Discovery of orbital-selective Cooper pairing in FeSe

Evidence of a distinct collective mode in Kagome superconductors

The collective modes of the superconducting order parameter fluctuation can provide key insights into the nature of the superconductor. Recently, a family of superconductors has emerged in non-magnetic kagome materials AV3Sb5 (A = K, Rb, Cs), exhibiting fertile emergent phenomenology. However, the collective behaviors of Cooper pairs have not been studied. Here, we report a distinct collective mode in CsV3-xTaxSb5 using scanning tunneling microscope/spectroscopy. The spectral line-shape is well-described by one isotropic and one anisotropic superconducting gap, and a bosonic mode due to electron-mode coupling. With increasing x, the two gaps move closer in energy, merge into two isotropic gaps of equal amplitude, and then increase synchronously. The mode energy decreases monotonically to well below 2 Δ and survives even after the charge density wave order is suppressed. We propose the interpretation of this collective mode as Leggett mode between different superconducting components or the Bardasis-Schrieffer mode due to a subleading superconducting component.

Atomic-Site-Dependent Pairing Gap in Monolayer FeSe/SrTiO3(001)-(√13 × √13)

The interfacial FeSe/TiO2-δ coupling induces high-temperature superconductivity in monolayer FeSe films. Using cryogenic atomically resolved scanning tunneling microscopy/spectroscopy, we obtained atomic-site dependent surface density of states, work function, and the pairing gap in the monolayer FeSe on the SrTiO3(001)-(√13 × √13)-R33.7° surface. Our results disclosed the out-of-plane Se-Fe-Se triple layer gradient variation, switched DOS for Fe sites on and off TiO5□, and inequivalent Fe sublattices, which gives global spatial modulation of pairing gap contaminants with the (√13 × √13) pattern. Moreover, the coherent lattice coupling induces strong inversion asymmetry and in-plane anisotropy in the monolayer FeSe, which is demonstrated to correlate with the particle-hole asymmetry in coherence peaks. These results disclose delicate atomic-scale correlations between pairing and lattice-electronic coupling in the Bardeen-Cooper-Schrieffer to Bose-Einstein condensation crossover regime, providing insights into understanding the pairing mechanism of multiorbital superconductivity.

Lateral Quantum Confinement Effect on High-TC Superconducting FeSe Monolayer

Despite decades of research in spatially confined superconducting systems to understand the modification of superconductivity from reduced length scales, the investigation of the quantum confinement effect on high-temperature superconductors remains an outstanding challenge. Here, we report scanning tunneling spectroscopy measurements on laterally confined FeSe monolayers on SrTiO3 substrates, which are formed by epitaxially growing FeSe films with a coverage less than one unit cell. Comparing to the uniform regions of FeSe monolayers, the peninsula regions at the monolayer boundary exhibit reduced Fermi energy and undiminished superconductivity, leading to a putative crossover from a Bardeen-Cooper-Schrieffer state to a Bose-Einstein condensate state. In isolated FeSe monolayer islands, superconductivity is shown to exist in samples of smaller volume in contrast to conventional superconductors, while the validity of Anderson's criterion remains fulfilled. Our work reveals lateral quantum confinement effects in unconventional superconductors to enrich the understanding of high-temperature superconductivity in low-dimensional systems.

ARPES detection of superconducting gap sign in unconventional superconductors

The superconducting gap symmetry is crucial in understanding the underlying superconductivity mechanism. Angle-resolved photoemission spectroscopy (ARPES) has played a key role in determining the gap symmetry in unconventional superconductors. However, it has been considered so far that ARPES can only measure the magnitude of the superconducting gap but not its phase; the phase has to be detected by other phase-sensitive techniques. Here we propose a method to directly detect the superconducting gap sign by ARPES. This method is successfully validated in a cuprate superconductor Bi2Sr2CaCu2O8+δ with a well-known d-wave gap symmetry. When two bands have a strong interband interaction, the resulted electronic structures in the superconducting state are sensitive to the relative gap sign between the two bands. Our present work provides an approach to detect the gap sign and can be applied to various superconductors, particularly those with multiple orbitals like the iron-based superconductors.

Electronic inhomogeneity and phase fluctuation in one-unit-cell FeSe films

One-unit-cell FeSe films on SrTiO3 substrates are of great interest owing to significantly enlarged pairing gaps characterized by two coherence peaks at ±10 meV and ±20 meV. In-situ transport measurement is desired to reveal novel properties. Here, we performed in-situ microscale electrical transport and combined scanning tunneling microscopy measurements on continuous one-unit-cell FeSe films with twin boundaries. We observed two spatially coexisting superconducting phases in domains and on boundaries, characterized by distinct superconducting gaps (Δ 1 ~15 meV vs.Δ 2 ~10 meV) and pairing temperatures (Tp1~52.0 K vs. Tp2~37.3 K), and correspondingly two-step nonlinear V ~ I α behavior but a concurrent Berezinskii-Kosterlitz-Thouless (BKT)-like transition occurring atT BKT ~28.7 K. Moreover, the onset transition temperatureT c onset ~54 K and zero-resistivity temperatureT c zero ~31 K are consistent with Tp1 andT BKT , respectively. Our results indicate the broadened superconducting transition in FeSe/SrTiO3 is related to intrinsic electronic inhomogeneity due to distinct two-gap features and phase fluctuations of two-dimensional superconductivity.

