On the Remarkable Superconductivity of FeSe and Its Close Cousins

Proximity Effect of Antiferromagnetic Material on FeSeTe Superconductor

We explore the proximity effect of 2D antiferromagnetic (AFM) MnPS3 on an exfoliated superconducting sample. First, we characterized a FeSeTe (FST) superconducting sample and then placed the AFM layer on top of the exfoliated FeSeTe. The superconducting transition temperature Tczero increased marginally for the AFM/FST sample, while we found a significant improvement in the upper critical field (Bc2) for the AFM/FST sample. We extracted Bc2 from electrical resistivity measurements under different magnetic fields in the B//c and B//ab plane. The thermal activation energy and its power law relation for low temperatures were studied using ρ(T) vs B data. The thermally activated flux flow effect is observed, resulting in a noticeable increase in the in-plane critical field. Moreover, the vortex glass transition does not exhibit any notable differences among the samples. The Hall effect shows a sign change from negative to positive below 150 K for AFM/FST, which suggests that two types of carriers mediated the transport due to the proximity effect. A considerable decrease in the critical current Ic is also observed. The two steps in the IV curves suggest possible quantum phase slips, which are more vital for the AFM/FST device.

Evidence for nematic fluctuations in FeSe superconductor: a57Fe Mössbauer spectroscopy study

There has been controversy about the driving force of the nematic order in the FeSe superconductor. Here, we present a detailed study of the57Fe Mössbauer spectra of FeSe single-crystal powders, focusing on the temperature dependences of the hyperfine parameters in the vicinity of the nematic transition temperature,Ts∼ 90 K. The nematicity-induced splitting ofdxzanddyzbands, obtained from the anomalous increase in quadrupole splitting nearTs, starts at 143 K. The temperature evolution of the lattice dynamics, deduced from the recoilless fractions and second-order Doppler shifts, is found to undergo successively two segments of phonon-softening (160 K-105 K) and phonon-hardening (105 K-90 K), related to the appearance of local orthorhombic distortions aboveTsand the establishing way of the associated nematic correlations. Analysis of the linewidths shows that spin fluctuations occur not only below 70 K but also acrossTs(105 K-70 K), accompanied by the non-Fermi liquid behavior of the electrons. The results demonstrate the strong interactions between lattice, spin, and electron degrees of freedom in the vicinity ofTsand that the lattice degrees of freedom may play an essential role in driving the nematic order for FeSe.

Effect of aliovalent substitution on the local structure of CaKFe4As4superconductor

We have investigated the local structure of the iron-based CaKFe4As4superconductor featuring distinct aliovalent substitutions at the Ca and K sites, that is CaKFe4As4, CaK0.9Sr0.1Fe4As4, CaK0.9Ba0.1Fe4As4and Ca0.9Na0.1K0.9Ba0.1Fe4As4. Temperature-dependent Fe K-edge extended x-ray absorption fine structure (EXAFS) measurements are used to determine the near-neighbors bondlengths and their stiffness. The EXAFS analysis reveals that the Fe-As bondlength undergoes negligible changes by substitution, however, the Fe-Fe bondlength and the As height are affected by the Sr substitution. The superconducting transition temperatures of CaK0.9Sr0.1Fe4As4and CaK0.9Ba0.1Fe4As4are very similar even if the mean As heights are significantly different suggesting that the anion height may not be a unique parameter to describe the superconductivity in CaKFe4As4. The mean As heights show a peculiar temperature dependence characteristic of CaKFe4As4system. Furthermore, the temperature-dependent mean square relative displacements reveal similar Fe-Fe bond stiffness in all samples, instead the Fe-As bond is substantially stiffer in case of CaK0.9Sr0.1Fe4As4. The local structure results are discussed in relation to the differing transport properties of aliovalent substituted 1144 superconductor.

