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...

The coexistence and competition between superconductivity and electronic orders, such as spin or charge density waves, have been a central issue in high transition-temperature (Tc) superconductors. Unlike other iron-based superconductors, FeSe exhibits nematic ordering without magnetism whose relationship with its superconductivity remains unclear. Moreover, a pressure-induced fourfold increase of Tc has been reported, which poses a profound mystery. Here we report high-pressure magnetotransport measurements in FeSe up to ∼15 GPa, which uncover the dome shape of magnetic phase superseding the nematic order. Above ∼6 GPa the sudden enhancement of superconductivity (Tc≤38.3 K) accompanies a suppression of magnetic order, demonstrating their competing nature with very similar energy scales. Above the magnetic dome, we find anomalous transport properties suggesting a possible pseudogap formation, whereas linear-in-temperature resistivity is observed in the normal states of the high-Tc phase above 6 GPa. The obtained phase diagram highlights unique features of FeSe among iron-based superconductors, but bears some resemblance to that of high-Tc cuprates.

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 investigate the electronic reconstruction across the tetragonal-orthorhombic structural transition in FeSe by employing polarization-dependent angle-resolved photoemission spectroscopy (ARPES) on detwinned single crystals. Across the structural transition, the electronic structures around the  and M points are modified from four-fold to two-fold symmetry due to the lifting of degeneracy in d xz /d yz orbitals.The d xz band shifts upward at the  point while it moves downward at the M point, suggesting that the electronic structure of orthorhombic FeSe is characterized by a momentum-dependent sign-changing orbital polarization. The elongated directions of the elliptical Fermi surfaces (FSs) at the  and M points are rotated by 90 degrees with respect to each other, which may be related to the absence of the antiferromagnetic order in FeSe. Keywords: PACS:Most of the parent compounds of the iron-based superconductors show the tetragonal-orthorhombic structural transition at T s and the stripe-type antiferromagnetic (AFM) order below T N ( T s ) [1,2]. Near the structural transition, an orbital order defined by the inequivalent electron occupation of 3d xz (xz) and 3d yz (yz) orbitals [3][4][5], has been reported by ARPES [6,7] and X-ray linear dichroism measurements [8] in several parent compounds. Experimental and theoretical studies suggested that the structural transition is caused by the electronic nematicity of the spin [9,10] or orbital [11][12][13] degrees of freedoms. Since superconductivity develops when such complex ordered states are suppressed, it is crucial to understand how the phase transitions couple to each other.In Ba(Fe,Co) 2 As 2 , the spin-driven nematicity has been suggested from the phase diagram in which T s and T N closely follow each other as the carrier is doped [14]. The scaling behavior between the nematic fluctuation and spin fluctuation was also reported by the nuclear magnetic resonance (NMR) and shear modulus measurements [10]. On the other hand, in NaFeAs, the orbital-driven nematicity has been proposed by ARPES [11]. In this compound, the structural transition at T s = 54 K is well separated from the AFM transition at T N = 43 K. Inequivalent shift in the xz/yz orbital bands appearing above T s changes the FSs from four-fold to two-fold symmetric shape [11,15], which may be a possible trigger of the stripe type AFM order and the orthorhombicity [11,16]. The variety of iron-based