Discovery of orbital ordering in Bi2Sr2CaCu2O8+x

The primordial ingredient of cuprate superconductivity is the CuO2 unit cell. Theories usually concentrate on the intra-atom Coulombic interactions dominating the 3d9 and 3d10 configurations of each copper ion. However, if Coulombic interactions also occur between electrons of the 2p6 orbitals of each planar oxygen atom, spontaneous orbital ordering may split their energy levels. This long-predicted intra-unit-cell symmetry breaking should generate an orbitally ordered phase, for which the charge transfer energy ε separating the 2p6 and 3d10 orbitals is distinct for the two oxygen atoms. Here we introduce sublattice-resolved ε(r) imaging to CuO2 studies and discover intra-unit-cell rotational symmetry breaking of ε(r). Spatially, this state is arranged in disordered Ising domains of orthogonally oriented orbital order bounded by dopant ions, and within whose domain walls low-energy electronic quadrupolar two-level systems occur. Overall, these data reveal a Q = 0 orbitally ordered state that splits the oxygen energy levels by ~50 meV, in underdoped CuO2.

Equation of State and Thermometry of the 2D SU(N) Fermi-Hubbard Model

We characterize the equation of state (EoS) of the SU(N>2) Fermi-Hubbard Model (FHM) in a two-dimensional single-layer square optical lattice. We probe the density and the site occupation probabilities as functions of interaction strength and temperature for N=3, 4, and 6. Our measurements are used as a benchmark for state-of-the-art numerical methods including determinantal quantum Monte Carlo and numerical linked cluster expansion. By probing the density fluctuations, we compare temperatures determined in a model-independent way by fitting measurements to numerically calculated EoS results, making this a particularly interesting new step in the exploration and characterization of the SU(N) FHM.

Electronic stripe patterns near the fermi level of tetragonal Fe(Se,S)

FeSe1-xSx remains one of the most enigmatic systems of Fe-based superconductors. While much is known about the orthorhombic parent compound, FeSe, the tetragonal samples, FeSe1-xSx with x > 0.17, remain relatively unexplored. Here, we provide an in-depth investigation of the electronic states of tetragonal FeSe0.81S0.19, using scanning tunneling microscopy and spectroscopy (STM/S) measurements, supported by angle-resolved photoemission spectroscopy (ARPES) and theoretical modeling. We analyze modulations of the local density of states (LDOS) near and away from Fe vacancy defects separately and identify quasiparticle interference (QPI) signals originating from multiple regions of the Brillouin zone, including the bands at the zone corners. We also observe that QPI signals coexist with a much stronger LDOS modulation for states near the Fermi level whose period is independent of energy. Our measurements further reveal that this strong pattern appears in the STS measurements as short range stripe patterns that are locally two-fold symmetric. Since these stripe patterns coexist with four-fold symmetric QPI around Fe-vacancies, the origin of their local two-fold symmetry must be distinct from that of nematic states in orthorhombic samples. We explore several aspects related to the stripes, such as the role of S and Fe-vacancy defects, and whether they can be explained by QPI. We consider the possibility that the observed stripe patterns may represent incipient charge order correlations, similar to those observed in the cuprates.

Kondo interaction in FeTe and its potential role in the magnetic order

Finding d-electron heavy fermion states has been an important topic as the diversity in d-electron materials can lead to many exotic Kondo effect-related phenomena or new states of matter such as correlation-driven topological Kondo insulator. Yet, obtaining direct spectroscopic evidence for a d-electron heavy fermion system has been elusive to date. Here, we report the observation of Kondo lattice behavior in an antiferromagnetic metal, FeTe, via angle-resolved photoemission spectroscopy, scanning tunneling spectroscopy and transport property measurements. The Kondo lattice behavior is represented by the emergence of a sharp quasiparticle and Fano-type tunneling spectra at low temperatures. The transport property measurements confirm the low-temperature Fermi liquid behavior and reveal successive coherent-incoherent crossover upon increasing temperature. We interpret the Kondo lattice behavior as a result of hybridization between localized Fe 3dxy and itinerant Te 5pz orbitals. Our observations strongly suggest unusual cooperation between Kondo lattice behavior and long-range magnetic order.

Interplay of hidden orbital order and superconductivity in CeCoIn5

Visualizing atomic-orbital degrees of freedom is a frontier challenge in scanned microscopy. Some types of orbital order are virtually imperceptible to normal scattering techniques because they do not reduce the overall crystal lattice symmetry. A good example is d_xz/d_yz (π,π) orbital order in tetragonal lattices. For enhanced detectability, here we consider the quasiparticle scattering interference (QPI) signature of such (π,π) orbital order in both normal and superconducting phases. The theory reveals that sublattice-specific QPI signatures generated by the orbital order should emerge strongly in the superconducting phase. Sublattice-resolved QPI visualization in superconducting CeCoIn₅ then reveals two orthogonal QPI patterns at lattice-substitutional impurity atoms. We analyze the energy dependence of these two orthogonal QPI patterns and find the intensity peaked near E = 0, as predicted when such (π,π) orbital order is intertwined with d-wave superconductivity. Sublattice-resolved superconductive QPI techniques thus represent a new approach for study of hidden orbital order.

