Dome-shaped magnetic order competing with high-temperature superconductivity at high pressures in FeSe

Lifting of Gap Nodes by Disorder in Tetragonal FeSe_{1-x}S_{x} Superconductors

The observation of time-reversal symmetry breaking and large residual density of states in tetragonal FeSe_{1-x}S_{x} suggests a novel type of ultranodal superconducting state with Bogoliubov Fermi surfaces (BFSs). Although such BFSs in centrosymmetric superconductors are expected to be topologically protected, the impurity effect of this exotic superconducting state remains elusive experimentally. Here, we investigate the impact of controlled defects introduced by electron irradiation on the superconducting state of tetragonal FeSe_{1-x}S_{x} (0.18≤x≤0.25). The temperature dependence of magnetic penetration depth is initially consistent with a model with BFSs in the pristine sample. After irradiation, we observe a nonmonotonic evolution of low-energy excitations with impurity concentrations. This nonmonotonic change indicates a transition from nodal to nodeless, culminating in gapless with Andreev bound states, reminiscent of the nodal s_{±} case. This points to the accidental nature of the possible BFSs in tetragonal FeSe_{1-x}S_{x}, which are susceptible to disruption by the disorder.

Bulk high-temperature superconductivity in pressurized tetragonal La2PrNi2O7

The Ruddlesden-Popper (R-P) bilayer nickelate, La3Ni2O7, was recently found to show signatures of high-temperature superconductivity (HTSC) at pressures above 14 GPa (ref. 1). Subsequent investigations achieved zero resistance in single-crystalline and polycrystalline samples under hydrostatic pressure conditions2-4. Yet, obvious diamagnetic signals, the other hallmark of superconductors, are still lacking owing to the filamentary nature with low superconducting volume fraction2,4,5. The presence of a new 1313 polymorph and competing R-P phases obscured proper identification of the phase for HTSC6-9. Thus, achieving bulk HTSC and identifying the phase at play are the most prominent tasks. Here we address these issues in the praseodymium (Pr)-doped La2PrNi2O7 polycrystalline samples. We find that substitutions of Pr for La effectively inhibit the intergrowth of different R-P phases, resulting in a nearly pure bilayer structure. For La2PrNi2O7, pressure-induced orthorhombic to tetragonal structural transition takes place at Pc ≈ 11 GPa, above which HTSC emerges gradually on further compression. The superconducting transition temperatures at 18-20 GPa reachT c onset = 82.5 K andT c zero = 60 K , which are the highest values, to our knowledge, among known nickelate superconductors. Importantly, bulk HTSC was testified by detecting clear diamagnetic signals below about 75 K with appreciable superconducting shielding volume fractions at a pressure of above 15 GPa. Our results not only resolve the existing controversies but also provide directions for exploring bulk HTSC in the bilayer nickelates.

The origin of the large T c variation in FeSe thin films probed by dual-beam pulsed laser deposition

FeSe is one of the most enigmatic superconductors. Among the family of iron-based compounds, it has the simplest chemical makeup and structure, and yet it displays superconducting transition temperature ( T c ) spanning 0 to 15 K for thin films, while it is typically 8 K for single crystals. This large variation of T c within one family underscores a key challenge associated with understanding superconductivity in iron chalcogenides. Here, using a dual-beam pulsed laser deposition (PLD) approach, we have fabricated a unique lattice-constant gradient thin film of FeSe which has revealed a clear relationship between the atomic structure and the superconducting transition temperature for the first time. The dual-beam PLD that generates laser fluence gradient inside the plasma plume has resulted in a continuous variation in distribution of edge dislocations within a single film, and a precise correlation between the lattice constant and T c has been observed here, namely, T c ∝ c - c 0 , where c is the c-axis lattice constant (and c 0 is a constant). This explicit relation in conjunction with a theoretical investigation indicates that it is the shifting of the d xy orbital of Fe which plays a governing role in the interplay between nematicity and superconductivity in FeSe.

Supplementary Information

The online version contains supplementary material available at 10.1007/s44214-024-00058-0.

Pressure-Modulated Structural and Magnetic Phase Transitions in Two-Dimensional FeTe: Tetragonal and Hexagonal Polymorphs

Two-dimensional (2D) Fe chalcogenides with their rich structures and properties are highly desirable for revealing the torturous transition mechanism of Fe chalcogenides and exploring their potential applications in spintronics and nanoelectronics. Hydrostatic pressure can effectively stimulate phase transitions between various ordered states, allowing one to successfully plot a phase diagram for a given material. Herein, the structural evolution and transport characteristics of 2D FeTe were systematically investigated under extreme conditions by comparing two distinct symmetries, i.e., tetragonal (t) and hexagonal (h) FeTe. We found that t-FeTe presented a pressure-induced transition from an antiferromagnetic state to a ferromagnetic state at ∼3 GPa, corresponding to the tetragonal collapse of the layered structure. Contrarily, the ferromagnetic order of h-FeTe was retained up to 15 GPa, which was evidently confirmed by electrical transport and Raman measurements. Furthermore, T-P phase diagrams for t-FeTe and h-FeTe were mapped under delicate critical conditions. Our results can provide a unique platform to elaborate the extraordinary properties of Fe chalcogenides and further develop their applications.

Spontaneous orbital polarization in the nematic phase of FeSe

The origin of nematicity in FeSe remains a critical outstanding question towards understanding unconventional superconductivity in proximity to nematic order. To understand what drives the nematicity, it is essential to determine which electronic degree of freedom admits a spontaneous order parameter independent from the structural distortion. Here we use X-ray linear dichroism at the Fe K pre-edge to measure the anisotropy of the 3d orbital occupation as a function of in situ applied stress and temperature across the nematic transition. Along with using X-ray diffraction to precisely quantify the strain state, we reveal a lattice-independent, spontaneously ordered orbital polarization within the nematic phase, as well as an orbital polarizability that diverges as the transition is approached from above. These results provide strong evidence that spontaneous orbital polarization serves as the primary order parameter of the nematic phase.

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.

