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.
Highlights
Superconductors exhibit a rich set of phenomena in a magnetic field due to the interplay of the electron orbital and spin degrees of freedoms
One of the most intriguing phenomena due to the strong Zeeman spin-splitting effect is the emergence of Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) states [1,2], in which the Cooper pairing occurs with nonzero total momentum
It is not widely recognized that the quantization 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 ωc near HC2 is comparable to the band’s Fermi energy εF [28]
Summary
Superconductors exhibit a rich set of phenomena in a magnetic field due to the interplay of the electron orbital and spin degrees of freedoms. The conditions for the FFLO instability in the presence of the orbital effect have been investigated by Gruenberg and Gunther [11] for a clean isotropic superconductor within the quasiclassical approach In this case, the emerging FFLO state is the Abrikosov vortex lattice with additional periodic modulation of the order parameter along the magnetic field. It is not widely recognized that the quantization 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 ωc near HC2 is comparable to the band’s Fermi energy εF [28].
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