Two superconducting states with broken time-reversal symmetry in FeSe1-xSx

Iron-chalcogenide superconductors FeSe1-xSx possess unique electronic properties such as nonmagnetic nematic order and its quantum critical point. The nature of superconductivity with such nematicity is important for understanding the mechanism of unconventional superconductivity. A recent theory suggested the possible emergence of a fundamentally new class of superconductivity with the so-called Bogoliubov Fermi surfaces (BFSs) in this system. However, such an ultranodal pair state requires broken time-reversal symmetry (TRS) in the superconducting state, which has not been observed experimentally. Here, we report muon spin relaxation (μSR) measurements in FeSe1-xSx superconductors for 0 ≤ x ≤ 0.22 covering both orthorhombic (nematic) and tetragonal phases. We find that the zero-field muon relaxation rate is enhanced below the superconducting transition temperature Tc for all compositions, indicating that the superconducting state breaks TRS both in the nematic and tetragonal phases. Moreover, the transverse-field μSR measurements reveal that the superfluid density shows an unexpected and substantial reduction in the tetragonal phase (x > 0.17). This implies that a significant fraction of electrons remain unpaired in the zero-temperature limit, which cannot be explained by the known unconventional superconducting states with point or line nodes. The TRS breaking and the suppressed superfluid density in the tetragonal phase, together with the reported enhanced zero-energy excitations, are consistent with the ultranodal pair state with BFSs. The present results reveal two different superconducting states with broken TRS separated by the nematic critical point in FeSe1-xSx, which calls for the theory of microscopic origins that account for the relation between nematicity and superconductivity.

Spin-Resolved Imaging of Antiferromagnetic Order in Fe4 Se5 Ultrathin Films on SrTiO3

Unraveling the magnetic order in iron chalcogenides and pnictides at atomic scale is pivotal for understanding their unconventional superconducting pairing mechanism, but is experimentally challenging. Here, by utilizing spin-polarized scanning tunneling microscopy, real-space spin contrasts are successfully resolved to exhibit atomically unidirectional stripes in Fe₄ Se₅ ultrathin films, the plausible closely related compound of bulk FeSe with ordered Fe-vacancies, which are grown by molecular beam epitaxy. As is substantiated by the first-principles electronic structure calculations, the spin contrast originates from a pair-checkerboard antiferromagnetic ground state with in-plane magnetization, which is modulated by a spin-lattice coupling. These measurements further identify three types of nanoscale antiferromagnetic domains with distinguishable spin contrasts, which are subject to thermal fluctuations into short-ranged patches at elevated temperatures. This work provides promising opportunities in understanding the emergent magnetic order and the electronic phase diagram for FeSe-derived superconductors.

Anisotropic Gap Structure and Sign Reversal Symmetry in Monolayer Fe(Se,Te)

The iron-based superconductors are an ideal platform to reveal the enigma of the unconventional superconductivity and potential topological superconductivity. Among them, the monolayer Fe(Se,Te)/SrTiO₃(001), which is proposed to be topological nontrivial, shows interface-enhanced high-temperature superconductivity in the two-dimensional limit. However, the experimental studies on the superconducting pairing mechanism of monolayer Fe(Se,Te) films are still limited. Here, by measuring the quasiparticle interference in monolayer Fe(Se,Te)/SrTiO₃(001), we report the observation of the anisotropic structure of the large superconducting gap and the sign change of the superconducting gap on different electron pockets. The results are well consistent with the "bonding-antibonding" s_±-wave pairing symmetry driven by spin fluctuations in conjunction with spin-orbit coupling. Our work is of basic significance not only for a unified superconducting formalism in the iron-based superconductors, but also for understanding of topological superconductivity in high-temperature 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.

Eliminating Orbital Selectivity from the Metal-Insulator Transition by Strong Magnetic Fluctuations

The orbital-selective electronic behavior is one of the most remarkable manifestations of strong electronic correlations in multiorbital systems. A prominent example is the orbital-selective Mott transition (OSMT), which is characterized by the coexistence of localized electrons in some orbitals, and itinerant electrons in other orbitals. The state-of-the-art theoretical description of the OSMT in two- and three-dimensional systems is based on local nonperturbative approximations to electronic correlations provided by dynamical mean-field theory or slave spin method. In this work we go beyond this local picture and focus on the effect of spatial collective electronic fluctuations on the OSMT. To this aim, we consider a half-filled Hubbard-Kanamori model on a cubic lattice with two orbitals that have different bandwidths. We show that strong magnetic fluctuations that are inherent in this system prevent the OSMT and favor the Néel transition that occurs at the same critical temperature for both orbitals.