Iron Vacancy Tunable Superconductor-Insulator Transition in FeSe/SrTiO_{3} Monolayer

The Fe_{4}Se_{5} with a sqrt[5]×sqrt[5] Fe vacancy order is suggested to be a Mott insulator and the parent state of bulk FeSe superconductor. The iron vacancy ordered state has been considered as a Mott insulator and the parent compound of bulk FeSe-based superconductors. However, for the superconducting FeSe/SrTiO_{3} monolayer (FeSe/STO) with an interface-enhanced high transition temperature (T_{c}), the electronic evolution from its Fe vacancy ordered parent phase to the superconducting state, has not been explored due to the challenge to realize an Fe vacancy order in the FeSe/STO monolayer, even though important to the understanding of superconductivity mechanism. In this study, we developed a new method to generate Fe vacancies within the FeSe/STO monolayer in a tunable fashion, with the assistance of atomic hydrogen. As a consequence, an insulating sqrt[5]×sqrt[5] Fe vacancy ordered monolayer is realized as the parent state. By using scanning tunneling microscopy and scanning tunneling spectroscopy, the spectral evolution from superconductivity to insulator is fully characterized. Surprisingly, a prominent spectral weight transfer occurs, thus implying a strong electron correlation effect. Moreover, the Fe vacancy induced insulating gap exhibits no Mott gap-like features. This work provides new insights in understanding the high-T_{c} superconductivity in FeSe/STO monolayer.

Atomic-Scale Andreev Probe of Unconventional Superconductivity

Recent emergence of low-dimensional unconventional superconductors and their exotic interface properties calls for new approaches to probe the pairing symmetry, a fundamental and frequently elusive property of the superconducting condensate. Here, we introduce the unique capability of tunneling Andreev reflection (TAR) to probe unconventional pairing symmetry, utilizing the sensitivity of this technique to specific Andreev reflections. Specifically, suppression of the lowest-order Andreev reflection due to quantum interference but emergence of the higher-order Andreev processes provides direct evidence of the sign-changing order parameter in the paradigmatic FeSe superconductor. TAR spectroscopy also reveals two superconducting gaps, points to a possibility of a nodal gap structure, and directly confirms that superconductivity is locally suppressed along the nematic twin boundary, with preferential and near-complete suppression of the larger energy gap. Our findings therefore enable new, atomic-scale insight into microscopic, inhomogeneous, and interfacial properties of emerging quantum materials.

Quantum Noise Spectroscopy of Dynamical Critical Phenomena

The transition between distinct phases of matter is characterized by the nature of fluctuations near the critical point. We demonstrate that noise spectroscopy can not only diagnose the presence of a phase transition, but can also determine fundamental properties of its criticality. In particular, by analyzing a scaling collapse of the decoherence profile, one can directly extract the critical exponents of the transition and identify its universality class. Our approach naturally captures the presence of conservation laws and distinguishes between classical and quantum phase transitions. In the context of quantum magnetism, our proposal complements existing techniques and provides a novel toolset optimized for interrogating two-dimensional magnetic materials.

Expanded quantum vortex liquid regimes in the electron nematic superconductors FeSe1-xSx and FeSe1-xTex

The quantum vortex liquid (QVL) is an intriguing state of type-II superconductors in which intense quantum fluctuations of the superconducting (SC) order parameter destroy the Abrikosov lattice even at very low temperatures. Such a state has only rarely been observed, however, and remains poorly understood. One of the key questions is the precise origin of such intense quantum fluctuations and the role of nearby non-SC phases or quantum critical points in amplifying these effects. Here we report a high-field magnetotransport study of FeSe_1-xS_x and FeSe_1-xTe_x which show a broad QVL regime both within and beyond their respective electron nematic phases. A clear correlation is found between the extent of the QVL and the strength of the superconductivity. This comparative study enables us to identify the essential elements that promote the QVL regime in unconventional superconductors and to demonstrate that the QVL regime itself is most extended wherever superconductivity is weakest.

Symmetry of Identical Particles, Modern Achievements in the Pauli Exclusion Principle, in Superconductivity and in Some Other Phenomena

In this review, the modern achievements in studies of the Pauli exclusion principle (PEP) and the properties of the identical particle systems when PEP is not fulfilled are discussed. The validity of conception of the spin in the framework of density functional theory (DFT) approaches is analyzed. The modern state of the recently discovered Fe-based superconductors is discussed in detail. These materials belong to the paramagnetic semimetal family and become superconductors upon doping. Recently, in 2020, room-temperature superconductivity was realized. However, from the following discussion in the SC community, it was not evident that the results of room-temperature superconductivity have been repeated by other laboratories. Thus, the question “is room temperature really achieved?” is still open. In the concluding remarks, we present the explanation of why the PEP limitations on the symmetry of identical particles system exist in nature, and following from it, some important consequences.

