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

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 onedimensional 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.

Quantum FFLO State in Clean Layered Superconductors

“…Using the expansion of the one-particle Green's function over the exact Landau-level basis, Eq. (4), one can derive the exact presentation for the kernel eigenvalue [23,28],…”

“…The Matsubara-frequency sums are logarithmically divergent and have to be cut at ω n ∼ Ω. This divergence can be eliminated using the zero-field gap equation giving [28], and the field-dependent part of the pairing-kernel eigenvalue is…”

“…(11) converges now in the limit of Ω → ∞. We can represent the functions J in this limit as [28] J ðH; T;…”

“…It is not widely recognized that the quantization actually may profoundly promote this instability due to the one-dimensional nature of the quasiparticle's spectrum at the Landau levels. Such quantization-induced FFLO states have been recently demonstrated in a special situation motivated by the physics of multiple-band iron-based superconductors, when one of the shallow bands is close to the extreme quantum limit so that the cyclotron frequency ω c near H C2 is comparable to the band's Fermi energy ϵ F [28].…”

Fulde-Ferrell-Larkin-Ovchinnikov State in Perpendicular Magnetic Fields in Strongly Pauli-Limited Quasi-Two-Dimensional Superconductors

“…For quasi-two-dimensional systems in perpendicular fields, Song and Koshelev proposed a theory of interplay between orbital-quantization effects and the FFLO state, and discussed the FFLO state in FeSe when H c. 31) In the present study, we assume weaker magnetic fields.…”