Superconducting Instabilities in Strongly Correlated Infinite-Layer Nickelates

The discovery of superconductivity in infinite-layer nickelates has added a new family of materials to the fascinating growing class of unconventional superconductors. By incorporating the strongly correlated multiorbital nature of the low-energy electronic degrees of freedom, we compute the leading superconducting instability from magnetic fluctuations relevant for infinite-layer nickelates. Specifically, by properly including the doping dependence of the Ni d_{x^{2}-y^{2}} and d_{z^{2}} orbitals as well as the self-doping band, we uncover a transition from d-wave pairing symmetry to nodal s_{±} superconductivity, driven by strong fluctuations in the d_{z^{2}}-dominated orbital states. We discuss the properties of the resulting superconducting condensates in light of recent tunneling and penetration depth experiments probing the detailed superconducting gap structure of these materials.

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.

Superconductivity and topologically nontrivial states in noncentrosymmetric XVSe2 (X = Pb, Sn): a first-principles study

Noncentrosymmetric superconductors are strong candidates for exploring intrinsic topological superconductivity. Here, we predict two new noncentrosymmetric superconductors SnVSe₂ and PbVSe₂ by a systematic first-principles study. These two compounds show good thermal and dynamic stabilities. Moreover, the band topology of both compounds is predicted to be nontrivial via Z₂ calculation and slab models. We also investigate the electron-phonon interactions in SnVSe₂ and PbVSe₂, indicating the T_c of SnVSe₂ and PbVSe₂ without external pressure are predicted to be ∼1.18 K and ∼0.22 K, respectively. Furthermore, the results on pressure engineering in PbVSe₂ imply that the T_c of PbVSe₂ can be tuned to 2.39 K for enhanced contributions from Pb layers under pressure up to 6.4 GPa. This work may provide new platforms for probing spin-triplet paring and may help with designing and developing new metal-intercalated transition metal dichalcogenides.

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.

Superconductivity in nickel-based 112 systems

Superconductivity has been discovered recently in infinite-layer nickel-based 112 thin films R_1−xA_xNiO₂ (R = La, Nd, Pr and A = Sr, Ca). They are isostructural to the infinite-layer cuprate (Ca,Sr)CuO₂ and are supposed to have a formal Ni 3d⁹ valence, thus providing a new platform to study the unconventional pairing mechanism of high-temperature superconductors. This important discovery immediately triggers a huge amount of innovative scientific curiosity in the field. In this paper, we try to give an overview of the recent research progress on the newly found superconducting nickelate systems, both from experimental and theoretical aspects. We mainly focus on the electronic structures, magnetic excitations, phase diagrams and superconducting gaps, and finally make some open discussions for possible pairing symmetries in Ni-based 112 systems.

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The infinite-layer nickel-based 112 thin films R_1−xA_xNiO₂ can host superconductivity up to 15 K

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R_1−xA_xNiO₂ is a multiband system, in which the short-range antiferromagnetic fluctuations can be detected

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R_1−xA_xNiO₂ has an unconventional superconducting pairing sate with a robust d-wave gap and a full gap without unified understanding

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The nickelate system provides a new platform for researching unconventional superconductivity

On the Superconducting Critical Temperature of Heavily Disordered Interfaces Hosting Multi-Gap Superconductivity

LaAlO3/SrTiO3 interfaces are a nice example of a two-dimensional electron gas, whose carrier density can be varied by top- and back-gating techniques. Due to the electron confinement near the interface, the two-dimensional band structure is split into sub-bands, and more than one sub-band can be filled when the carrier density increases. These interfaces also host superconductivity, and the interplay of two-dimensionality, multi-band character, with the possible occurrence of multi-gap superconductivity and disorder calls for a better understanding of finite-bandwidth effects on the superconducting critical temperature of heavily disordered multi-gap superconductors.

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.

Multiband Superconductivity with Sign-Preserving Order Parameter in Kagome Superconductor CsV_{3}Sb_{5}

The superconductivity of a kagome superconductor CsV_{3}Sb_{5} is studied by scanning tunneling microscopy and spectroscopy at ultralow temperature with high resolution. Two kinds of superconducting gaps with multiple sets of coherent peaks and residual zero-energy density of states (DOS) are observed on both half-Cs and Sb surfaces, implying multiband superconductivity. In addition, in-gap states can be induced by magnetic impurities but not by nonmagnetic impurities, suggesting a sign-preserving or s-wave superconducting order parameter. Moreover, the interplay between charge density waves (CDW) and superconductivity differs on various bands, resulting in different density-of-states distributions. Our results suggest that the superconducting gap is likely isotropic on the sections of Fermi surface that play little roles in CDW, and the superconducting gaps on the sections of Fermi surface with anisotropic CDW gaps are likely anisotropic as well. The residual spectral weights at zero energy are attributed to the extremely small superconducting gap on the tiny oval Fermi pockets. Our study provides critical clues for further understanding the superconductivity and its relation to CDW in CsV_{3}Sb_{5}.

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.

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.