Temperature dependent local inhomogeneity and magnetic moments of (Li1-xFex)OHFeSe superconductors

We have combined the extended X-ray absorption fine structure (EXAFS) and X-ray emission spectroscopy (XES) to investigate the local structure and the local iron magnetic moments of (Li_1-xFe_x)OHFeSe (x∼0.2) superconductors. The local structure, studied by Fe K-edge EXAFS measurements, is found to be inhomogeneous that is characterized by different Fe-Se bond lengths. The inhomogeneous phase exhibits a peculiar temperature dependence with lattice anomalies in the local structural parameters at the critical temperature T_c (36 K) and at the spin density wave (SDW) transition temperature T_N (130 K). Fe Kβ XES shows iron to be in a low spin state with the local Fe magnetic moment evolving anomalously as a function of temperature. Apart from a quantitative measurement of the local structure of (Li_1-xFe_x)OHFeSe, providing direct evidence of nanoscale inhomogeneity, the results provide further evidence of the vital role that the coupled electronic, lattice and magnetic degrees of freedom play in the iron-based superconductors.

Unconventional localization of electrons inside of a nematic electronic phase

Among iron-based superconductors, FeSe displays an anomalous electronic nematic state, strong electronic correlations, and orbitally dependent band shifts that can influence its superconducting pairing. Here, we report detailed magnetotransport studies of thin flakes of FeSe that reveal unconventional transport, in which the hole carriers remain highly mobile, whereas the mobility of the electron carriers is low, and weakly temperature dependent, inside the nematic phase. This suggests an unusual localization of negative charge carriers that may be caused by orbital-dependent enhanced correlations, scattering of spin fluctuations, and/or a topological electronic transition. As the superconductivity is suppressed by reducing the flake thickness, it suggests that the electron pockets participate actively in pairing. By doping, electron pockets expand, enabling high-Tc superconductivity.

The magnetotransport behavior inside the nematic phase of bulk FeSe reveals unusual multiband effects that cannot be reconciled with a simple two-band approximation proposed by surface-sensitive spectroscopic probes. In order to understand the role played by the multiband electronic structure and the degree of two-dimensionality, we have investigated the electronic properties of exfoliated flakes of FeSe by reducing their thickness. Based on magnetotransport and Hall resistivity measurements, we assess the mobility spectrum that suggests an unusual asymmetry between the mobilities of the electrons and holes, with the electron carriers becoming localized inside the nematic phase. Quantum oscillations in magnetic fields up to 38 T indicate the presence of a hole-like quasiparticle with a lighter effective mass and a quantum scattering time three times shorter, as compared with bulk FeSe. The observed localization of negative charge carriers by reducing dimensionality can be driven by orbitally dependent correlation effects, enhanced interband spin fluctuations, or a Lifshitz-like transition, which affect mainly the electron bands. The electronic localization leads to a fragile two-dimensional superconductivity in thin flakes of FeSe, in contrast to the two-dimensional high-Tc induced with electron doping via dosing or using a suitable interface.

Dirac-cone-like electronic states on nematic antiferromagnetic FeSe and FeTe

We investigate the Dirac-cone-like (DCL) topological electronic properties of nematic-like antiferromagnetic (AFM) states of monolayer FeSe and FeTe designed artificially through first-principles calculations and Wannier-function-based tight-binding (WFTB) method. Our calculations reveal most of them have a pair of DCL bands on the Γ-Xline in the Brillouin zone (BZ) near the Fermi level and open a gap of about 20 meV in the absence and presence of spin-orbit coupling (SOC), respectively, similar to the lowest-energy pair-checkerboard AFM FeSe. We further confirm that they are weak topological insulators based on nonzeroZ₂and fragile surface states, which are calculated by the WFTB method. For FeSe and FeTe in pair-checkerboard AFM states, we find that the in-plane compression strain in a certain range can give rise to another pair of DCL bands located on the Γ-X' line in the BZ. In addition, the magnetic moments, energies, and Fe-Se/Te distances for various nematic-like AFM configurations are presented. These calculations the combining effect of magnetism and topology in a single material and the understanding of the superconducting phenomena in iron-based FeSe and FeTe.

