Thermodynamic Evidence for the Fulde-Ferrell-Larkin-Ovchinnikov State in the KFe2As2 Superconductor

Abstract

We have investigated the magnetic phase diagram near the upper critical field of KFe2As2 by magnetic torque and specific heat experiments, using a high-resolution piezo-rotary positioner to precisely control the parallel orientation of the magnetic field with respect to the FeAs layers. We observe a clear double transition when the field is oriented strictly in-plane, and a characteristic upturn of the upper critical field line well beyond the Pauli limit at 4.7 T. This provides firm evidence that an FFLO state is realized in this iron-based KFe2As2 superconductor.While the upper critical field (Hc2) of type-II superconductors is usually determined by the orbital limit for superconductivity [1], there are rare cases in which the Pauli paramagnetic limit, at which the Zeeman split Fermi surfaces suppress Cooper pairing, occurs instead [2,3]. When a superconductor approaches the latter, an exotic superconducting state was predicted by Fulde, Ferrell, Larkin and Ovchinnikov [4,5]. Under certain conditions, a superconductor could overcome the Pauli limit by forming the 'FFLO' state in which the Cooper pairs have a finite center-of-mass momentum. Cooper pairing between the Zeeman split Fermi surfaces is possible only with an oscillating component of the order parameter amplitude in real space. Only a few observations of the FFLO state have been reported to date despite its high technological relevance for high magnetic field applications. The Q-phase in the heavy fermion superconductor CeCoIn5 is regarded as a possible realization [6][7][8], although the superconductivity coexists with an incommensurate spin-density wave [8]. In some layered organic superconductors, evidence has been provided for an FFLO state without magnetic order [9][10][11][12][13][14][15][16]. The rarity of the FFLO state is due to the strict requirements on its occurrence. It needs a very large Ginzburg-Landau parameter ≡ / ≫ 1 ( : penetration depth, : coherence length), and a Maki parameter greater than 1.85 [17,18]. Only in this case does the Pauli limit occur below the orbital limit. In addition, the superconductor must be in the clean limit [19,20]. Low dimensionality and anisotropic Fermi surfaces can further stabilize the FFLO state [21]. The Hc2 line in the magnetic (H-T) phase diagram shows a characteristic saturation at the Pauli limit, where the second-order transition (SOT) changes into a discontinuous first-order transition (FOT). However, as soon an FFLO state is formed, a characteristic increase of Hc2 occurs to fields beyond the Pauli limi. KFe2As2 is the overdoped end member of the Ba1-xKxFe2As2 family of the multiband Fe-based superconductors with Tc of ~3.4 K. In recent magnetostriction experiments it was found that Hc2 is Pauli limited for fields applied parallel to the FeAs layers [22,23]. However,

Reentrant Fulde-Ferrell-Larkin-Ovchinnikov superfluidity in the honeycomb lattice

“…The FFLO phase can be stable at low temperature and relatively large magnetic field (above the critical magnetic field of the Clogston-Chandrasekhar or Pauli limit [43,44]). There are experimental and theoretical premises that the FFLO state can be found in quasi-2D organic [45][46][47][48], heavy-fermion [49][50][51][52][53][54] or iron-based [54][55][56][57][58][59][60] superconductors. In this type of materials, a firstorder phase transition from the superconducting to the normal state has been reported [46-49, 51-53, 55-57].…”

Orbital effect for the Fulde-Ferrell-Larkin-Ovchinnikov phase in a quasi-two-dimensional superconductor in a parallel magnetic field

“…[27,28] is that the orbital effect is of the relative order of t 2 ⊥ /T 2 c0 1. From the experimental side, plenty of experimental works on Q2D organic and some other superconductors have been performed [29][30][31][32][33][34][35][36][37][38][39][40][41] to establish the possible existence of the FFLO phase in a parallel magnetic field.The goal of our paper is to consider the orbital effect in a parallel magnetic field in a Q2D conductor at zero temperature, in contrast to Refs. [27,28].…”

Lifshitz Transitions Induced by Magnetic Field

“…Similarly to the one-dimensional system (Sect. 2), some types of the IBSCs show a tendency to exhibit the FFLO phase [31,35,[54][55][56] and the BCS-BEC crossover [57][58][59][60][61]. The second possibility is a result of the proximity between the bottom (or top) of the band and the Fermi level, which is found in the Fe(Te,Se) superconductor.…”