Dual Orbital Degeneracy Lifting in a Strongly Correlated Electron System

The local structure of NaTiSi_{2}O_{6} is examined across its Ti-dimerization orbital-assisted Peierls transition at 210 K. An atomic pair distribution function approach evidences local symmetry breaking preexisting far above the transition. The analysis unravels that, on warming, the dimers evolve into a short range orbital degeneracy lifted (ODL) state of dual orbital character, persisting up to at least 490 K. The ODL state is correlated over the length scale spanning ∼6 sites of the Ti zigzag chains. Results imply that the ODL phenomenology extends to strongly correlated electron systems.

Theory of optical responses in clean multi-band superconductors

Electromagnetic responses in superconductors provide valuable information on the pairing symmetry as well as physical quantities such as the superfluid density. However, at the superconducting gap energy scale, optical excitations of the Bogoliugov quasiparticles are forbidden in conventional Bardeen-Cooper-Schrieffer superconductors when momentum is conserved. Accordingly, far-infrared optical responses have been understood in the framework of a dirty-limit theory by Mattis and Bardeen for over 60 years. Here we show, by investigating the selection rules imposed by particle-hole symmetry and unitary symmetries, that intrinsic momentum-conserving optical excitations can occur in clean multi-band superconductors when one of the following three conditions is satisfied: (i) inversion symmetry breaking, (ii) symmetry protection of the Bogoliubov Fermi surfaces, or (iii) simply finite spin-orbit coupling with unbroken time reversal and inversion symmetries. This result indicates that clean-limit optical responses are common beyond the straightforward case of broken inversion symmetry. We apply our theory to optical responses in FeSe, a clean multi-band superconductor with inversion symmetry and significant spin-orbit coupling. This result paves the way for studying clean-limit superconductors through optical measurements.

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.

Time-reversal symmetry breaking in the Fe-chalcogenide superconductors

Topological superconductivity has been sought in a variety of heterostructure systems, the interest being that a material displaying such a phenomenon could prove to be the ideal platform to support Majorana fermions, which in turn could be the basis for advanced qubit technologies. Recently, the high-T_c family of superconductors, FeTe_1-xSe_x, have been shown to exhibit the property of topological superconductivity and further, evidence has been found for the presence of Majorana fermions. We have studied the interplay of topology, magnetism, and superconductivity in the FeTe_1-x Se _x family using high-resolution laser-based photoemission. At the bulk superconducting transition, a gap opens at the chemical potential as expected. However, a second gap is observed to open at the Dirac point in the topological surface state. The associated mass acquisition in the topological state points to time-reversal symmetry breaking, probably associated with the formation of ferromagnetism in the surface layer. The presence of intrinsic ferromagnetism combined with strong spin-orbit coupling provides an ideal platform for a range of exotic topological phenomena.

Single particle tunneling spectrum of superconducting Nd1-xSrxNiO2 thin films

The pairing mechanism in cuprates remains as one of the most challenging issues in condensed matter physics. Recently, superconductivity was discovered in thin films of the infinite-layer nickelate Nd1-xSrxNiO2 (x = 0.12-0.25) which is believed to have the similar 3d9 orbital electrons as that in cuprates. Here we report single-particle tunneling measurements on the superconducting nickelate thin films. We find predominantly two types of tunneling spectra, one shows a V-shape feature which can be fitted well by a d-wave gap function with gap maximum of about 3.9 meV, another one exhibits a full gap of about 2.35 meV. Some spectra demonstrate mixed contributions of these two components. Combining with theoretical calculations, we attribute the d-wave gap to the pairing potential of the [Formula: see text] orbital. Several possible reasons are given for explaining the full gap feature. Our results indicate both similarities and distinctions between the newly found Ni-based superconductors and cuprates.

Synergy between Hund-Driven Correlations and Boson-Mediated Superconductivity

Multiorbital systems such as the iron-based superconductors provide a new avenue to attack the long-standing problem of superconductivity in strongly correlated systems. In this work we study the superconductivity driven by a generic bosonic mechanism in a multiorbital model including the full dynamical electronic correlations induced by the Hubbard U and the Hund's coupling. We show that superconductivity survives much more in a Hund's metal than in an ordinary correlated metal with the same degree of correlation. The redistribution of spectral weight characteristic of the Hund's metal reflects also in the enhancement of the orbital-selective character of the superconducting gaps, in agreement with experiments in iron-based superconductors.

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.

Triplet Resonating Valence Bond State and Superconductivity in Hund's Metals

A central idea in strongly correlated systems is that doping a Mott insulator leads to a superconductor by transforming the resonating valence bonds (RVBs) into spin-singlet Cooper pairs. Here, we argue that a spin-triplet RVB (tRVB) state, driven by spatially, or orbitally anisotropic ferromagnetic interactions can provide the parent state for triplet superconductivity. We apply this idea to the iron-based superconductors, arguing that strong on site Hund's interactions develop intra-atomic tRVBs between the t_{2g} orbitals. On doping, the presence of two iron atoms per unit cell allows these interorbital triplets to coherently delocalize onto the Fermi surface, forming a fully gapped triplet superconductor. This mechanism gives rise to a unique staggered structure of on site pair correlations, detectable as an alternating π phase shift in a scanning Josephson tunneling microscope.