Review of Single Crystal Synthesis of 11 Iron-Based Superconductors

The 11 system in the iron-based superconducting family has become one of the most extensively studied materials in the research of high-temperature superconductivity, due to their simple structure and rich physical properties. Many exotic properties, such as multiband electronic structure, electronic nematicity, topology and antiferromagnetic order, provide strong support for the theory of high-temperature superconductivity, and have been at the forefront of condensed matter physics in the past decade. One noteworthy aspect is that a high upper critical magnetic field, large critical current density and lower toxicity give the 11 system good application prospects. However, the research on 11 iron-based superconductors faces numerous obstacles, mainly stemming from the challenges associated with producing high-quality single crystals. Since the discovery of FeSe superconductivity in 2008, researchers have made significant progress in crystal growth, overcoming the hurdles that initially impeded their studies. Consequently, they have successfully established the complete phase diagrams of 11 iron-based superconductors, including FeSe_1-xTe_x, FeSe_1-xS_x and FeTe_1-xS_x. In this paper, we aim to provide a comprehensive summary of the preparation methods employed for 11 iron-based single crystals over the past decade. Specifically, we will focus on hydrothermal, chemical vapor transport (CVT), self-flux and annealing methods. Additionally, we will discuss the quality, size, and superconductivity properties exhibited by single crystals obtained through different preparation methods. By exploring these aspects, we can gain a better understanding of the advantages and limitations associated with each technique. High-quality single crystals serve as invaluable tools for advancing both the theoretical understanding and practical utilization of high-temperature superconductivity.

Modulations in Superconductors: Probes of Underlying Physics

The importance of modulations is elevated to an unprecedented level, due to the delicate conditions required to bring out exotic phenomena in quantum materials, such as topological materials, magnetic materials, and superconductors. Recently, state-of-the-art modulation techniques in material science, such as electric-double-layer transistor, piezoelectric-based strain apparatus, angle twisting, and nanofabrication, have been utilized in superconductors. They not only efficiently increase the tuning capability to the broader ranges but also extend the tuning dimensionality to unprecedented degrees of freedom, including quantum fluctuations of competing phases, electronic correlation, and phase coherence essential to global superconductivity. Here, for a comprehensive review, these techniques together with the established modulation methods, such as elemental substitution, annealing, and polarization-induced gating, are contextualized. Depending on the mechanism of each method, the modulations are categorized into stoichiometric manipulation, electrostatic gating, mechanical modulation, and geometrical design. Their recent advances are highlighted by applications in newly discovered superconductors, e.g., nickelates, Kagome metals, and magic-angle graphene. Overall, the review is to provide systematic modulations in emergent superconductors and serve as the coordinate for future investigations, which can stimulate researchers in superconductivity and other fields to perform various modulations toward a thorough understanding of quantum materials.

Pressure Dependence of Superconductivity in a Charge-Density-Wave Superconductor Bi2Rh3Se2

The structural and superconducting properties of a Bi-based compound, Bi₂Rh₃Se₂, are investigated over a wide pressure range. Bi₂Rh₃Se₂ is a superconductor with a superconducting transition temperature, T_c, of 0.7 K. This compound is in a charge-density-wave (CDW) state below 240 K, which implies the coexistence of superconducting and CDW states at low temperatures. Here, the superconducting properties of Bi₂Rh₃Se₂ are studied from the perspective of the temperature dependence of electrical resistance (R) at high pressures (p's). The pressure dependence of T_c of Bi₂Rh₃Se₂ shows a slow increase in T_c at 0-15.5 GPa, and the T_c slowly decreases with pressure above 15.5 GPa, which is markedly different from that of normal superconductors because the value of T_c should simply decrease owing to the decrease in density of states (DOS) on the Fermi level, N(ε_F), driven by a simple shrinkage of the lattice under pressure. To ascertain the origin of such a dome-like T_c-p behavior, the crystal structure of Bi₂Rh₃Se₂ was explored over a wide pressure range of 0-20 GPa on the basis of powder X-ray diffraction; no structural phase transitions or simple shrinkage of the lattice was observed. This result implies that the increase in T_c against pressure cannot simply be explained from a structural point of view. In other words, a direct relation between superconductivity and crystal structure was not found. On the other hand, the CDW transition became ambiguous at pressures higher than 3.8 GPa, suggesting that the T_c had been suppressed by the CDW transition in a low pressure range. Thus, the findings suggest that for Bi₂Rh₃Se₂, T_c is enhanced through the suppression of CDW transition, which may be reasonable because the CDW-ordered state restrains the charge fluctuation to weaken the electron-phonon coupling and opens the gap to decrease the density of states on the Fermi level. The obtained dome-like T_c-p behavior indicates the possibility of Bi₂Rh₃Se₂ being an exotic superconductor.

Fermiology and Origin of T_{c} Enhancement in a Kagome Superconductor Cs(V_{1-x}Nb_{x})_{3}Sb_{5}

Kagome metals AV_{3}Sb_{5} (A=K, Rb, and Cs) exhibit a characteristic superconducting ground state coexisting with a charge density wave (CDW), whereas the mechanisms of the superconductivity and CDW have yet to be clarified. Here we report a systematic angle-resolved photoemission spectroscopy (ARPES) study of Cs(V_{1-x}Nb_{x})_{3}Sb_{5} as a function of Nb content x, where isovalent Nb substitution causes an enhancement of superconducting transition temperature (T_{c}) and the reduction of CDW temperature (T_{CDW}). We found that the Nb substitution shifts the Sb-derived electron band at the Γ point downward and simultaneously moves the V-derived band around the M point upward to lift up the saddle point (SP) away from the Fermi level, leading to the reduction of the CDW-gap magnitude and T_{CDW}. This indicates a primary role of the SP density of states to stabilize the CDW. The present result also suggests that the enhancement of superconductivity by Nb substitution is caused by the cooperation between the expansion of the Sb-derived electron pocket and the recovery of the V-derived density of states at the Fermi level.

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.

Patterned diamond anvils prepared via laser writing for electrical transport measurements of thin quantum materials under pressure

Quantum materials exhibit intriguing properties with important scientific values and huge technological potential. Electrical transport measurements under hydrostatic pressure have been influential in unraveling the underlying physics of many quantum materials in bulk form. However, such measurements have not been applied widely to samples in the form of thin flakes, in which new phenomena can emerge, due to the difficulty in attaching fine wires to a thin sample suitable for high-pressure devices. Here, we utilize a home-built direct laser writing system to functionalize a diamond anvil to directly integrate the capability of conducting electrical transport measurements of thin flakes with a pressure cell. With our methodology, the culet of a diamond anvil is equipped with a set of custom-designed conducting tracks. We demonstrate the superiority of these tracks as electrodes for the studies of thin flakes by presenting the measurement of pressure-enhanced superconductivity and quantum oscillations in a flake of MoTe₂.

