Thermal depinning and transverse-field tilting transitions in a planar vortex array pinned by a columnar defect

TL;DR

This paper investigates how a vortex line array pinned by a columnar defect responds to thermal fluctuations and transverse magnetic fields, revealing phase transitions including roughening and soliton proliferation, with implications for vortex matter in superconductors.

Contribution

It introduces a reduced one-dimensional model capturing the effects of a columnar defect on vortex arrays, identifying phase transitions driven by temperature and transverse fields.

Findings

Identifies a roughening transition at finite temperature.

Describes a soliton proliferation transition in the low-temperature phase.

Predicts a phase diagram for transverse-field and temperature effects.

Abstract

We study a thermal and a transverse magnetic field response of a vortex line array confined to a plane with a single columnar pinning defect. By integrating out ``bulk'' degrees of freedom away from the columnar defect we reduce this two-dimensional problem to a one-dimensional one, localized on the defect and exhibiting a long-range elasticity along the defect. We show that as a function of temperature, for a magnetic field aligned with the defect this system exhibits a one-dimensional analog of a roughening transition, with a low-temperature ``smooth'' phase corresponding to a vortex array pinned by the defect, and a high-temperature ``rough'' phase in which at long scales thermal fluctuations effectively average away the pinning by the defect. We also find that in the low-temperature pinned phase, the vortex lattice tilt response to a transverse magnetic field proceeds via a soliton proliferation transition, governed by an integrable sine-Hilbert equation and analogous to the well-known commensurate-incommensurate transition in sine-Gordon systems. The distinguishing feature here is the long-range nature of the one-dimensional elasticity, leading to a logarithmic soliton energy and interaction. We predict the transverse-field -- temperature phase diagram and discuss extension of our results to a bulk vortex array in the presence of a distribution of columnar defects.