Non-Hermitian Luttinger liquids and flux line pinning in planar superconductors

Abstract

As a model of thermally excited flux liquids connected by a weak link, we study the effectof a single line defect on vortex filaments oriented parallel to the surface of a thin planarsuperconductor. This problem can be mapped onto the physics of a Luttinger liquid ofinteracting bosons in one spatial dimension with a point impurity. When the appliedmagnetic field is tilted relative to the line defect, the corresponding quantum bosonHamiltonian is non-Hermitian. We analyse this problem using a combination of analyticand numerical (density matrix renormalization group) methods, uncovering a delicateinterplay between enhancement of pinning due to Luttinger liquid effects and depinningdue to the tilted magnetic field. Interactions allow a single columnar defect to be veryeffective in suppressing vortex tilt when the Luttinger liquid parameter .