Preformed Cooper Pairs in Layered FeSe-Based Superconductors

Tuning the BCS-BEC crossover of electron-hole pairing with pressure

In graphite, a moderate magnetic field confines electrons and holes into their lowest Landau levels. In the extreme quantum limit, two insulating states with a dome-like field dependence of the their critical temperatures are induced by the magnetic field. Here, we study the evolution of the first dome (below 60 T) under hydrostatic pressure up to 1.7 GPa. With increasing pressure, the field-temperature phase boundary shifts towards higher magnetic fields, yet the maximum critical temperature remains unchanged. According to our fermiology data, pressure amplifies the density and the in-plane effective cyclotron mass of hole-like and electron-like carriers. Thanks to this information, we verify the persistent relevance of the BCS relation between the critical temperature and the density of states in the weak-coupling boundary of the dome. In contrast, the strong-coupling summit of the dome does not show any detectable change with pressure. We argue that this is because the out-of-plane BCS coherence length approaches the interplane distance that shows little change with pressure. Thus, the BCS-BEC crossover is tunable by magnetic field and pressure, but with a locked summit.

Phonon modes and electron-phonon coupling at the FeSe/SrTiO3 interface

The remarkable increase in superconducting transition temperature (Tc) observed at the interface of one-unit-cell FeSe films on SrTiO3 substrates (1 uc FeSe/STO)1 has attracted considerable research into the interface effects2-6. Although this high Tc is thought to be associated with electron-phonon coupling (EPC)2, the microscopic coupling mechanism and its role in the superconductivity remain elusive. Here we use momentum-selective high-resolution electron energy loss spectroscopy to atomically resolve the phonons at the FeSe/STO interface. We uncover new optical phonon modes, coupling strongly with electrons, in the energy range of 75-99 meV. These modes are characterized by out-of-plane vibrations of oxygen atoms in the interfacial double-TiOx layer and the apical oxygens in STO. Our results also demonstrate that the EPC strength and superconducting gap of 1 uc FeSe/STO are closely related to the interlayer spacing between FeSe and the TiOx terminated STO. These findings shed light on the microscopic origin of the interfacial EPC and provide insights into achieving large and consistent Tc enhancement in FeSe/STO and potentially other superconducting systems.

Inferior Interfacial Superconductivity in 1 UC FeSe/SrVO3/SrTiO3 with Screened Interfacial Electron-Phonon Coupling

Single-unit cell (1 UC) FeSe interfaced with TiOx or FeOx exhibits significantly enhanced superconductivity compared to that of bulk FeSe, with interfacial electron-phonon coupling (EPC) playing a crucial role. However, the reduced dimensionality in 1 UC FeSe, which may drive superconducting fluctuations, complicates our understanding of the enhancement mechanisms. We construct a new superconducting interface, 1 UC FeSe/SrVO3/SrTiO3. Here, the itinerant electrons of highly metallic SrVO3 films can screen all high-energy Fuchs-Kliewer phonons, including those of SrTiO3, making it the first FeSe/oxide system with screened interfacial EPC while maintaining the 1 UC FeSe thickness. Despite comparable doping levels, the heavily electron-doped 1 UC FeSe/SrVO3 exhibits a pairing temperature (Tg ∼ 48 K) lower than those of FeSe/SrTiO3 and FeSe/LaFeO3. Our findings disentangle the contributions of interfacial EPC from dimensionality in terms of enhancing Tg in FeSe/oxide interfaces, underscoring the critical importance of interfacial EPC. This FeSe/VOx interface also provides a platform for studying interfacial superconductivity.

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.

Significantly enhanced superconductivity in monolayer FeSe films on SrTiO3(001) via metallic δ-doping

Superconductivity transition temperature (Tc) marks the inception of a macroscopic quantum phase-coherent paired state in fermionic systems. For 2D superconductivity, the paired electrons condense into a coherent superfluid state at Tc, which is usually lower than the pairing temperature, between which intrinsic physics including Berezinskii-Kosterlitz-Thouless transition and pseudogap state are hotly debated. In the case of monolayer FeSe superconducting films on SrTiO3(001), although the pairing temperature (Tp) is revealed to be 65-83 K by using spectroscopy characterization, the measured zero-resistance temperature ([Formula: see text]) is limited to 20 K. Here, we report significantly enhanced superconductivity in monolayer FeSe films by δ-doping of Eu or Al on SrTiO3(001) surface, in which [Formula: see text] is enhanced by 12 K with a narrowed transition width ΔTc ∼ 8 K, compared with non-doped samples. Using scanning tunneling microscopy/spectroscopy measurements, we demonstrate lowered work function of the δ-doped SrTiO3(001) surface and enlarged superconducting gaps in the monolayer FeSe with improved morphology/electronic homogeneity. Our work provides a practical route to enhance 2D superconductivity by using interface engineering.