Pressure-induced monotonic enhancement of Tc to over 30 K in superconducting Pr0.82Sr0.18NiO2 thin films

The successful synthesis of superconducting infinite-layer nickelate thin films with the highest T_c ≈ 15 K has ignited great enthusiasm for this material class as potential analogs of the high-T_c cuprates. Pursuing a higher T_c is always an imperative task in studying a new superconducting material system. Here we report high-quality Pr_0.82Sr_0.18NiO₂ thin films with T_c^onset ≈ 17 K synthesized by carefully tuning the amount of CaH₂ in the topotactic chemical reduction and the effect of pressure on its superconducting properties by measuring electrical resistivity under various pressures in a cubic anvil cell apparatus. We find that the onset temperature of the superconductivity, T_c^onset, can be enhanced monotonically from ~17 K at ambient pressure to ~31 K at 12.1 GPa without showing signatures of saturation upon increasing pressure. This encouraging result indicates that the T_c of infinite-layer nickelates superconductors still has room to go higher and it can be further boosted by applying higher pressures or strain engineering in the heterostructure films.

Suppression of Superconductivity and Nematic Order in Fe1-ySe1-xSx (0 ≤ x ≤ 1; y ≤ 0.1) Crystals by Anion Height Disorder

Connections between crystal chemistry and critical temperature T_c have been in the focus of superconductivity, one of the most widely studied phenomena in physics, chemistry, and materials science alike. In most Fe-based superconductors, materials chemistry and physics conspire so that T_c correlates with the average anion height above the Fe plane, i.e., with the geometry of the FeAs₄ or FeCh₄ (Ch = Te, Se, or S) tetrahedron. By synthesizing Fe_1-ySe_1-xS_x (0 ≤ x ≤ 1; y ≤ 0.1), we find that in alloyed crystals T_c is not correlated with the anion height like it is for most other Fe superconductors. Instead, changes in T_c(x) and tetragonal-to-orthorhombic (nematic) transition T_s(x) upon cooling are correlated with disorder in Fe vibrations in the direction orthogonal to Fe planes, along the crystallographic c-axis. The disorder stems from the random nature of S substitution, causing deformed Fe(Se,S)₄ tetrahedra with different Fe-Se and Fe-S bond distances. Our results provide evidence of T_c and T_s suppression by disorder in anion height. The connection to local crystal chemistry may be exploited in computational prediction of new superconducting materials with FeSe/S building blocks.

Magnetic Anisotropy Control with Curie Temperature above 400 K in a van der Waals Ferromagnet for Spintronic Device

The technological appeal of van der Waals ferromagnetic materials is the ability to control magnetism under external fields with desired thickness toward novel spintronic applications. For practically useful devices, ferromagnetism above room temperature or tunable magnetic anisotropy is highly demanded but remains challenging. To date, only a few layered materials exhibit unambiguous ferromagnetic ordering at room temperature via gating techniques or interface engineering. Here, it is demonstrated that the magnetic anisotropy control and dramatic modulation of Curie temperature (T_c ) up to 400 K are realized in layered Fe₅ GeTe₂ via the high-pressure diamond-anvil-cell technique. Magnetic phases manifesting with in-plane anisotropic, out-of-plane anisotropic and nearly isotropic magnetic states can be tuned in a controllable way, depicted by the phase diagram with a maximum T_c up to 360 K. Remarkably, the T_c can be gradually enhanced to above 400 K owing to the Fermi surface evolution during a pressure loading-deloading process. Such an observation sheds light on the understanding and control of emergent magnetic states in practical spintronic applications.

Pure nematic quantum critical point accompanied by a superconducting dome

SignificanceThe notion of the quantum critical point (QCP) is at the core of modern condensed matter physics. Near a QCP of the symmetry-breaking order, associated quantum-mechanical fluctuations are intensified, which can lead to unconventional superconductivity. Indeed, dome-shaped superconducting phases are often observed near the magnetic QCPs, which supports the spin fluctuation-driven superconductivity. However, the fundamental question remains as to whether a nonmagnetic QCP of electronic nematic order characterized by spontaneous rotational symmetry breaking can promote superconductivity in real materials. Here, we provide an experimental demonstration that a pure nematic QCP exists near the center of a superconducting dome in nonmagnetic FeSe[Formula: see text] Te_x. This result evidences that nematic fluctuations enhanced around the nematic QCP can boost superconductivity.

Research Progress of FeSe-based Superconductors Containing Ammonia/Organic Molecules Intercalation

As an important part of Fe-based superconductors, FeSe-based superconductors have become a hot field in condensed matter physics. The exploration and preparation of such superconducting materials form the basis of studying their physical properties. With the help of various alkali/alkaline-earth/rare-earth metals, different kinds of ammonia/organic molecules have been intercalated into the FeSe layer to form a large number of FeSe-based superconductors with diverse structures and different layer spacing. Metal cations can effectively provide carriers to the superconducting FeSe layer, thus significantly increasing the superconducting transition temperature. The orientation of organic molecules often plays an important role in structural modification and can be used to fine-tune superconductivity. This review introduces the crystal structures and superconducting properties of several typical FeSe-based superconductors containing ammonia/organic molecules intercalation discovered in recent years, and the effects of FeSe layer spacing and superconducting transition temperature are briefly summarized.

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.

Two distinct superconducting states controlled by orientations of local wrinkles in LiFeAs

For iron-based superconductors, the phase diagrams under pressure or strain exhibit emergent phenomena between unconventional superconductivity and other electronic orders, varying in different systems. As a stoichiometric superconductor, LiFeAs has no structure phase transitions or entangled electronic states, which manifests an ideal platform to explore the pressure or strain effect on unconventional superconductivity. Here, we observe two types of superconducting states controlled by orientations of local wrinkles on the surface of LiFeAs. Using scanning tunneling microscopy/spectroscopy, we find type-I wrinkles enlarge the superconducting gaps and enhance the transition temperature, whereas type-II wrinkles significantly suppress the superconducting gaps. The vortices on wrinkles show a C₂ symmetry, indicating the strain effects on the wrinkles. By statistics, we find that the two types of wrinkles are categorized by their orientations. Our results demonstrate that the local strain effect with different directions can tune the superconducting order parameter of LiFeAs very differently, suggesting that the band shifting induced by directional pressure may play an important role in iron-based superconductivity.

