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

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.

The physics of the crossover between weak-coupling Bardeen–Cooper–Schrieffer (BCS) and strong-coupling Bose–Einstein condensate (BEC) limits gives a unified framework of quantum-bound (superfluid) states of interacting fermions. This crossover has been studied in the ultracold atomic systems, but is extremely difficult to be realized for electrons in solids. Recently, the superconducting semimetal FeSe with a transition temperature Tc=8.5 K has been found to be deep inside the BCS–BEC crossover regime. Here we report experimental signatures of preformed Cooper pairing in FeSe, whose energy scale is comparable to the Fermi energies. In stark contrast to usual superconductors, large non-linear diamagnetism by far exceeding the standard Gaussian superconducting fluctuations is observed below T*∼20 K, providing thermodynamic evidence for prevailing phase fluctuations of superconductivity. Nuclear magnetic resonance and transport data give evidence of pseudogap formation at ∼T*. The multiband superconductivity along with electron–hole compensation in FeSe may highlight a novel aspect of the BCS–BEC crossover physics.

In most unconventional superconductors, the importance of antiferromagnetic fluctuations is widely acknowledged. In addition, cuprate and iron-pnictide high-temperature superconductors often exhibit unidirectional (nematic) electronic correlations, including stripe and orbital orders, whose fluctuations may also play a key role for electron pairing. In these materials, however, such nematic correlations are intertwined with antiferromagnetic or charge orders, preventing the identification of the essential role of nematic fluctuations. This calls for new materials having only nematicity without competing or coexisting orders. Here we report systematic elastoresistance measurements in FeSe 1−x S x superconductors, which, unlike other iron-based families, exhibit an electronic nematic order without accompanying antiferromagnetic order. We find that the nematic transition temperature decreases with sulfur content x; whereas, the nematic fluctuations are strongly enhanced. Near x ≈ 0.17, the nematic susceptibility diverges toward absolute zero, revealing a nematic quantum critical point. The obtained phase diagram for the nematic and superconducting states highlights FeSe 1−x S x as a unique nonmagnetic system suitable for studying the impact of nematicity on superconductivity.electronic nematicity | iron-based superconductors | nematic susceptibility | unconventional superconductivity | quantum critical point T he prime candidate for the unconventional mechanism of superconductivity in many strongly correlated electron systems including cuprate, iron-based, and heavy-fermion superconductors is based on magnetic fluctuations (1-4). In these materials, domeshaped superconducting phases appear in the vicinity of end point of the antiferromagnetic (AFM) order, where spin fluctuations are strongly enhanced. Recently, however, other competing or coexisting orders that break rotational symmetry of the system have been frequently found in these materials (5-8), and the importance of fluctuations of these orders on superconducting pairing has been suggested theoretically (9-12).In underdoped cuprate superconductors, unidirectional electronic correlations (stripe correlations) appear in the pseudogap state, whose relation with superconductivity is a center of debate. It has become more complicated after the charge density wave (CDW) order has been observed in a portion of this pseudogap region of the phase diagram (5). In iron pnictides, the tetragonal-toorthorhombic structural transition always precedes or coincides with the AFM transition (3). Below the structural transition temperature T s , electronic nematicity that represents a large electronic anisotropy breaking the C 4 rotational symmetry, is observed (7), which may have a similar aspect with the stripe correlations in underdoped cuprates. In both cases, however, the nematicity is largely coexisting and intertwined with other CDW and AFM orders. Large nematic fluctuations have been experimentally observed in BaFe 2 As 2 systems above T s , and these nematic fluctuati...

Junctions and interfaces consisting of unconventional superconductors provide an excellent experimental playground to study exotic phenomena related to the phase of the order parameter. Not only does the complex structure of unconventional order parameters have an impact on the Josephson effects, but it also may profoundly alter the quasiparticle excitation spectrum near a junction. Here, by using spectroscopic-imaging scanning tunneling microscopy, we visualize the spatial evolution of the LDOS near twin boundaries (TBs) of the nodal superconductor FeSe. The π=2 rotation of the crystallographic orientation across the TB twists the structure of the unconventional order parameter, which may, in principle, bring about a zero-energy LDOS peak at the TB. The LDOS at the TB observed in our study, in contrast, does not exhibit any signature of a zero-energy peak, and an apparent gap amplitude remains finite all the way across the TB. The low-energy quasiparticle excitations associated with the gap nodes are affected by the TB over a distance more than an order of magnitude larger than the coherence length ξ ab . The modification of the low-energy states is even more prominent in the region between two neighboring TBs separated by a distance ≈7ξ ab . In this region, the spectral weight near the Fermi level (≈ AE 0.2 meV) due to the nodal quasiparticle spectrum is almost completely removed. These behaviors suggest that the TB induces a fully gapped state, invoking a possible twist of the order parameter structure, which breaks time-reversal symmetry.