Mechanism Regulating Self-Intercalation in Layered Materials

Recent experimental breakthrough demonstrated a powerful synthesis approach for intercalating the van der Waals gap of layered materials to achieve property modulation, thereby opening an avenue for exploring new physics and devising novel applications, but the mechanism governing intercalant assembly patterns and properties remains unclear. Based on extensive structural search and energetics analysis by ab initio calculations, we reveal a Sabatier-like principle that dictates spatial arrangement of self-intercalated atoms in transition metal dichalcogenides. We further construct a robust descriptor quantifying that strong intercalant-host interactions favor a monodispersing phase of intercalated atoms that may exhibit ferromagnetism, while weak interactions lead to a trimer phase with attenuated or quenched magnetism, which further evolves into tetramer and hexagonal phases at increasing intercalant density. These findings elucidate the mechanism underpinning experimental observations and paves the way for rational design and precise control of self-intercalation in layered materials.

Phase Coherence of Pairs of Cooper Pairs as Quasi-Long-Range Order of Half-Vortex Pairs in a Two-Dimensional Bilayer System

It is known that the loss of phase coherence of Cooper pairs in two-dimensional superconductivity corresponds to the unbinding of vortex-antivortex pairs with the quasi-long-range order in the order-parameter phase field, described by the Berezinskii-Kosterlizt-Thouless (BKT) transition of a 2D XY model. Here we show that the second-order Josephson coupling can induce an exotic superconducting phase in a bilayer system. By using tensor-network methods, the partition function of the 2D classical model is expressed as a product of 1D quantum transfer operator, whose eigenequation can be solved by an algorithm of matrix product states rigorously. From the singularity shown by the entanglement entropy of the 1D quantum analog, various phase transitions can be accurately determined. Below the BKT phase transition, an interlayer Ising long-range order is established at T_{Ising}, and the phase coherence of both intralayers and interlayers is locked together. For two identical layers, the Ising transition coincides with the BKT transition at a multicritical point. For two inequivalent layers, however, there emerges an intermediate quasi-long-range order phase (T_{Ising}<T<T_{BKT}), where the vortex-antivortex bindings occur in the layer with the larger intralayer coupling, but only half-vortex pairs with topological strings exist in the other layer, corresponding to the phase coherence of pairs of Cooper pairs. So our study provides a promising way to realize the charge-4e superconductivity in a bilayer system.

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.

High-Yield Exfoliation of Monolayer 1T'-MoTe2 as Saturable Absorber for Ultrafast Photonics

Liquid-phase exfoliation can be developed for the large-scale production of two-dimensional materials for photonic applications. Although atomically thin 2D transition metal dichalcogenides (TMDs) show enhanced nonlinear optical properties or photoluminescence quantum yield relative to the bulk phase, these properties are weak in the absolute sense due to the ultrashort optical path, and they are also sensitive to layer-dependent symmetry properties. Another practical issue is that the chemical stability of some TMDs (e.g., Weyl semimetals) decreases dramatically as the thickness scales down to monolayer, precluding application as optical components in air. To address these issues, a way of exfoliating TMDs that ensures instantaneous passivation needs to be developed. Here, we employed a polymer-assisted electrochemical exfoliation strategy to synthesize PVP-passivated TMDs monolayers that could be spin coated and restacked into organic-inorganic superlattices with well-defined X-ray diffraction patterns. The segregation of restacked TMDs (e.g., MoS₂) by PVP allows the inversion asymmetry of individual layers to be maintained in these superlattices, which allows second harmonic generation and photoluminescence to be linearly scaled with thickness. PVP-passivated monolayer 1T'-MoTe₂ saturable absorber fabricated from these flakes exhibits fast response and recovery time (<150 fs) and pulse stability. Continuous-wave mode-locking based on 1T'-MoTe₂ saturable absorber in a fiber ring laser cavity has been realized, attaining a fundamental repetition rate of 3.15 MHz and pulse duration as short as 867 fs at 1563 nm.

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.

Possible Evidence for Berezinskii-Kosterlitz-Thouless Transition in Ba(Fe0.914Co0.086)2As2 Crystals

In this study, we measure the in-plane transport properties of high-quality Ba(Fe_0.914Co_0.086)₂As₂ single crystals. Signatures of vortex unbinding Berezinskii–Kosterlitz–Thouless (BKT) transition are shown from both the conventional approach and the Fisher–Fisher–Huse dynamic scaling analysis, in which a characteristic Nelson–Kosterlitz jump is demonstrated. We also observe a non-Hall transverse signal exactly at the superconducting transition, which is explained in terms of guided motion of unbound vortices.

High temperature superconductivity at FeSe/LaFeO3 interface

Enormous enhancement of superconducting pairing temperature (Tg) to 65 K in FeSe/SrTiO3 has made it a spotlight. Despite the effort of interfacial engineering, FeSe interfaced with TiOx remains the unique case in hosting high Tg, hindering a decisive understanding on the general mechanism and ways to further improving Tg. Here we constructed a new high-Tg interface, single-layer FeSe interfaced with FeOx-terminated LaFeO3. Large superconducting gap and diamagnetic response evidence that the superconducting pairing can emerge near 80 K, highest amongst all-known interfacial superconductors. Combining various techniques, we reveal interfacial charge transfer and strong interfacial electron-phonon coupling (EPC) in FeSe/LaFeO3, showing that the cooperative pairing mechanism works beyond FeSe-TiOx. Intriguingly, the stronger interfacial EPC than that in FeSe/SrTiO3 is likely induced by the stronger interfacial bonding in FeSe/LaFeO3, and can explain the higher Tg according to recent theoretical calculations, pointing out a workable route in designing new interfaces to achieve higher Tg.