The evolution of superconductivity in LiFeAs with respect to pressure or strain remains elusive. Here, the authors observe different response of superconducting states due to different orientations of local wrinkles on the surface of LiFeAs.

Pressure-induced reconstitution of Fermi surfaces and spin fluctuations in S-substituted FeSe

FeSe is a unique high-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_c$$\end{document}Tc iron-based superconductor in which nematicity, superconductivity, and magnetism are entangled with each other in the P-T phase diagram. We performed \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{77}$$\end{document}77Se-nuclear magnetic resonance measurements under pressures of up to 3.9 GPa on 12% S-substituted FeSe, in which the complex overlap between the nematicity and magnetism are resolved. A pressure-induced Lifshitz transition was observed at 1.0 GPa as an anomaly of the density of states and as double superconducting (SC) domes accompanied by different types of antiferromagnetic (AF) fluctuations. The low-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{c}}$$\end{document}Tc SC dome below 1 GPa is accompanied by strong AF fluctuations, whereas the high-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{c}}$$\end{document}Tc SC dome develops above 1 GPa, where AF fluctuations are fairly weak. These results suggest the importance of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d_{xy}$$\end{document}dxy orbital and its intra-orbital coupling for the high-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T_{\mathrm{c}}$$\end{document}Tc superconductivity.

Double Superconducting Dome and Triple Enhancement of T_{c} in the Kagome Superconductor CsV_{3}Sb_{5} under High Pressure

CsV_{3}Sb_{5} is a newly discovered Z_{2} topological kagome metal showing the coexistence of a charge-density-wave (CDW)-like order at T^{*}=94  K and superconductivity (SC) at T_{c}=2.5  K at ambient pressure. Here, we study the interplay between CDW and SC in CsV_{3}Sb_{5} via measurements of resistivity, dc and ac magnetic susceptibility under various pressures up to 6.6 GPa. We find that the CDW transition decreases with pressure and experience a subtle modification at P_{c1}≈0.6-0.9  GPa before it vanishes completely at P_{c2}≈2  GPa. Correspondingly, T_{c}(P) displays an unusual M-shaped double dome with two maxima around P_{c1} and P_{c2}, respectively, leading to a tripled enhancement of T_{c} to about 8 K at 2 GPa. The obtained temperature-pressure phase diagram resembles those of unconventional superconductors, illustrating an intimated competition between CDW-like order and SC. The competition is found to be particularly strong for the intermediate pressure range P_{c1}≤P≤P_{c2} as evidenced by the broad superconducting transition and reduced superconducting volume fraction. The modification of CDW order around P_{c1} has been discussed based on the band structure calculations. This work not only demonstrates the potential to raise T_{c} of the V-based kagome superconductors, but also offers more insights into the rich physics related to the electron correlations in this novel family of topological kagome metals.

Recent Advances in 2D Superconductors

The emergence of superconductivity in 2D materials has attracted much attention and there has been rapid development in recent years because of their fruitful physical properties, such as high transition temperature (T_c ), continuous phase transition, and enhanced parallel critical magnetic field (B_c ). Tremendous efforts have been devoted to exploring different physical parameters to figure out the mechanisms behind the unexpected superconductivity phenomena, including adjusting the thickness of samples, fabricating various heterostructures, tuning the carrier density by electric field and chemical doping, and so on. Here, different types of 2D superconductivity with their unique characteristics are introduced, including the conventional Bardeen-Cooper-Schrieffer superconductivity in ultrathin films, high-T_c superconductivity in Fe-based and Cu-based 2D superconductors, unconventional superconductivity in newly discovered twist-angle bilayer graphene, superconductivity with enhanced B_c , and topological superconductivity. A perspective toward this field is then proposed based on academic knowledge from the recently reported literature. The aim is to provide researchers with a clear and comprehensive understanding about the newly developed 2D superconductivity and promote the development of this field much further.

Incommensurate smectic phase in close proximity to the high-Tc superconductor FeSe/SrTiO3

Superconductivity is significantly enhanced in monolayer FeSe grown on SrTiO₃, but not for multilayer films, in which large strength of nematicity develops. However, the link between the high-transition temperature superconductivity in monolayer and the correlation related nematicity in multilayer FeSe films is not well understood. Here, we use low-temperature scanning tunneling microscopy to study few-layer FeSe thin films grown by molecular beam epitaxy. We observe an incommensurate long-range smectic phase, which solely appears in bilayer FeSe films. The smectic order still locally exists and gradually fades away with increasing film thickness, while it suddenly vanishes in monolayer FeSe, indicative of an abrupt smectic phase transition. Surface alkali-metal doping can suppress the smectic phase and induce high-T_c superconductivity in bilayer FeSe. Our observations provide evidence that the monolayer FeSe is in close proximity to the smectic phase, and its superconductivity is likely enhanced by this electronic instability as well.

The relation between enhanced superconductivity in monolayer FeSe grown on SrTiO₃ and the large nematicity in multilayer FeSe on SrTiO₃ remains not well understood. Here, the authors observe a long-range smectic phase in bilayer FeSe films but vanishes in monolayer FeSe, providing a new instability to help enhance the superconductivity.

Tracing the ionic evolution during ILG induced phase transformation in strontium cobaltite thin films

Ionic liquid gating (ILG) that drives the ions incorporate into or extract from the crystal lattice, has emerged as a new pathway to design materials. Although many intriguing emergent phenomena, novel physical properties and functionalities have been obtained, the gating mechanism governing the ion and charge transport remains unexplored. Here, by using the model system of brownmillerite SrCoO_2.5 and the corresponding electric-field controlled tri-state phase transformation among the pristine SrCoO_2.5, hydrogenated HSrCoO_2.5 and oxidized perovskite SrCoO_3-δ through the dual ion switch, the ionic diffusion and electronic transport processes were carefully investigated. Through controlling gating experiment by design, we find out that the collaborative interaction between charge transport and ion diffusion plays an essential role to prompt the hydrogen or oxygen ions incorporate into the crystal lattice of SrCoO_2.5, and therefore leading to formation of new phases. At region closer to the electrode, the electron can shuttle more readily in (out) the material, correspondingly the incorporation of hydrogen (oxygen) ions and phase transformation is largely affiliated. With the compensated charge of electron as well as the reaction front gradually moving away from the electrode, the new phases would be developed successively across the entire thin film. This result unveils the underlying mechanism in the electric-field control of ionic incorporation and extraction, and therefore provides important strategy to achieve high efficient design of material functionalities in complex oxide materials.

