Transverse Meissner Physics of Planar Superconductors with Columnar Pins

Abstract

The statistical mechanics of thermally excited vortex lines with columnar defects can be mapped onto the physics of interacting quantum particles with quenched random disorder in one less dimension. The destruction of the Bose glass phase in Type II superconductors, when the external magnetic field is tilted sufficiently far from the column direction, is described by a poorly understood non-Hermitian quantum phase transition. We present here exact results for this transition in (1+1)-dimensions, obtained by mapping the problem in the hard core limit onto one-dimensional fermions described by a non-Hermitian tight binding model. Both site randomness and the relatively unexplored case of bond randomness are considered. Analysis near the mobility edge and near the band center in the latter case is facilitated by a real space renormalization group procedure used previously for Hermitian quantum problems with quenched randomness in one dimension.

arXiv comment23 pages, 22 figures

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• Elastic systems with correlated disorder: Response to tilt and application to surface growth
• Tilted elastic lines with columnar and point disorder, non-Hermitian quantum mechanics and spiked random matrices: pinning and localization
• Langevin Dynamics of the vortex matter two-stage melting transition in Bi_2Sr_2CaCu_2O${}_{8+\delta }$ in the presence of straight and of tilted columnar defects
• Delocalization of interacting directed polymers on a periodic substrate: Localization length and critical exponents from non-Hermitian spectra
• $\mathcal{P}\mathcal{T}$-symmetric two-photon quantum Rabi models
• Effects of kinked linear defects on planar flux line arrays