Fermi systems in the cross-over regime between weakly coupled Bardeen-Cooper-Schrieffer (BCS) and strongly coupled Bose-Einstein-condensate (BEC) limits are among the most fascinating objects to study the behavior of an assembly of strongly interacting particles. The physics of this cross-over has been of considerable interest both in the fields of condensed matter and ultracold atoms. One of the most challenging issues in this regime is the effect of large spin imbalance on a Fermi system under magnetic fields. Although several exotic physical properties have been predicted theoretically, the experimental realization of such an unusual superconducting state has not been achieved so far. Here we show that pure single crystals of superconducting FeSe offer the possibility to enter the previously unexplored realm where the three energies, Fermi energy e F , superconducting gap Δ, and Zeeman energy, become comparable. Through the superfluid response, transport, thermoelectric response, and spectroscopic-imaging scanning tunneling microscopy, we demonstrate that e F of FeSe is extremely small, with the ratio Δ=e F ∼ 1(∼ 0:3) in the electron (hole) band. Moreover, thermal-conductivity measurements give evidence of a distinct phase line below the upper critical field, where the Zeeman energy becomes comparable to e F and Δ. The observation of this field-induced phase provides insights into previously poorly understood aspects of the highly spin-polarized Fermi liquid in the BCS-BEC cross-over regime.BCS-BEC cross-over | Fermi energy | quasiparticle interference | iron-based superconductors | exotic superconducting phase S uperconductivity in most metals is well explained by the weak-coupling Bardeen-Cooper-Schrieffer (BCS) theory, where the pairing instability arises from weak attractive interactions in a degenerate fermionic system. In the opposite limit of Bose-Einstein condensate (BEC), composite bosons consisting of strongly coupled fermions condense into a coherent quantum state (1, 2). In BCS superconductors, the superconducting transition temperature is usually several orders of magnitude smaller than the Fermi temperature, T c =T F = 10 −5 -10 −4 , whereas in the BEC limit T c =T F is of the order of 10 −1 . Even in the high-T c cuprates, T c =T F is merely of the order of 10 −2 at optimal doping. Of particular interest is the BCS-BEC cross-over regime with intermediate coupling strength. In this regime the size of interacting pairs (∼ ξ), which is known as the coherence length, becomes comparable to the average distance between particles (∼ 1=k F ), i.e., k F ξ ∼ 1 (3-5), where k F is the Fermi momentum. This regime is expected to have the highest values of T c =T F = 0:1 − 0:2 and Δ=« F ∼ 0:5 ever observed in any fermionic superfluid.One intriguing issue concerns the role of spin imbalance: whether it will lead to a strong modification of the properties of the Fermi system in the cross-over regime. This problem has been of considerable interest not only in the context of superconductivity but also in ultraco...

We have observed Shubnikov-de Haas oscillations in FeSe. The Fermi surface deviates significantly from predictions of band-structure calculations and most likely consists of one electron and one hole thin cylinder. The carrier density is in the order of 0.01 carriers/ Fe, an order-of-magnitude smaller than predicted. Effective Fermi energies as small as 3.6 meV are estimated. These findings call for elaborate theoretical investigations incorporating both electronic correlations and orbital ordering.

We report measurements of resistance and ac magnetic susceptibility on FeSe single crystals under high pressure up to 27.2 kbar. The structural phase transition is quickly suppressed with pressure, and the associated anomaly is not seen above ∼18 kbar. The superconducting transition temperature evolves nonmonotonically with pressure, showing a minimum at ∼ 12 kbar. We find another anomaly at 21.2 K at 11.6 kbar. This anomaly most likely corresponds to the antiferromagnetic phase transition found in µSR measurements [M. Bendele et al., Phys. Rev. Lett. 104, 087003 (2010)]. The antiferromagnetic and superconducting transition temperatures both increase with pressure up to ∼ 25 kbar and then level off. The width of the superconducting transition anomalously broadens in the pressure range where the antiferromagnetism coexists.

We report Shubnikov-de Haas (SdH) oscillation measurements on FeSe under high pressure up to P = 16.1 kbar. We find a sudden change in SdH oscillations at the onset of the pressure-induced antiferromagnetism at P ∼ 8 kbar. We argue that this change can be attributed to a reconstruction of the Fermi surface by the antiferromagnetic order. The negative dTc/dP observed in a range between P ∼ 8 and 12 kbar may be explained by the reduction in the density of states due to the reconstruction. The ratio of the transition temperature to the effective Fermi energy remains high under high pressure: kBTc/EF ∼ 0.1 even at P = 16.1 kbar.

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