Observation of an electronic order along [110] direction in FeSe

Multiple ordered states have been observed in unconventional superconductors. Here, we apply scanning tunneling microscopy to probe the intrinsic ordered states in FeSe, the structurally simplest iron-based superconductor. Besides the well-known nematic order along [100] direction, we observe a checkerboard charge order in the iron lattice, which we name a [110] electronic order in FeSe. The [110] electronic order is robust at 77 K, accompanied with the rather weak [100] nematic order. At 4.5 K, The [100] nematic order is enhanced, while the [110] electronic order forms domains with reduced correlation length. In addition, the collective [110] order is gaped around [−40, 40] meV at 4.5 K. The observation of this exotic electronic order may shed new light on the origin of the ordered states in FeSe.

Understanding the relation of different electronic orders in high temperature superconductors is of fundamental interest. Here, the authors observe a checkerboard charge order along [110] direction of FeSe.

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.

On the Remarkable Superconductivity of FeSe and Its Close Cousins

Emergent electronic phenomena in iron-based superconductors have been at the forefront of condensed matter physics for more than a decade. Much has been learned about the origins and intertwined roles of ordered phases, including nematicity, magnetism, and superconductivity, in this fascinating class of materials. In recent years, focus has been centered on the peculiar and highly unusual properties of FeSe and its close cousins. This family of materials has attracted considerable attention due to the discovery of unexpected superconducting gap structures, a wide range of superconducting critical temperatures, and evidence for nontrivial band topology, including associated spin-helical surface states and vortex-induced Majorana bound states. Here, we review superconductivity in iron chalcogenide superconductors, including bulk FeSe, doped bulk FeSe, FeTe1−xSex, intercalated FeSe materials, and monolayer FeSe and FeTe1−xSex on SrTiO3. We focus on the superconducting properties, including a survey of the relevant experimental studies, and a discussion of the different proposed theoretical pairing scenarios. In the last part of the paper, we review the growing recent evidence for nontrivial topological effects in FeSe-related materials, focusing again on interesting implications for superconductivity.

Fluctuations and pairing in Fe-based superconductors: light scattering experiments

Inelastic scattering of visible light (Raman effect) offers a window into properties of correlated metals such as spin, electron and lattice dynamics as well as their mutual interactions. In this review we focus on electronic and spin excitations in Fe-based pnictides and chalcogenides, in particular but not exclusively superconductors. After a general introduction to the basic theory including the selection rules for the various scattering processes we provide an overview over the major experimental results. In the superconducting state below the transition temperatureTcthe pair-breaking effect can be observed, and the gap energies may be derived and associated with the gaps on the electron and hole bands. In spite of the similarities of the overall band structures the results are strongly dependent on the family and may even change qualitatively within one family. In some of the compounds strong collective modes appear belowTc. In Ba1-xKxFe2As2, which has the most isotropic gap of all Fe-based superconductors, there are indications that these modes are exciton-like states appearing in the presence of a hierarchy of pairing tendencies. The strong in-gap modes observed in Co-doped NaFeAs are interpreted in terms of quadrupolar orbital excitations which become undamped in the superconducting state. The doping dependence of the scattering intensity in Ba(Fe1-xCox)2As2is associated with a nematic resonance above a quantum critical point and interpreted in terms of a critical enhancement at the maximalTc. In the normal state the response from particle-hole excitations reflects the resistivity. In addition, there are strongly temperature-dependent contributions from presumably critical fluctuations in the energy range ofkBTwhich can be compared to the elastic properties. Currently it is not settled whether the fluctuations observed by light scattering are related to spin or charge. Another controversy relates to putative two-magnon excitations, typically in the energy range below 0.5 eV. Whereas this response presumably originates from charge excitations in most of the Fe-based compounds theory and experiment suggest that the excitations in the 60 meV range in FeSe stem from localized spins in a nearly frustrated system.

Fabrication and evaluation via nuclear quadrupole resonance of a palm cubic-anvil pressure cell

A "palm" cubic-anvil pressure cell (PCAC) having an outer diameter of 60 mm, the smallest cubic-anvil cell to date, was fabricated to insert in a large-bore superconducting magnet. The pressure cell has a sample space of ϕ 2.5 × 1.5 mm², which is fairly large for a pressure cell that can reach a high pressure above 4 GPa. Pressure homogeneity was monitored from the ⁶³Cu nuclear-quadrupole-resonance linewidth of Cu₂O up to 6.7 GPa. The linewidth first increased with increasing pressure up to 4 GPa and then saturated above 4 GPa. The pressure homogeneity was better than that of a piston-cylinder pressure cell. The PCAC is advantageous because a large sample space and high pressure homogeneity are secured even at high pressures.

Visualization of Local Magnetic Moments Emerging from Impurities in Hund's Metal States of FeSe

Understanding the origin of the magnetism of high temperature superconductors is crucial for establishing their unconventional pairing mechanism. Recently, theory predicts that FeSe is close to a magnetic quantum critical point, and thus weak perturbations such as impurities could induce local magnetic moments. To elucidate such quantum instability, we have employed scanning tunneling microscopy and spectroscopy. In particular, we have grown FeSe film on superconducting Pb(111) using molecular beam epitaxy and investigated magnetic excitation caused by impurities in the proximity-induced superconducting gap of FeSe. Our study provides deep insight into the origin of the magnetic ordering of FeSe by showing the way local magnetic moments develop in response to impurities near the magnetic quantum critical point.

Observation of a C-type short-range antiferromagnetic order in layer spacing expanded FeS

We report neutron diffraction studies of FeS single crystals obtained from Rb _x Fe_2-y S₂ single crystals via a hydrothermal method. While no 5 × 5 iron vacancy order or block antiferromagnetic order typical of Rb _x Fe_2-y S₂ is found in our samples, we observe C-type short-range antiferromagnetic order with moments pointed along the c axis hosted by a different phase of FeS with an expanded interlayer spacing. The Néel temperature for this magnetic order is determined to be 170 ± 4 K. Our finding of a variant FeS structure hosting this C-type antiferromagnetic order demonstrates that the known FeS phase synthesized in this method is in the vicinity of a magnetically ordered ground state, providing insights into understanding a variety of phenomena observed in FeS and the related FeSe_1-x S _x iron chalcogenide system.