Isostructural Spin-Density-Wave and Superconducting Gap Anisotropies in Iron-Arsenide Superconductors

When passing through a phase transition, electronic system saves energy by opening energy gaps at the Fermi level. Delineating the energy gap anisotropy provides insights into the origin of the interactions that drive the phase transition. Here, we report the angle-resolved photoemission spectroscopy (ARPES) study on the detailed gap anisotropies in both the tetragonal magnetic and superconducting phases in Sr_{1-x}Na_{x}Fe_{2}As_{2}. First, we found that the spin-density-wave (SDW) gap is strongly anisotropic in the tetragonal magnetic phase. The gap magnitude correlates with the orbital character of Fermi surface closely. Second, we found that the SDW gap anisotropy is isostructural to the superconducting gap anisotropy regarding to the angular dependence, gap minima locations, and relative gap magnitudes. Our results indicate that the superconducting pairing interaction and magnetic interaction share the same origin. The intraorbital scattering plays an important role in constructing these interactions resulting in the orbital-selective magnetism and superconductivity in iron-based superconductors.

Raman Response in the Nematic Phase of FeSe

Raman experiments on bulk FeSe revealed that the low-frequency part of the B_{1g} Raman response R_{B1g}(Ω), which probes nematic fluctuations, rapidly decreases below the nematic transition at T_{n}∼85  K. Such behavior is expected when a gap opens up and at a first glance is inconsistent with the fact that FeSe remains a metal below T_{n}. We argue that the drop of R_{B1g}(Ω) can be ascribed to the fact that the nematic order drastically changes the orbital content of low-energy excitations near hole and electron pockets, making them nearly mono-orbital. In this situation, the B_{1g} Raman response gets reduced by the same vertex corrections that enforce charge conservation in the symmetric Raman channel. The reduction holds at low frequencies and gives rise to gaplike behavior of R_{B1g}(Ω). We also show that the enhancement of the B_{1g} Raman response near T_{n} is consistent with the sign change of the nematic order parameter between hole and electron pockets.

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.

Evidence for an Fulde-Ferrell-Larkin-Ovchinnikov State with Segmented Vortices in the BCS-BEC-Crossover Superconductor FeSe

We present resistivity and thermal-conductivity measurements of superconducting FeSe in intense magnetic fields up to 35 T applied parallel to the ab plane. At low temperatures, the upper critical field μ_{0}H_{c2}^{ab} shows an anomalous upturn, while thermal conductivity exhibits a discontinuous jump at μ_{0}H^{*}≈24  T well below μ_{0}H_{c2}^{ab}, indicating a first-order phase transition in the superconducting state. This demonstrates the emergence of a distinct field-induced superconducting phase. Moreover, the broad resistive transition at high temperatures abruptly becomes sharp upon entering the high-field phase, indicating a dramatic change of the magnetic-flux properties. We attribute the high-field phase to the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state, where the formation of planar nodes gives rise to a segmentation of the flux-line lattice. We point out that strongly orbital-dependent pairing as well as spin-orbit interactions, the multiband nature, and the extremely small Fermi energy are important for the formation of the FFLO state in FeSe.

Bosonic Mode and Impurity-Scattering in Monolayer Fe(Te,Se) High-Temperature Superconductors

The electron pairing mechanism has always been one of the most challenging problems in high-temperature superconductors. Fe(Te,Se), as the superconductor with intrinsic topological property, may host Majorana bound states and has attracted tremendous interest. While in bulk Fe(Te,Se) the pairing mechanism has been experimentally investigated, it remains little understood in its two-dimensional limit counterpart. Here, by in situ scanning tunneling spectroscopy, we show clear evidence of the bosonic mode Ω beyond the superconducting gap Δ in monolayer FeTe_0.5Se_0.5/SrTiO₃(001) high-temperature superconductor. Statistically, Ω shows an obvious anticorrelation with Δ and appears below 2Δ, consistent with the spin-excitation nature. Furthermore, the in-gap bound states induced by two types of magnetically different impurities support the sign-reversing pairing scenario. Our results not only suggest that the spin-excitation-like bosonic mode within a sign-reversing pairing plays an essential role in monolayer FeTe_0.5Se_0.5/SrTiO₃(001) but also offer the crucial information for investigating the high-temperature superconductivity in interfacial iron selenides.

Momentum-resolved superconducting energy gaps of Sr2RuO4 from quasiparticle interference imaging

