Vortices in a cylinder: Localization after depinning

Abstract

Edge effects in the depinned phase of flux lines in hollow superconducting cylinder with columnar defects and electric current along the cylinder are investigated. Far from the ends of the cylinder vortices are distributed almost uniformly (delocalized). Nevertheless, near the edges these free vortices come closer together and form well resolved dense bunches. A semiclassical picture of this localization after depinning is described. For a large number of vortices their density $\rho (x)$ has square root singularity at the border of the bunch ($\rho (x)$ is semicircle in the simplest case). However, by tuning the strength of current, the various singular regimes for $\rho (x)$ may be reached. Remarkably, this singular behaviour reproduces the phase transitions discussed during the past decade within the random matrix regularization of 2d-Gravity.

4 pages, REVTEX, 2 eps figures

References in corpus (8)

• Vortex Pinning and Non-Hermitian Quantum Mechanics
• Non-Hermitian Delocalization and Eigenfunctions
• Non-Hermitian Localization and Population Biology
• Distribution of Eigenvalues in Non-Hermitian Anderson Model
• Theory of directed localization in one dimension
• Quantum Disordered Systems with a Direction
• Sequence Effects on DNA Entropic Elasticity
• Localization in an imaginary vector potential

Cited by in corpus (9)

• Exceptional Topology of Non-Hermitian Systems
• Metal-insulator phase transition in a non-Hermitian Aubry-André-Harper Model
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• Localization Transition in Incommensurate non-Hermitian Systems
• Anderson localization and topological phase transitions in non-Hermitian Aubry-André-Harper models with p-wave pairing
• "Single Ring Theorem" and the Disk-Annulus Phase Transition
• Equivalence and superposition of real and imaginary quasiperiodicities
• "Lifshitz tails" and extended states in an Imaginary random potential
• Theory of Localization in a Disordered Ring in a Non-Hermitian Field