Highly-Tunable Crystal Structure and Physical Properties in FeSe-Based Superconductors

Here, crystal structure, electronic structure, chemical substitution, pressure-dependent superconductivity, and thickness-dependent properties in FeSe-based superconductors are systemically reviewed. First, the superconductivity versus chemical substitution is reviewed, where the doping at Fe or Se sites induces different effects on the superconducting critical temperature (Tc). Meanwhile, the application of high pressure is extremely effective in enhancing Tc and simultaneously induces magnetism. Second, the intercalated-FeSe superconductors exhibit higher Tc from 30 to 46 K. Such an enhancement is mainly caused by the charge transfer from the intercalated organic and inorganic layer. Finally, the highest Tc emerging in single-unit-cell FeSe on the SrTiO3 substrate is discussed, where electron-phonon coupling between FeSe and the substrate could enhance Tc to as high as 65 K or 100 K. The step-wise increment of Tc indicates that the synergic effect of carrier doping and electron-phonon coupling plays a critical role in tuning the electronic structure and superconductivity in FeSe-based superconductors.

Bulk Superconductivity and Role of Fluctuations in the Iron-Based Superconductor FeSe at High Pressures

The iron-based superconductor FeSe offers a unique possibility to study the interplay of superconductivity with purely nematic as well magnetic-nematic order by pressure (p) tuning. By measuring specific heat under p up to 2.36 GPa, we study the multiple phases in FeSe using a thermodynamic probe. We conclude that superconductivity is bulk across the entire p range and competes with magnetism. In addition, whenever magnetism is present, fluctuations exist over a wide temperature range above both the bulk superconducting and the magnetic transitions. Whereas the magnetic fluctuations are likely temporal, the superconducting fluctuations may be either temporal or spatial. These observations highlight similarities between FeSe and underdoped cuprate superconductors.

Extended Magnetic Dome Induced by Low Pressures in Superconducting FeSe_{1-x}S_{x}

We report muon spin rotation and magnetization measurements under pressure on Fe_{1+δ}Se_{1-x}S_{x} with x≈0.11. Above p≈0.6  GPa we find a microscopic coexistence of superconductivity with an extended dome of long range magnetic order that spans a pressure range between previously reported separated magnetic phases. The magnetism initially competes on an atomic scale with the coexisting superconductivity leading to a local maximum and minimum of the superconducting T_{c}(p). The maximum of T_{c} corresponds to the onset of magnetism while the minimum coincides with the pressure of strongest competition. A shift of the maximum of T_{c}(p) for a series of single crystals with x up to 0.14 roughly extrapolates to a putative magnetic and superconducting state at ambient pressure for x≥0.2.

Pressure-induced Lifshitz transition in FeSe$_{0.88}$S$_{0.12}$ probed via $^{77}$Se-NMR

Recently, FeSe$_{1-x}$S$_x$ systems have received much attention because of the unique pressure-temperature phase diagram. We performed $^{77}$Se-NMR measurements on a single crystal of FeSe$_{0.88}$S$_{0.12}$ to investigate its microscopic properties. The shift of $^{77}$Se spectra exhibits anomalous enhancement at $1.0~\mathrm{GPa}$, suggesting a topological change in the Fermi surfaces, so-called Lifshitz transition, occurs at $1.0~\mathrm{GPa}$. The magnetic fluctuation simultaneously changes its properties, which implies a change in the dominant nesting vector. Edited by: A. Goñi, A. Cantarero, J. S. Reparaz

High-pressure polymorphism of BaFe2Se3

BaFe₂Se₃ is a potential superconductor material exhibiting transition at 11 K and ambient pressure. Here we extended the structural and performed electrical resistivity measurements on this compound up to 51 GPa and 20 GPa, respectively, in order to distinguish if the superconductivity in this sample is intrinsic to the BaFe₂Se₃ phase or if it is originating from minor FeSe impurities that show a similar superconductive transition temperature. The electrical resistance measurements as a function of pressure show that at 5 GPa the superconducting transition is observed at around 10 K, similar to the one previously observed for this sample at ambient pressure. This indicates that the superconductivity in this sample is most likely intrinsic to the BaFe₂Se₃ phase and not to FeSe with T _c  >  20 K at these pressures. Further increase in pressure suppressed the superconductive signal and the sample remained in an insulating state up to the maximum achieved pressure of 20 GPa. Single-crystal and powder x-ray diffraction measurements revealed two structural transformations in BaFe₂Se₃: a second order transition above 3.5 GPa from Pnma (CsAg₂I₃-type structure) to Cmcm (CsCu₂Cl₃-type structure) and a first order transformation at 16.6 GPa. Here, γ-BaFe₂Se₃ transforms into δ-BaFe₂Se₃ (Cmcm, CsCu₂Cl₃-type average structure) via a first order phase transition mechanism. This transition is characterized by a significant shortening of the b lattice parameter of γ-BaFe₂Se₃ (17%) and accompanied by an anisotropic expansion in the orthogonal ac plane at the transition point.

Effect of pressure on the self-hole-doped superconductor RbGd2Fe4As4O2

RbGd₂Fe₄As₄O₂ is a newly discovered self-hole-doped stoichiometric superconductor, which has a hybrid structure with separated double FeAs layers and exhibits a high superconducting transition temperature T _c  =  35 K. Here, we report the effect of pressure (P) on its T _c and normal-state transport properties by measuring the temperature dependence of resistivity ρ(T) under various pressures up to 14 GPa with a cubic anvil cell apparatus. We found that the T _c is suppressed monotonically to ca. 12.5 K upon increasing pressure to 14 GPa with a slope change of T _c(P) at around 4 GPa. In addition, the low-temperature normal-state ρ(T), which is proportional to T ⁿ , also evolves gradually from a non-Fermi-liquid with n  =  1 at ambient pressure to a Fermi liquid with n  =  2 at P  ⩾  4 GPa. Accompanying with the non-Fermi-liquid to Fermi-liquid crossover, the quadratic temperature coefficient of resistivity, which reflects the effective mass of charge carriers, also experiences a significant reduction as commonly observed in the vicinity of a magnetic quantum critical point (QCP). Our results indicate that the stoichiometric RbGd₂Fe₄As₄O₂ at ambient pressure might be located near a QCP such that the enhanced critical spin fluctuations lead to high-T _c superconductivity. The application of pressure should broaden the electronic bandwidth and weaken the spin fluctuations, and then restore a Fermi-liquid ground state with lower T _c.

