Interplay between orbital-quantization effects and the Fulde-Ferrell-Larkin-Ovchinnikov instability in multiple-band layered superconductors

TL;DR

This paper investigates how Landau quantization and the FFLO instability interact in a two-band layered superconductor under magnetic field, revealing conditions for reentrant high-field superconductivity and novel order parameter modulations.

Contribution

It provides an exact analysis of Landau quantization effects in the shallow band and uncovers new regimes of FFLO states and reentrant superconductivity in layered multiband systems.

Findings

Landau quantization significantly promotes FFLO state formation.

Reentrant high-field superconducting states can occur at low temperatures.

Alternating FFLO states with sign-changing order parameters between layers are possible.

Abstract

We explore superconducting instability for a clean two-band layered superconductor with deep and shallow bands in the magnetic field applied perpendicular to the layers. In the shallow band, the quasiclassical approximation is not applicable, and Landau quantization has to be accounted for exactly. The electronic spectrum of this band in the magnetic field is composed of the one-dimensional Landau-level minibands. With increasing magnetic field the system experiences series of Lifshitz transitions when the chemical potential enters and exits the minibands. These transitions profoundly influence the shape of the upper critical field at low temperatures. In addition, the Zeeman spin splitting may cause the nonuniform state with interlayer modulation of the superconducting order parameter (Fulde-Ferrell-Larkin-Ovchinnikov state). Typically, the quantization effects in the shallow band strongly promote the formation of this state. The uniform state remains favorable only in the exceptional resonance cases when the spin-splitting energy exactly matches the Landau-level spacing. Furthermore, for specific relations between electronic spectrum parameters, the alternating FFLO state may realize, in which the order parameter changes sign between the neighboring layers. For all above cases, the reentrant high-field superconducting states may emerge at low temperatures if the shallow band has significant contribution to the Cooper pairing.