Non-Hermitian Luttinger liquids and vortex physics

We study the effect of a single line defect on vortex filaments oriented parallel to the surface of a thin planar high-Tc superconductor. When the applied field is tilted relative to the line defect, the physics is described by a non-Hermitian Luttinger liquid of interacting quantum bosons in one spatial dimension with a point defect. With a combination of analytic and numerical methods we uncover a delicate interplay between enhancement of pinning due to Luttinger-liquid effects and depinning due to the tilted magnetic field. Interactions dramatically affect the transverse magnetization when the Luttinger-liquid parameter g ⩽ 1.