Unconventional Antiferromagnetic Quantum Critical Point in Ba(Fe_{0.97}Cr_{0.03})_{2}(As_{1-x}P_{x})_{2}

We have systematically studied physical properties of Ba(Fe_{0.97}Cr_{0.03})_{2}(As_{1-x}P_{x})_{2}, where superconductivity in BaFe_{2}(As_{1-x}P_{x})_{2} is fully suppressed by just 3% of Cr substitution of Fe. A quantum critical point is revealed at x∼0.42, where non-Fermi-liquid behaviors similar to those in BaFe_{2}(As_{1-x}P_{x})_{2} are observed. Neutron diffraction and inelastic neutron scattering measurements suggest that the quantum critical point is associated with the antiferromagnetic order, which is not of conventional spin-density-wave type as evidenced by the ω/T scaling of spin excitations. On the other hand, no divergence of low-temperature nematic susceptibility is observed when x is decreased to 0.42 from higher doping level, demonstrating that there are no nematic quantum critical fluctuations. Our results suggest that non-Fermi-liquid behaviors in iron-based superconductors can be solely resulted from the antiferromagnetic quantum critical fluctuations, which cast doubts on the role of nematic fluctuations played in the normal-state properties in iron-based superconductors.

Realization of continuous electron doping in bulk iron selenides and identification of a new superconducting zone

It is known that iron selenide superconductors exhibit unique characteristics distinct from iron pnictides, especially in the electron-doped region. However, a comprehensive study of continuous carrier doping and the corresponding crystal structures of FeSe is still lacking, mainly due to the difficulties in controlling the carrier density in bulk materials. Here we report the successful synthesis of a new family of bulk Lix(C3N2H10)0.37FeSe, which features a continuous superconducting dome harboring Lifshitz transition within the wide range of 0.06 ⩽ x ⩽ 0.68 . We demonstrate that with electron doping, the anion height of FeSe layers deviates linearly away from the optimized values of pnictides and pressurized FeSe. This feature leads to a new superconducting zone with unique doping dependence of the electronic structures and strong orbital-selective electronic correlation. Optimal superconductivity is achieved when the F e 3 d t 2 g orbitals have almost the same intermediate electronic correlation strength, with moderate mass enhancement between 3 ~ 4 in the two separate superconducting zones. Our results shed new light on achieving unified mechanism of superconductivity in iron-based superconductors.

Unusual effects of Be doping in the iron-based superconductor FeSe

Recent superconducting transition temperatures (T _c) over 100 K for monolayer FeSe on SrTiO₃ have renewed interest in the bulk parent compound. In KCl:AlCl₃ flux-transport-grown crystals of FeSe_0.94Be_0.06, FeSe_0.97Be_0.03 and, for comparison, FeSe, this work reports doping of FeSe using Be-among the smallest of possible dopants, corresponding to an effective 'chemical pressure'. According to lattice parameter measurements, 6% Be doping shrank the tetragonal FeSe lattice equivalent to a physical pressure of 0.75 GPa. Using this flux-transport method of sample preparation, 6% of Be was the maximum amount of dopant achievable. At this maximal composition of FeSe_0.94Be_0.06, the lattice unit cell shrinks by 2.4%, T _c-measured in the bulk via specific heat-increases by almost 10%, the T _c versus pressure behavior shifts its peak [Formula: see text] downwards by ~1 GPa, the high temperature structural transition around T _S  =  89 K increases by 1.9 K (in contrast to other dopants in FeSe which uniformly depress T _S), and the low temperature specific heat γ increases by 10% compared to pure FeSe. Also, upon doping by 6% Be the residual resistivity ratio, ρ(300 K)/ρ(T  →  0), increases by almost a factor of four, while ρ(300 K)/ρ([Formula: see text]) increases by 50%.

Collapse of Critical Nematic Fluctuations in FeSe under Pressure

We report the evolution of the electronic nematic susceptibility in FeSe via Raman scattering as a function of hydrostatic pressure up to 5.8 GPa where the superconducting transition temperature T_{c} reaches its maximum. The critical nematic fluctuations observed at low pressure vanish above 1.6 GPa, indicating they play a marginal role in the fourfold enhancement of T_{c} at higher pressures. The collapse of nematic fluctuations appears to be linked to a suppression of low energy electronic excitations which manifests itself by optical phonon anomalies at around 2 GPa, in agreement with lattice dynamical and electronic structure calculations using local density approximation combined with dynamical mean field theory. Our results reveal two different regimes of nematicity in the phase diagram of FeSe under pressure: a d-wave Pomeranchuk instability of the Fermi surface at low pressure and a magnetic driven orthorhombic distortion at higher pressure.

Simple analytical model of the effect of high pressure on the critical temperature and other thermodynamic properties of superconductors

Within the general conformal transformation method a simplified analytical model is proposed to study the effect of external hydrostatic pressure on low- and high-temperature superconducting systems. A single fluctuation in the density of states, placed away from the Fermi level, as well as external pressure are included in the model to derive equations for the superconducting gap, free energy difference, and specific heat difference. The zero- and sub-critical temperature limits are discussed by the method of successive approximations. The critical temperature is found as a function of high external pressure. It is shown that there are four universal types of the response of the system, in terms of dependence of the critical temperature on increasing external pressure. Some effects, which should be possible to be observed experimentally in s-wave superconductors, the cuprates (i.e. high-T_c superconductors) and other superconducting materials of the new generation such as two-gap superconductors, are revealed and discussed. An equation for the ratio \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{ {\mathcal R} }}}_{{\bf{1}}}$$\end{document}ℛ1 ≡ 2Δ(0)/T_c, as a function of the introduced parameters, is derived and solved numerically. Analysis of other thermodynamic quantities and the characteristic ratio \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\boldsymbol{ {\mathcal R} }}}_{{\bf{2}}}$$\end{document}ℛ2 ≡ ΔC(T_c)/C_N(T_c) is performed numerically, and mutual relations between the discussed quantities are investigated. The simple analytical model presented in the paper may turn out to be helpful in searching for novel superconducting components with higher critical temperatures induced by pressure effects.