Orbital-Selective High-Temperature Cooper Pairing Developed in the Two-Dimensional Limit

For multiband superconductors, the orbital multiplicity yields orbital differentiation in normal-state properties and can lead to orbital-selective spin-fluctuation Cooper pairing. The orbital-selective phenomenon has become increasingly pivotal in clarifying the pairing "enigma", particularly for multiband high-temperature superconductors. Meanwhile, in one-unit-cell (1-UC) FeSe/SrTiO₃, since the standard electron-hole Fermi pocket nesting scenario is inapplicable, the actual pairing mechanism is subject to intense debate. Here, by measuring high-resolution Bogoliubov quasiparticle interference, we report observations of highly anisotropic magnetic Cooper pairing in 1-UC FeSe. Theoretically, it is important to incorporate orbitally selective effects of electronic correlations within a spin-fluctuation pairing calculation, where the d_xy orbital becomes coherence-suppressed. The resulting pairing gap is compatible with the experimental findings, which suggests that high-T_c Cooper pairing with orbital selectivity applies to 2D-limit 1-UC FeSe. Our findings imply the general existence of orbital selectivity in iron-based superconductors and the universal significance of electron correlations in high-T_c superconductors.

Iron pnictides and chalcogenides: a new paradigm for superconductivity

Superconductivity is a remarkably widespread phenomenon that is observed in most metals cooled to very low temperatures. The ubiquity of such conventional superconductors, and the wide range of associated critical temperatures, is readily understood in terms of the well-known Bardeen-Cooper-Schrieffer theory. Occasionally, however, unconventional superconductors are found, such as the iron-based materials, which extend and defy this understanding in unexpected ways. In the case of the iron-based superconductors, this includes the different ways in which the presence of multiple atomic orbitals can manifest in unconventional superconductivity, giving rise to a rich landscape of gap structures that share the same dominant pairing mechanism. In addition, these materials have also led to insights into the unusual metallic state governed by the Hund's interaction, the control and mechanisms of electronic nematicity, the impact of magnetic fluctuations and quantum criticality, and the importance of topology in correlated states. Over the fourteen years since their discovery, iron-based superconductors have proven to be a testing ground for the development of novel experimental tools and theoretical approaches, both of which have extensively influenced the wider field of quantum materials.

Self-flux-grown Ba4Fe4ClO9.5−x crystals exhibiting structures with tunable modulation

The synthesis and X-ray structural study of the new family of compounds Ba₄Fe₄ClO_9.5−x with tunable structural modulation are reported. The framework of the structure has the Ba₂Fe₄O_9.5−x composition, with open hexagonal channels extending along the c-axis. The channels are filled with linear [Ba–Cl–Ba] triplets. The oxygen stoichiometry and the oxidation state of iron both are controlled by the redox conditions during crystal preparation. The modulation of the crystal structure arises from the distribution of the oxygen atoms in the framework and iron coordination polyhedra are a combination of FeO₄-tetrahedra, FeO₅-bipyramids, and FeO₆-octahedra. The structure modulation also originates from the ordered or disordered distribution of the [Ba–Cl–Ba] triplets filling the channels which is also affected by the conditions of the thermal treatment of the crystals. The structure investigation reveals a composition variation from Ba₄Fe₄ClO_9.5 (x = 0), in which Fe exhibits a 3+ oxidation state, to Ba₄Fe₄ClO₈ (x = 1.5) with the framework built exclusively of FeO₄ tetrahedra.

Ba₄Fe₄ClO_9.5−x compounds are built of a Ba₂Fe₄O_9.5−x framework with open hexagonal channels. (Ba–Cl–Ba) trimers located in the channels and the framework O atoms cause incommensurability, which is tuned under different annealing conditions.

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

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, characterized by Cooper pairs condensed at finite momentum, has been a long-sought state that remains unresolved in many classes of fermionic systems, including superconductors and ultracold atoms. A fascinating aspect of the FFLO state is the emergence of periodic nodal planes in real space, but its observation is still lacking. Here we investigate the superconducting order parameter at high magnetic fields H applied perpendicular to the ab plane in a high-purity single crystal of FeSe. The heat capacity and magnetic torque provide thermodynamic evidence for a distinct superconducting phase at the low-temperature/high-field corner of the phase diagram. Despite the bulk superconductivity, spectroscopic-imaging scanning tunneling microscopy performed on the same crystal demonstrates that the order parameter vanishes at the surface upon entering the high-field phase. These results provide the first demonstration of a pinned planar node perpendicular to H, which is consistent with a putative FFLO state.

