Quantum FFLO State in Clean Layered Superconductors

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.

Bereziskii-Kosterlitz-Thouless transition in the Weyl system PtBi2

“…2D superconductivity and BKT transitions are of particular interest when they take place in materials with brocken inversion symmetry (ℐ) and strong spin-orbit coupling, where the electron spin degeneracy of Bloch states is lifted. This may lead to unconventional superconducting states, such as a mixed singlet and triplet superconductivity [35][36][37] , or a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) finite momentum pairing [38][39][40][41][42][43] . It can also enable the realization of a Weyl semimetal phase, which, coupled to superconductivity, constitutes an ideal platform to study unconventional superconducting states or topological superconductivity [44][45][46][47][48][49][50][51] .…”

Competing pairing interactions responsible for the large upper critical field in a stoichiometric iron-based superconductor CaKFe4As4

“…3(b) cannot be fully captured by only considering the two-band model with large Pauli paramagnetic effects, α ∼ 3.2. The formation of the FFLO state in a system with a cylindrical Fermi surface requires a large Zeeman energy and a critical Maki's parameter of α c = 4.76 [2], compared to α c = 1.8 [39] for a threedimensional Fermi surface. CaKFe 4 As 4 has a complex Fermi surface with two-dimensional cylindrical and highly warped sheets and together with a large value of α creates the conditions for the emergence of an FFLO state [1].…”

“…It also describes the complex interplay between different pairing gaps and symmetry and can shed light on the nature of the superconducting mechanism. Furthermore, the temperature dependence of the upper critical field can also provide evidence for the presence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state [1,2] in which the order parameter varies in space. The iron-based superconductors have unusually large values of the upper critical field which reveal exotic effects caused by the interplay of orbital and paramagnetic pair-breaking in multiband superconductors with unconventional pairing symmetry [3].…”

“…This model accounts for the presence of two different bands, with interband scattering (λ 11 , λ 22 ) and intraband effects (λ 12 , λ 21 ) and includes paramagnetic effects and allows for the presence of an FFLO inhomogeneous state at highfields and low temperatures [1]. An FFLO state is characterized by a real-space modulation of the superconducting order parameter either in amplitude or phase such that the system energy is minimized under the constraints of a large Zeeman energy and superconducting condensation energy [2]. As the FFLO wave vector Q appears spontaneously below a certain temperature, T FFLO , the spinodal instability line in H c2 (T ) at a finite Q acquires the characteristic upturn [1].…”

Quasiparticle Nodal Plane in the Fulde-Ferrell-Larkin-Ovchinnikov state of FeSe

“…5b). This state corresponds to the FFLO state involving Cooper pairs with higher-order Landau levels of index n ≥ 1 [3,[19][20][21]. However, we can exclude this scenario, because superconducting order parameter remains finite in some region of the ab plane, which is inconsistent with the uniform suppression of superconductivity at the top surface.…”