Sr2RuO4 has long been the focus of intense research interest because of conjectures that it is a correlated topological superconductor. It is the momentum space (k-space) structure of the superconducting energy gap [Formula: see text] on each band i that encodes its unknown superconducting order parameter. However, because the energy scales are so low, it has never been possible to directly measure the [Formula: see text] of Sr2RuO4 Here, we implement Bogoliubov quasiparticle interference (BQPI) imaging, a technique capable of high-precision measurement of multiband [Formula: see text] At T = 90 mK, we visualize a set of Bogoliubov scattering interference wavevectors [Formula: see text] consistent with eight gap nodes/minima that are all closely aligned to the [Formula: see text] crystal lattice directions on both the α and β bands. Taking these observations in combination with other very recent advances in directional thermal conductivity [E. Hassinger et al., Phys. Rev. X 7, 011032 (2017)], temperature-dependent Knight shift [A. Pustogow et al., Nature 574, 72-75 (2019)], time-reversal symmetry conservation [S. Kashiwaya et al., Phys. Rev B, 100, 094530 (2019)], and theory [A. T. Rømer et al., Phys. Rev. Lett. 123, 247001 (2019); H. S. Roising, T. Scaffidi, F. Flicker, G. F. Lange, S. H. Simon, Phys. Rev. Res. 1, 033108 (2019); and O. Gingras, R. Nourafkan, A. S. Tremblay, M. Côté, Phys. Rev. Lett. 123, 217005 (2019)], the BQPI signature of Sr2RuO4 appears most consistent with [Formula: see text] having [Formula: see text] [Formula: see text] symmetry.

Dictionary learning in Fourier-transform scanning tunneling spectroscopy

Modern high-resolution microscopes are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such microscopes remains a formidable challenge. Fourier analysis is commonly used to analyze the structure of such images. However, the Fourier transform fundamentally suffers from severe phase noise when applied to aperiodic images. Here, we report the development of an algorithm based on nonconvex optimization that directly uncovers the fundamental motifs present in a real-space image. Apart from being quantitatively superior to traditional Fourier analysis, we show that this algorithm also uncovers phase sensitive information about the underlying motif structure. We demonstrate its usefulness by studying scanning tunneling microscopy images of a Co-doped iron arsenide superconductor and prove that the application of the algorithm allows for the complete recovery of quasiparticle interference in this material.

Aperiodic structure imaging suffers limitations when utilizing Fourier analysis. The authors report an algorithm that quantitatively overcomes these limitations based on nonconvex optimization, demonstrated by studying aperiodic structures via the phase sensitive interference in STM images.

Topological ultranodal pair states in iron-based superconductors

Bogoliubov Fermi surfaces are contours of zero-energy excitations that are protected in the superconducting state. Here we show that multiband superconductors with dominant spin singlet, intraband pairing of spin-1/2 electrons can undergo a transition to a state with Bogoliubov Fermi surfaces if spin-orbit coupling, interband pairing and time reversal symmetry breaking are also present. These latter effects may be small, but drive the transition to the topological state for appropriate nodal structure of the intra-band pair. Such a state should display nonzero zero-bias density of states and corresponding residual Sommerfeld coefficient as for a disordered nodal superconductor, but occurring even in the pure case. We present a model appropriate for iron-based superconductors where the topological transition associated with creation of a Bogoliubov Fermi surface can be studied. The model gives results that strongly resemble experiments on FeSe_1−xS_x across the nematic transition, where this ultranodal behavior may already have been observed.

Experiments indicate an abrupt change in the pairing gap near the nematic transition in the FeSe_1−xS_x iron-based superconductor. Here, Setty et al. propose to explain them via a novel spin-1/2 paired state with topologically protected zero-energy excitations over a finite area nodal surface.

Anisotropic effect of a magnetic field on the neutron spin resonance in FeSe

We use inelastic neutron scattering to study the effect of a magnetic field on the neutron spin resonance (E r = 3.6 meV) of superconducting FeSe (T c = 9 K). While a field aligned along the in-plane direction broadens and suppresses the resonance, a c-axis aligned field does so much more efficiently, consistent with the anisotropic field-induced suppression of the superfluid density from the heat capacity measurements. These results suggest that the resonance in FeSe is associated with the superconducting electrons arising from orbital selective quasiparticle excitations between the hole and electron Fermi surfaces.

Knight Shift and Leading Superconducting Instability from Spin Fluctuations in Sr_{2}RuO_{4}

Recent nuclear magnetic resonance studies [A. Pustogow et al., Nature 574, 72 (2019)] have challenged the prevalent chiral triplet pairing scenario proposed for Sr_{2}RuO_{4}. To provide guidance from microscopic theory as to which other pair states might be compatible with the new data, we perform a detailed theoretical study of spin fluctuation mediated pairing for this compound. We map out the phase diagram as a function of spin-orbit coupling, interaction parameters, and band structure properties over physically reasonable ranges, comparing when possible with photoemission and inelastic neutron scattering data information. We find that even-parity pseudospin singlet solutions dominate large regions of the phase diagram, but in certain regimes spin-orbit coupling favors a near-nodal odd-parity triplet superconducting state, which is either helical or chiral depending on the proximity of the γ band to the van Hove points. A surprising near degeneracy of the nodal s^{'} and d_{x^{2}-y^{2}} wave solutions leads to the possibility of a near-nodal time-reversal symmetry broken s^{'}+id_{x^{2}-y^{2}} pair state. Predictions for the temperature dependence of the Knight shift for fields in and out of plane are presented for all states.

