Quantum FFLO state in clean layered superconductors

TL;DR

This paper demonstrates that Landau quantization can induce FFLO states in clean layered superconductors under magnetic fields, even when Zeeman effects are weak, expanding the conditions under which such states can exist.

Contribution

It reveals that Landau quantization promotes FFLO states in layered superconductors regardless of strong Zeeman effects, a novel insight into superconducting instabilities.

Findings

Quantization corrections promote FFLO states at low temperatures.

FFLO states can exist in materials with weak Zeeman splitting.

Maximum FFLO temperature ratio is linked to Landau-level separation.

Abstract

We investigate the influence of Landau quantization on the superconducting instability for a pure layered superconductor in the magnetic field directed perpendicular to the layers. We demonstrate that the quantization corrections to the Cooper-pairing kernel with finite Zeeman spin splitting promote the formation of the nonuniform state in which the order parameter is periodically modulated along the magnetic field, i.e., between the layers (Fulde-Ferrell-Larkin-Ovchinnikov [FFLO] state). The conventional uniform state experiences such a quantization-induced FFLO instability at low temperatures even in a common case of predominantly orbital suppression of superconductivity when the Zeeman spin splitting is expected to have a relatively weak effect. The maximum relative FFLO temperature is given by the ratio of the superconducting transition temperature and the Fermi energy. This maximum is realized when the ratio of the spin-spitting energy and the Landau-level separation is half-integer. These results imply that the FFLO states may exist not only in the Pauli-limited superconductors but also in very clean materials with small Zeeman spin-splitting energy. We expect that the described quantization-promoted FFLO instability is a general phenomenon, which may be found in materials with different electronic spectra and order-parameter symmetries.