Two distinct superconducting pairing states divided by the nematic end point in FeSe1-x S x

Unconventional superconductivity often competes or coexists with other electronic orders. In iron-based superconductors, a central issue has been the relationship between superconductivity and electronic nematicity, spontaneous breaking of the lattice rotational symmetry. Using spectroscopic-imaging scanning tunneling microscopy, we simultaneously investigated the electronic structure and the superconducting gap in FeSe_1-x S _x , where the nematicity diminishes above the nematic end point (NEP) at x = 0.17. The nematic band structure appears as anisotropic quasiparticle-interference patterns that gradually become isotropic with increasing x without anomalies at the NEP. By contrast, the superconducting gap, which is intact in the nematic phase, discontinuously shrinks above the NEP. This implies that the presence or absence of nematicity results in two distinct pairing states, whereas the pairing interaction is insensitive to the strength of nematicity.

Tunable critical temperature for superconductivity in FeSe thin films by pulsed laser deposition

Stabilized FeSe thin films in ambient pressure with tunable superconducting critical temperature would be a promising candidate for superconducting electronic devices. By carefully controlling the depositions on twelve kinds of substrates using a pulsed laser deposition technique single crystalline FeSe thin films were fabricated. The high quality of the thin films was confirmed by X-ray diffraction with a full width at half maximum of 0.515° in the rocking curve and clear four-fold symmetry in φ-scan. The films have a maximum T_c ~ 15 K on the CaF₂ substrate and were stable in ambient conditions air for more than half a year. Slightly tuning the stoichiometry of the FeSe targets, the superconducting critical temperature becomes adjustable below 15 K with quite narrow transition width less than 2 K. These FeSe thin films deposited on different substrates are optimized respectively. The T_c of these optimized films show a relation with the out-of-plane (c-axis) lattice parameter of the FeSe films.

Abrupt change of the superconducting gap structure at the nematic critical point in FeSe1-xSx

The emergence of the nematic electronic state that breaks rotational symmetry is one of the most fascinating properties of the iron-based superconductors, and has relevance to cuprates as well. FeSe has a unique ground state in which superconductivity coexists with a nematic order without long-range magnetic ordering, providing a significant opportunity to investigate the role of nematicity in the superconducting pairing interaction. Here, to reveal how the superconducting gap evolves with nematicity, we measure the thermal conductivity and specific heat of FeSe1 - x S x , in which the nematicity is suppressed by isoelectronic sulfur substitution and a nematic critical point (NCP) appears at [Formula: see text] We find that, in the whole nematic regime ([Formula: see text]), the field dependence of two quantities consistently shows two-gap behavior; one gap is small but highly anisotropic with deep minima or line nodes, and the other is larger and more isotropic. In stark contrast, in the tetragonal regime ([Formula: see text]), the larger gap becomes strongly anisotropic, demonstrating an abrupt change in the superconducting gap structure at the NCP. Near the NCP, charge fluctuations of [Formula: see text] and [Formula: see text] orbitals are enhanced equally in the tetragonal side, whereas they develop differently in the orthorhombic side. Our observation therefore directly implies that the orbital-dependent nature of the nematic fluctuations has a strong impact on the superconducting gap structure and hence on the pairing interaction.

Reemergence of high-Tc superconductivity in the (Li1-xFe x )OHFe1-ySe under high pressure

In order to elucidate pressure-induced second superconducting phase (SC-II) in A _x Fe_2-ySe₂ (A = K, Rb, Cs, and Tl) having an intrinsic phase separation, we perform a detailed high-pressure magnetotransport study on the isoelectronic, phase-pure (Li_1-xFe _x )OHFe_1-ySe single crystals. Here we show that its ambient-pressure superconducting phase (SC-I) with a critical temperature T_c ≈ 40 K is suppressed gradually to below 2 K and an SC-II phase emerges above P_c ≈ 5 GPa with T_c increasing progressively to above 50 K up to 12.5 GPa. Our high-precision resistivity data uncover a sharp transition of the normal state from Fermi liquid for SC-I to non-Fermi liquid for SC-II phase. In addition, the reemergence of high-T_c SC-II is found to accompany with a concurrent enhancement of electron carrier density. Without structural transition below 10 GPa, the observed SC-II with enhanced carrier density should be ascribed to an electronic origin presumably associated with pressure-induced Fermi surface reconstruction.

Nematicity, magnetism and superconductivity in FeSe

Iron-based superconductors are well known for their complex interplay between structure, magnetism and superconductivity. FeSe offers a particularly fascinating example. This material has been intensely discussed because of its extended nematic phase, whose relationship with magnetism is not obvious. Superconductivity in FeSe is highly tunable, with the superconducting transition temperature, T _c, ranging from 8 K in bulk single crystals at ambient pressure to almost 40 K under pressure or in intercalated systems, and to even higher temperatures in thin films. In this topical review, we present an overview of nematicity, magnetism and superconductivity, and discuss the interplay of these phases in FeSe. We focus on bulk FeSe and the effects of physical pressure and chemical substitutions as tuning parameters. The experimental results are discussed in the context of the well-studied iron-pnictide superconductors and interpretations from theoretical approaches are presented.

Maximizing T c by tuning nematicity and magnetism in FeSe1-x S x superconductors

A fundamental issue concerning iron-based superconductivity is the roles of electronic nematicity and magnetism in realising high transition temperature (T c). To address this issue, FeSe is a key material, as it exhibits a unique pressure phase diagram involving non-magnetic nematic and pressure-induced antiferromagnetic ordered phases. However, as these two phases in FeSe have considerable overlap, how each order affects superconductivity remains perplexing. Here we construct the three-dimensional electronic phase diagram, temperature (T) against pressure (P) and isovalent S-substitution (x), for FeSe1-x S x . By simultaneously tuning chemical and physical pressures, against which the chalcogen height shows a contrasting variation, we achieve a complete separation of nematic and antiferromagnetic phases. In between, an extended non-magnetic tetragonal phase emerges, where T c shows a striking enhancement. The completed phase diagram uncovers that high-T c superconductivity lies near both ends of the dome-shaped antiferromagnetic phase, whereas T c remains low near the nematic critical point.