Fragile Pressure-Induced Magnetism in FeSe Superconductors with a Thickness Reduction

The emergence of high transition temperature (T_c) superconductivity in bulk FeSe under pressure is associated with the tuning of nematicity and magnetism. However, sorting out the relative contributions from magnetic and nematic fluctuations to the enhancement of T_c remains challenging. Here, we design and conduct a series of high-pressure experiments on FeSe thin flakes. We find that as the thickness decreases the nematic phase boundary on temperature-pressure phase diagrams remains robust while the magnetic order is significantly weakened. A local maximum of T_c is observed outside the nematic phase region, not far from the extrapolated nematic end point in all samples. However, the maximum T_c value is reduced associated with the weakening of magnetism. No high-T_c phase is observed in the thinnest sample. Our results strongly suggest that nematic fluctuations alone can only have a limited effect while magnetic fluctuations are pivotal on the enhancement of T_c in FeSe.

Computational methods for 2D materials modelling

Materials with thickness ranging from a few nanometers to a single atomic layer present unprecedented opportunities to investigate new phases of matter constrained to the two-dimensional plane. Particle-particle Coulomb interaction is dramatically affected and shaped by the dimensionality reduction, driving well-established solid state theoretical approaches to their limit of applicability. Methodological developments in theoretical modelling and computational algorithms, in close interaction with experiments, led to the discovery of the extraordinary properties of two-dimensional materials, such as high carrier mobility, Dirac cone dispersion and bright exciton luminescence, and inspired new device design paradigms. This review aims to describe the computational techniques used to simulate and predict the optical, electronic and mechanical properties of two-dimensional materials, and to interpret experimental observations. In particular, we discuss in detail the particular challenges arising in the simulation of two-dimensional constrained fermions and quasiparticles, and we offer our perspective on the future directions in this field.

Tomonaga-Luttinger Liquid in the Topological Edge Channel of Multilayer FeSe

A two-dimensional topological insulator exhibits helical edge states topologically protected against single-particle backscattering. Such protection breaks down, however, when electron-electron interactions are significant or when edge reconstruction occurs, leading to a suppressed density of states (DOS) at the Fermi level that follows universal scaling with temperature and energy, characteristic of Tomonaga-Luttinger liquid (TLL). Here, we grow multilayer FeSe on SrTiO₃ by molecular beam epitaxy and observe robust edge states at both the {100}Se and the {110}Se steps using scanning tunneling microscopy/spectroscopy. We determine the DOS follows a power law, resulting in the Luttinger parameter K of 0.26 ± 0.02 and 0.43 ± 0.07 for the {100}Se and {110}Se edges, respectively. The smaller K for the {100}Se edge also indicates strong correlations, attributed to ferromagnetic ordering likely present due to checkerboard antiferromagnetic fluctuations in FeSe. These results demonstrate TLL in FeSe helical edge channels, providing an exciting model system for novel topological excitations arising from superconductivity and interacting helical edge states.

Quadrupolar charge dynamics in the nonmagnetic FeSe1-x S x superconductors

We use polarization-resolved electronic Raman spectroscopy to study quadrupolar charge dynamics in a nonmagnetic [Formula: see text] superconductor. We observe two types of long-wavelength [Formula: see text] symmetry excitations: 1) a low-energy quasi-elastic scattering peak (QEP) and 2) a broad electronic continuum with a maximum at 55 meV. Below the tetragonal-to-orthorhombic structural transition at [Formula: see text], a pseudogap suppression with temperature dependence reminiscent of the nematic order parameter develops in the [Formula: see text] symmetry spectra of the electronic excitation continuum. The QEP exhibits critical enhancement upon cooling toward [Formula: see text] The intensity of the QEP grows with increasing sulfur concentration x and maximizes near critical concentration [Formula: see text], while the pseudogap size decreases with the suppression of [Formula: see text] We interpret the development of the pseudogap in the quadrupole scattering channel as a manifestation of transition from the non-Fermi liquid regime, dominated by strong Pomeranchuk-like fluctuations giving rise to intense electronic continuum of excitations in the fourfold symmetric high-temperature phase, to the Fermi liquid regime in the broken-symmetry nematic phase where the quadrupole fluctuations are suppressed.

