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

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.

27 pages, 17 figures; corrected typos, added references

References in corpus (5)

• Observation of resonance condensation of fermionic atom pairs
• Flux pinning properties of superconductors with an array of blind holes
• Non-Hermitian Luttinger liquids and flux line pinning in planar superconductors
• Non-Hermitian Luttinger Liquids and Vortex Physics
• Vortex pinning by a columnar defect in planar superconductors with point disorder

Cited by in corpus (10)

• Tilted elastic lines with columnar and point disorder, non-Hermitian quantum mechanics and spiked random matrices: pinning and localization
• Liquid crystal cells with "dirty" substrates
• Transverse Meissner Physics of Planar Superconductors with Columnar Pins
• Stability and distortions of liquid crystal order in a cell with a heterogeneous substrate
• Pinning of Flux Lines by Planar Defects
• Planar defects and the fate of the Bragg glass phase of type-II superconductors
• Smectic order, pinning, and phase transition in a smectic liquid crystal cell with a random substrate
• Smectic vortex glass
• The generic Mott transition in the sine-Gordon model through an embedded worm algorithm
• Effects of kinked linear defects on planar flux line arrays