High-order replica bands in monolayer FeSe/SrTiO3 revealed by polarization-dependent photoemission spectroscopy

The mechanism of the enhanced superconductivity in monolayer FeSe/SrTiO₃ has been enthusiastically studied and debated over the past decade. One specific observation has been taken to be of central importance: the replica bands in the photoemission spectrum. Although suggestive of electron-phonon interaction in the material, the essence of these spectroscopic features remains highly controversial. In this work, we conduct angle-resolved photoemission spectroscopy measurements on monolayer FeSe/SrTiO₃ using linearly polarized photons. This configuration enables unambiguous characterization of the valence electronic structure with a suppression of the spectral background. We consistently observe high-order replica bands derived from various Fe 3d bands, similar to those observed on bare SrTiO₃. The intensity of the replica bands is unexpectedly high and different between d_xy and d_yz bands. Our results provide new insights on the electronic structure of this high-temperature superconductor and the physical origin of the photoemission replica bands.

The origin of the photoemission replica bands in monolayer FeSe/SrTiO₃ remains controversial. Here, the authors perform angle-resolved photoemission spectroscopy with polarized photon on FeSe/SrTiO₃ and observe high-order replica bands with high intensity from various Fe 3d bands, suggesting a mixed mechanism.

Interfacial Electron-Phonon Coupling Constants Extracted from Intrinsic Replica Bands in Monolayer FeSe/SrTiO_{3}

The observation of replica bands by angle-resolved photoemission spectroscopy has ignited interest in the study of electron-phonon coupling at low carrier densities, particularly in monolayer FeSe/SrTiO_{3}, where the appearance of replica bands has motivated theoretical work suggesting that the interfacial coupling of electrons in the FeSe layer to optical phonons in the SrTiO_{3} substrate might contribute to the enhanced superconducting pairing temperature. Alternatively, it has also been recently proposed that such replica bands might instead originate from extrinsic final state losses associated with the photoemission process. Here, we perform a quantitative examination of replica bands in monolayer FeSe/SrTiO_{3}, where we are able to conclusively demonstrate that the replica bands are indeed signatures of intrinsic electron-boson coupling, and not associated with final state effects. A detailed analysis of the energy splittings and relative peak intensities between the higher-order replicas, as well as other self-energy effects, allows us to determine that the interfacial electron-phonon coupling in the system corresponds to a value of λ=0.19±0.02, providing valuable insights into the enhancement of superconductivity in monolayer FeSe/SrTiO_{3}. The methodology employed here can also serve as a new and general approach for making more rigorous and quantitative comparisons to theoretical calculations of electron-phonon interactions and coupling constants.

Spectroscopic evidence of superconductivity pairing at 83 K in single-layer FeSe/SrTiO3 films

Single-layer FeSe films grown on the SrTiO₃ substrate (FeSe/STO) have attracted much attention because of their possible record-high superconducting critical temperature (T_c) and distinct electronic structures. However, it has been under debate on how high its T_c can really reach due to the inconsistency of the results from different measurements. Here we report spectroscopic evidence of superconductivity pairing at 83 K in single-layer FeSe/STO films. By preparing high-quality single-layer FeSe/STO films, we observe strong superconductivity-induced Bogoliubov back-bending bands that extend to rather high binding energy ~ 100 meV by high-resolution angle-resolved photoemission measurements. They provide a new definitive benchmark of superconductivity pairing that is directly observed up to 83 K. Moreover, we find that the pairing state can be further divided into two temperature regions. These results indicate that either T_c as high as 83 K is achievable, or there is a pseudogap formation from superconductivity fluctuation in single-layer FeSe/STO films.

How high the superconducting transition temperature can reach in single layer FeSe/SrTiO₃ films has been under debate. Here, the authors use Bogoliubov back-bending bands as a benchmark and demonstrate that superconductivity pairing can be realized up to 83 K in this system.

Hidden Pseudogap and Excitation Spectra in a Strongly Coupled Two-Band Superfluid/Superconductor

We investigate single-particle excitation properties in the normal state of a two-band superconductor or superfluid throughout the Bardeen–Cooper–Schrieffer (BCS) to Bose–Einstein-condensation (BEC) crossover, within the many-body T-matrix approximation for multichannel pairing fluctuations. We address the single-particle density of states and the spectral functions consisting of two contributions associated with a weakly interacting deep band and a strongly interacting shallow band, relevant for iron-based multiband superconductors and multicomponent fermionic superfluids. We show how the pseudogap state in the shallow band is hidden by the deep band contribution throughout the two-band BCS-BEC crossover. Our results could explain the missing pseudogap in recent scanning tunneling microscopy experiments in FeSe superconductors.