Orbital-Induced Crossover of the Fulde-Ferrell-Larkin-Ovchinnikov Phase into Abrikosov-like States

TL;DR

This study demonstrates how increasing orbital effects in a quasi-two-dimensional superconductor induce a transition from the FFLO state to vortex lattice states, revealing complex high-field superconducting phases.

Contribution

We provide experimental evidence and theoretical analysis of the orbital-induced crossover from FFLO to Abrikosov-like vortex states in a layered superconductor.

Findings

Superconducting transition changes from second to first order with field tilt.

High-field superconducting phase exhibits complex vortex states.

Theoretical model confirms orbital effects induce FFLO to vortex state transition.

Abstract

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can emerge in superconductors for which the orbital critical field exceeds the Pauli limit. Here, we present angular-resolved specific-heat data of the quasi-two-dimensional organic superconductor $\kappa$-(ET)$_2$Cu(NCS)$_2$, with a focus on high fields in the regime of the FFLO transition. For an increasing out-of-plane tilt of the applied magnetic field, which leads to an increase of orbital contributions, we found that the nature of the superconducting transition changes from second to first order and that a further transition appears within the high-field superconducting phase. However, the superconducting state above the Pauli limit is stable for field tilt of several degrees. Since any finite perpendicular component of the magnetic field necessarily leads to quantization of the orbital motion, the resulting vortex lattice states compete with the modulated order parameter of the FFLO state leading to complex high-field superconducting phases. By solving the linearized self-consistency equation within weak-coupling BCS theory, we show that our results are clear experimental evidence of an orbital-induced transformation of the FFLO order-parameter into Abrikosov-like states of higher Landau levels.