The extended Lawrence-Doniach model: the temperature evolution of the in-plane magnetic field anisotropy

TL;DR

This paper extends the Lawrence-Doniach model to describe the temperature-dependent in-plane magnetic field anisotropy in layered superconductors, incorporating interlayer coupling and spin effects, and aligns well with experimental data.

Contribution

The authors generalize the Lawrence-Doniach model for high magnetic fields, capturing re-entrant superconductivity and multiple temperature regimes of anisotropy.

Findings

Identification of four temperature regimes of anisotropy.

Agreement with experimental measurements on (TMTSF)₂ClO₄.

Description of re-entrant superconductivity without Pauli pair breaking.

Abstract

Using the quasi-classical formalism we provide the description of the temperature and field-direction dependence of the in-plane upper critical field in layered superconductors, taking into account the interlayer Josephson coupling and the paramagnetic spin splitting. We generalize the Lawrence-Doniach model for the case of high magnetic fields and show that the re-entrant superconductivity is naturally described by our formalism when neglecting the Pauli pair breaking effect. We demonstrate that in layered superconductors the in-plane anisotropy of the onset of superconductivity exhibits four different\ temperature regimes: from the Ginzburg-Landau type in the vicinity of the critical temperature $T_{c0}$ with anisotropies of coherence lengths, up to the FFLO type induced by the strong interference between the modulation vector and the orbital effect. Our results are in agreement with the experimental measurements of the field-angle dependence of the superconducting onset temperature of the organic compound (TMTSF)$_{2} $ClO$_{4}$.