract

We report self-consistent calculations of the microscopic electronic structure of the so-called giant vortex states. These multiquantum vortex states, detected by recent magnetization measurements on submicron disks, are qualitatively different from the Abrikosov vortices in the bulk. We find that, in addition to multiple branches of bound states in the core region, the local tunneling density of states exhibits Tomasch oscillations caused by the single-particle interference arising from quantum confinement. These features should be directly observable by scanning tunneling spectroscopy.S uperconducting vortices are topological singularities in the order parameter (1). In a bulk system, each vortex carries a single flux quantum, whereas vortices with multiple flux quanta are not favorable energetically (2). In small superconductors, however, the situation may be different. Today's nanotechnology can provide valuable insight into the nature of mesoscopic superconductors, whose linear dimensions can be comparable to the coherence length or the inter-vortex distance of the Abrikosov lattice. The following question then arises naturally: does single-quantum vortex matter survive the limit of decreasing sample size? More than 30 years ago, Fink and Presson (3) gave the intriguing answer ''not always'' in their pioneering work on a related system: a thin cylinder in parallel field. They have shown it theoretically, within the framework of the phenomenological Ginzburg-Landau (GL) theory, and also provided experimental evidence (4) for the existence of an enormous superfluid eddy current on the surface of a thin cylinder. They called this state a giant vortex state.Although the work of Fink and Presson was largely forgotten for the next several decades, it nevertheless anticipated the present excitement in the field of nanoscale superconductivity. With recent advances in the controlled fabrication and study of nanometer-scale superconductors, the concept of giant vortex was brought back to focus by Moshchalkov and coworkers a few years ago (5). Their experiments on mesoscopic squares and square rings have indeed revealed that small superconductors do not always favor many-vortex states reminiscent of the Abrikosov vortex lattice. The measured H-T phase boundaries of these small structures were explained in terms of giant vortex states in the GL picture (5). Subsequent experiments on submicron disks (6) have further shown the existence of giant vortex states inside the phase boundaries. Within the GL framework (6-10) some of the abrupt changes in the magnetization observed have been attributed, e.g., to the collapse of a multivortex state into a giant vortex, or to transitions among different giant vortex states.This phase of vortex matter has a single vortex occupying the sample, carrying multiple f luxoid (3, 11, 12) quanta. Such a state has no immediate analogue in bulk systems, and would only be similar to vortex states predicted for artificially patterned structures (13,14). Moshchalkov et al. (15) have also sugge...

Tomasch effect in nanoscale superconductors

“…An energy gap created around the Fermi level, E F , in homogeneous superconductivity and low-lying bound states existing in the core of vortex states [5][6][7][8][9][10][11] were successfully predicted and coincide with experimental results from tunneling conductance and scanning tunneling microscopy (STM) [12][13][14][15] . Nanoscale superconductors have also received considerable attention in the last decades due to developments in nanotechnology and their unique properties such as shell effect, 16 quantum-size effect [17][18][19][20][21] and quantum-size cascades under magnetic field 22 .…”

“…29,30 As a result, Tomasch oscillations appear as periodic oscillations in the density of states (DOS) in superconducting junctions, at energies larger than the superconducting gap. 10,27,28,31 These oscillations could be further enhanced when considering layered structures formed by intercalating successive metallic and superconducting regions. In this case the order parameter is by design non-homogeneous.…”

Creating nanostructured superconductors on demand by local current annealing

“…Early work focused on the effect of condensate confinement in mesoscopic disks [2][3][4], and the effect of symmetry [5] in comparing disks, squares [6], and mesoscopic triangles [7]. Focus on vortex states in mesoscopic superconductors, both theoretical and experimental, revealed multi-vortex Abrikosov-like states with spatial arrangements of singly quantized vortices, or giant vortex states depending on details of the condensate confinement [8][9][10][11][12][13][14][15][16].…”

Vortex structures and zero-energy states in the BCS-to-BEC evolution ofp-wave resonant Fermi gases

“…The analysis on the quantum depletion has been theoretically extended to the BCS-BEC crossover regime [18][19][20][21][22][23] and the depletions in the particle density were experimentally observed in rotating Fermi gases with an s-wave resonance [24,25]. Furthermore, the structures of giant vortices with |κ| > 1 have been extensively studied in s-wave superfluids by a large number of authors [26][27][28][29][30][31][32].…”