Dimensional crossover in a mesoscopic superconducting loop of finite width

Abstract

Superconducting structures with the size of the order of the superconducting coherence length ξ(T ) have a critical temperature T c , oscillating as a function of the applied perpendicular magnetic field H (or flux Φ). For a thin-wire superconducting loop, the oscillations in T c are perfectly periodic with H (this is the well-known Little-Parks effect), while for a singly connected superconducting disk the oscillations are pseudoperiodic, i.e. the magnetic period decreases as H grows. In the present paper, we study the intermediate case: a loop made of thick wires. By increasing the size of the opening in the middle, the disk-like behaviour of T c (H) with a quasi-linear background (characteristic for '3-dimensional' (3D) behaviour) is shown to evolve into a parabolic T c (H) background ('2D'), superimposed with perfectly periodic oscillations. The calculations are performed using the linearized Ginzburg-Landau theory, with the proper normal/vacuum boundary conditions at both the internal and the external interface. Above a certain crossover magnetic flux Φ, T c (Φ) of the loops becomes quasi-linear, and the flux period matches with the case of the filled disk. This dimensional transition is similar to the 2D-3D transition for thin films in a parallel magnetic field, where vortices enter the material as soon as the film thickness t > 1.8 ξ(T ). For the loops studied here, the crossover point appears for w ≈ 1.8 ξ(T ) as well, with w the width of the wires forming the loop. In the 3D regime, a "giant vortex state" establishes, where superconductivity is concentrated near the sample's outer interface. The vortex is then localized inside the loop's opening. 74.60.Ec, 74.25.Dw, 74.20.De, Typeset using REVT E X

Flux transitions in a superconducting ring

“…In the case of rings, this crossover applies to the background line of this boundary, which has the Little-Parks oscillations superimposed on it. 34,35 This is actually a dimensional crossover: at low fields the sample behaves as a thin slab and b = 5(3µ) 1/2 ; at high fields it behaves as half a plane and b = 0.847µ. Again, the crossover occurs at µ ∼ 100.…”

“…In this regime |ψ| ≪ 1, so that the Ginzburg-Landau equations are linearized and the case of the ring can be solved exactly. 32,33,34 The purpose of the present section is to point out that there exists a critical point in the N-S boundary. As will be seen in the following sections, it appears that this critical point plays a major role in the "superheating" stability of the superconducting states.…”

Multivortex and giant vortex states near the expulsion and penetration fields in thin mesoscopic superconducting squares

“…Circular mesoscopic disks have been the most popular in this respect, both theoretically [1][2][3][4][5][6] and experimentally. [7][8][9][10][11][12][13] Two types of vortex states were found in such mesoscopic superconducting disks: ͑i͒ giant vortex states ͑GVSs͒, where the order parameter has a single zero and ͑ii͒ multivortex states ͑MVSs͒ consisting of several singly quantized vortices ͑mostly situated on shells͒. Experimentally, one measured the resistivity 7,8 and the magnetization 9,10 of the superconducting disk for the different vortex states.…”

“…[7][8][9][10][11][12][13] Two types of vortex states were found in such mesoscopic superconducting disks: ͑i͒ giant vortex states ͑GVSs͒, where the order parameter has a single zero and ͑ii͒ multivortex states ͑MVSs͒ consisting of several singly quantized vortices ͑mostly situated on shells͒. Experimentally, one measured the resistivity 7,8 and the magnetization 9,10 of the superconducting disk for the different vortex states. Since these quantities do not provide direct information on the vortex configuration, there was no direct proof for the existence of the different types of vortex states in mesoscopic superconductors.…”

Magnetic coupling between mesoscopic superconducting rings

“…[1][2][3]) and rings (see for example Refs. [4][5][6][7]). The properties of single mesoscopic rings of finite thickness are studied in detail in our previous papers [5].…”