Electronic Origin of Tc in Bulk and Monolayer FeSe

FeSe is classed as a Hund’s metal, with a multiplicity of d bands near the Fermi level. Correlations in Hund’s metals mostly originate from the exchange parameter J, which can drive a strong orbital selectivity in the correlations. The Fe-chalcogens are the most strongly correlated of the Fe-based superconductors, with dxy the most correlated orbital. Yet little is understood whether and how such correlations directly affect the superconducting instability in Hund’s systems. By applying a recently developed ab initio theory, we show explicitly the connections between correlations in dxy and the superconducting critical temperature Tc. Starting from the ab initio results as a reference, we consider various kinds of excursions in parameter space around the reference to determine what controls Tc. We show small excursions in J can cause colossal changes in Tc. Additionally we consider changes in hopping by varying the Fe-Se bond length in bulk, in the free standing monolayer M-FeSe, and M-FeSe on a SrTiO3 substrate (M-FeSe/STO). The twin conditions of proximity of the dxy state to the Fermi energy, and the strength of J emerge as the primary criteria for incoherent spectral response and enhanced single- and two-particle scattering that in turn controls Tc. Using c-RPA, we show further that FeSe in monolayer form (M-FeSe) provides a natural mechanism to enhance J. We explain why M-FeSe/STO has a high Tc, whereas M-FeSe in isolation should not. Our study opens a paradigm for a unified understanding what controls Tc in bulk, layers, and interfaces of Hund’s metals by hole pocket and electron screening cloud engineering.

High-pressure phase diagrams of FeSe1-xTex: correlation between suppressed nematicity and enhanced superconductivity

The interplay among magnetism, electronic nematicity, and superconductivity is the key issue in strongly correlated materials including iron-based, cuprate, and heavy-fermion superconductors. Magnetic fluctuations have been widely discussed as a pairing mechanism of unconventional superconductivity, but recent theory predicts that quantum fluctuations of nematic order may also promote high-temperature superconductivity. This has been studied in FeSe_1−xS_x superconductors exhibiting nonmagnetic nematic and pressure-induced antiferromagnetic orders, but its abrupt suppression of superconductivity at the nematic end point leaves the nematic-fluctuation driven superconductivity unconfirmed. Here we report on systematic studies of high-pressure phase diagrams up to 8 GPa in high-quality single crystals of FeSe_1−xTe_x. When Te composition x(Te) becomes larger than 0.1, the high-pressure magnetic order disappears, whereas the pressure-induced superconducting dome near the nematic end point is continuously found up to x(Te) ≈ 0.5. In contrast to FeSe_1−xS_x, enhanced superconductivity in FeSe_1−xTe_x does not correlate with magnetism but with the suppression of nematicity, highlighting the paramount role of nonmagnetic nematic fluctuations for high-temperature superconductivity in this system.

Despite studies in FeSe_1−xS_x, it is yet unconfirmed whether nematic fluctuation can induce superconductivity. Here, the authors study single crystals of FeSe_1−xTe_x showing enhanced superconductivity upon suppression of nematicity.

Spatially dispersing Yu-Shiba-Rusinov states in the unconventional superconductor FeTe0.55Se0.45

By using scanning tunneling microscopy (STM) we find and characterize dispersive, energy-symmetric in-gap states in the iron-based superconductor FeTe_0.55Se_0.45, a material that exhibits signatures of topological superconductivity, and Majorana bound states at vortex cores or at impurity locations. We use a superconducting STM tip for enhanced energy resolution, which enables us to show that impurity states can be tuned through the Fermi level with varying tip-sample distance. We find that the impurity state is of the Yu-Shiba-Rusinov (YSR) type, and argue that the energy shift is caused by the low superfluid density in FeTe_0.55Se_0.45, which allows the electric field of the tip to slightly penetrate the sample. We model the newly introduced tip-gating scenario within the single-impurity Anderson model and find good agreement to the experimental data.