FeSe quantum dots for in vivo multiphoton biomedical imaging

An immense demand in biomedical imaging is to develop efficient photoluminescent probes with high biocompatibility and quantum yield, as well as multiphoton absorption performance to improve penetration depth and spatial resolution. Here, iron selenide (FeSe) quantum dots (QDs) are reported to meet these criteria. The synthesized QDs exhibit two- and three-photon excitation property at 800- and 1080-nm wavelengths and high quantum yield (ca. 40%), which are suitable for second-window imaging. To verify their biosuitability, poly(ethylene glycol)-conjugated QDs were linked with human epidermal growth factor receptor 2 (HER2) antibodies for in vitro/in vivo two-photon imaging in HER2-overexpressed MCF7 cells and a xenograft breast tumor model in mice. Imaging was successfully carried out at a depth of up to 500 μm from the skin using a nonlinear femtosecond laser at an excitation wavelength of 800 nm. These findings may open up a way to apply biocompatible FeSe QDs to multiphoton cancer imaging.

k_{z} Selective Scattering within Quasiparticle Interference Measurements of FeSe

Quasiparticle interference (QPI) provides a wealth of information relating to the electronic structure of a material. However, it is often assumed that this information is constrained to two-dimensional electronic states. We show that this is not necessarily the case. For FeSe, a system dominated by surface defects, we show that it is actually all electronic states with negligible group velocity in the z axis that are contained within the experimental data. By using a three-dimensional tight-binding model of FeSe, fit to photoemission measurements, we directly reproduce the experimental QPI scattering dispersion, within a T-matrix formalism, by including both k_{z}=0 and k_{z}=π electronic states. This result unifies both tunnelling based and photoemission based experiments on FeSe and highlights the importance of k_{z} within surface sensitive measurements of QPI.

Correlation at two-dimensional charge-transfer FeSe interface

The charge transfer and spin coupling effects are explored at the interface of two-dimensional (2D) superconducting FeSe nanosheets and molecular photochromic potassium-7,7,8,8-tetracyanoquinodimethane (KTCNQ). Light-induced conductivity in 2D FeSe nanosheets is enhanced by the electron doping from KTCNQ by the destabilized spin-Peierls phase through their interface. Furthermore, the spin coupling at the interface of FeSe and KTCNQ shifts the dimerization transition temperature of KTCNQ. Our results suggest 2D exfoliated FeSe nanosheets as a versatile strongly correlated platform for the study of interfacial electron doping and spin coupling.

Real-Space Imaging of Orbital Selectivity on SrTiO3(001) Surface

Real-space access of the orbital degree of freedom in complex oxides is still challenging due to intricate electronic hybridization. Here, we report a direct observation of reproducible orbital-selective tunneling on a novel SrTiO₃(001) surface by scanning tunneling microscopy. The electronic structures reversibly switch between two different sets of symmetries depending on the sample bias, which is accompanied by a remarkable change in energy-dependent spectroscopy data. Tunneling spectrum combined with density functional theory calculations elucidates that symmetry-breaking at the surface determines the crystal-splitting field of e_g/t_2g orbitals with a strong in-plane anisotropy so that electrons alternatingly fill e_g and t_2g orbitals during the imaging process with different biases. This surface superstructure provides a new strategy toward understanding orbital textures and orbital selectivity in complex oxides.

Gap suppression at a Lifshitz transition in a multi-condensate superconductor

In multi-orbital materials, superconductivity can exhibit several coupled condensates. In this context, quantum confinement in two-dimensional superconducting oxide interfaces offers new degrees of freedom to engineer the band structure and selectively control the occupancy of 3d orbitals by electrostatic doping. Here, we use resonant microwave transport to extract the superfluid stiffness of the (110)-oriented LaAlO₃/SrTiO₃ interface in the entire phase diagram. We provide evidence of a transition from single-condensate to two-condensate superconductivity driven by continuous and reversible electrostatic doping, which we relate to the Lifshitz transition between 3d bands based on numerical simulations of the quantum well. We find that the superconducting gap is suppressed while the second band is populated, challenging Bardeen-Cooper-Schrieffer theory. We ascribe this behaviour to the existence of superconducting order parameters with opposite signs in the two condensates due to repulsive coupling. Our findings offer an innovative perspective on the possibility to tune and control multiple-orbital physics in superconducting interfaces.

Local orbital degeneracy lifting as a precursor to an orbital-selective Peierls transition

Fundamental electronic principles underlying all transition metal compounds are the symmetry and filling of the d-electron orbitals and the influence of this filling on structural configurations and responses. Here we use a sensitive local structural technique, x-ray atomic pair distribution function analysis, to reveal the presence of fluctuating local-structural distortions at high temperature in one such compound, CuIr₂S₄. We show that this hitherto overlooked fluctuating symmetry-lowering is electronic in origin and will modify the energy-level spectrum and electronic and magnetic properties. The explanation is a local, fluctuating, orbital-degeneracy-lifted state. The natural extension of our result would be that this phenomenon is likely to be widespread amongst diverse classes of partially filled nominally degenerate d-electron systems, with potentially broad implications for our understanding of their properties.

A common feature of many transition metal materials is global symmetry breaking at low temperatures. Here the authors show that such materials are characterized by fluctuating symmetry-lowering distortions that exist pre-formed in higher temperature phases with greater average symmetry.