A single-unit-cell film of the iron-based superconductor FeSe grown on SrTiO3(001) shows zero electrical resistance up to about 100 K (onset near 109 K) - roughly an order of magnitude above the 8-9 K transition temperature of bulk FeSe and far above the zero-resistance temperatures accessible in earlier ex situ transport measurements of the same system. The source paper states that the mechanism of this high interfacial TcT_{\rm c} is yet to be understood, with interface-enhanced electron-phonon coupling suggested but not established. A decade of subsequent spectroscopy, transport, structural characterization and theory has established several necessary ingredients (charge transfer from the substrate, cross-interfacial coupling to SrTiO3 phonons, strong correlations, atomic-scale interface structure) and has sharpened the controversy (notably over the interpretation of the photoemission replica bands), but a quantitative, generally accepted account of which interaction drives the pairing, and in what proportions, is still missing. The open problem is to identify and quantitatively establish the microscopic mechanism of the approximately 100 K interfacial superconductivity, together with the auxiliary questions on the intrinsic normal-state transport of the monolayer, the role of the substrate's 105 K structural transition, and the interpretation of the very large extrapolated zero-temperature critical field.

Background

FeSe is the structurally simplest member of the iron-based superconductor family: superconductivity resides in two-dimensional Fe-Se layers, and the bulk compound superconducts at only Tc≃8−9T_{\rm c}\simeq8-9 K. In 2012 it was discovered that a film just one unit cell thick (a single Fe-Se layer, 1-UC) grown by molecular beam epitaxy (MBE, a technique that deposits atoms one layer at a time in ultrahigh vacuum) on the (001) surface of SrTiO3 (STO, a perovskite oxide dielectric) behaves completely differently. Angle-resolved photoemission spectroscopy (ARPES, which maps the electronic band structure and superconducting energy gaps at the surface) found a large superconducting gap of about 15-20 meV that closes near 65-70 K, together with an electronic structure unlike bulk FeSe: the hole Fermi pockets at the Brillouin-zone center are gone and only heavily electron-doped pockets remain. However, conventional electrical transport measurements, which require capping the film and removing it from vacuum, detected zero resistance only below about 30 K, leaving the true zero-resistance transition temperature (TcT_{\rm c}) of the pristine interface unresolved.

Ge et al. (Nature Materials 14, 285-289; 2015) resolved this methodological gap with an in situ four-point-probe (4PP) transport measurement: four sharp metal tips contact the as-grown monolayer inside the vacuum system, so the pristine interface is never exposed. On conducting Nb-doped STO they observed superconducting (zero-voltage) current-voltage curves up to about 109 K, establishing zero resistance above 100 K in the FeSe/SrTiO3 system. The paper explicitly flags what the measurement cannot do and does not explain. First, above TcT_{\rm c} the sample conduction is dominated by the conducting substrate, which has a much larger cross section, so the normal-state resistance of the monolayer itself cannot be determined in this geometry. Second, the measured transition is sample-dependent (about 109 K on one sample, about 99 K on another; the accessible preprint reports a Ginzburg-Landau fit of the critical current giving Tc=111±4T_{\rm c}=111\pm4 K), and occasionally linear, non-superconducting current-voltage curves appear, attributed to sample inhomogeneity or local tip-induced damage. Third, SrTiO3 itself undergoes a cubic-to-tetragonal structural phase transition near 105 K, and the paper states that the effect of this substrate transition on the interfacial superconductivity is yet to be understood. Fourth, superconductivity survives an 11 T out-of-plane field at 3 K, indicating a very large upper critical field Hc2H_{\rm c2} (the field at which superconductivity is destroyed; an extrapolation of order μ0Hc2(0)∼116\mu_0H_{\rm c2}(0)\sim116 T is quoted in the published record), whose relation to intrinsic pairing strength versus extrapolation assumptions is not established. Most importantly, the paper states that the mechanism of the high-TcT_{\rm c} superconductivity is yet to be understood, while noting that interface-enhanced electron-phonon coupling may have played a role.

Several interface ingredients have been identified and debated since. Charge transfer: the substrate, particularly when it contains surface oxygen vacancies, transfers electrons to the FeSe layer and eliminates the hole pockets. Interfacial electron-phonon coupling: electrons in FeSe couple to surface optical phonons of SrTiO3, including Fuchs-Kliewer modes (polar surface phonons that generate a long-range electric field penetrating into the film) and an interfacial mode near 80-100 meV; the striking evidence is the appearance of replica bands in ARPES - copies of the FeSe bands displaced by one phonon quantum, the spectroscopic fingerprint of such coupling. Strain and atomic structure: the epitaxial lattice mismatch compresses the FeSe in-plane lattice, and scanning-transmission-electron-microscopy work has resolved picoscale interfacial structure, including a Ti-O double layer at the interface. Strong correlations: the near-degenerate Fe 3d orbitals and Hund's coupling (the intra-atomic exchange interaction that favors parallel spins on the Fe ion and, here, suppresses electron kinetic energy and amplifies correlation effects) make monolayer FeSe strongly correlated, and theories based on spin fluctuations, orbital-selective pairing (a state in which carriers in some Fe 3d orbitals pair while those in others remain essentially normal), or correlation-enhanced electron-phonon coupling have all been proposed. Whether any single one of these ingredients, or a cooperative combination, quantitatively produces the roughly tenfold enhancement of TcT_{\rm c} is the central open question of the field.

Problem Statement

Identify and quantitatively establish the microscopic mechanism by which a single-unit-cell FeSe film on SrTiO3(001) sustains zero electrical resistance up to about 100 K (onset near 109 K on the best samples), roughly an order of magnitude above the TcT_{\rm c} of bulk FeSe. Specifically, identify which of the following interactions, acting alone or cooperatively, set the pairing scale, and, to the extent the evidence supports it, quantitatively establish the relative contributions of (i) cross-interfacial electron-phonon coupling between FeSe electrons and SrTiO3 surface/interfacial optical phonons (including Fuchs-Kliewer and localized interfacial modes), (ii) charge transfer and electron doping from the substrate (including the roles of oxygen vacancies, band bending and surface termination), (iii) epitaxial strain and the associated electronic reconstruction (the interface-driven rearrangement of the band structure, such as the removal of the hole pockets), and (iv) strong-correlation/many-body effects, to the pairing strength, the gap magnitude, and the transport transition temperature. The open problem also includes the experimental sub-questions raised by the source measurement that bear on the same objective: the intrinsic normal-state sheet resistance and transport of the monolayer, which the original in situ four-point-probe geometry on conducting Nb-doped SrTiO3 cannot determine because the substrate dominates conduction above TcT_{\rm c}; whether and how the substrate's cubic-tetragonal structural transition near 105 K couples to the interfacial superconductivity; and whether the very large extrapolated zero-temperature critical field (reported of order μ0Hc2(0)∼116\mu_0H_{\rm c2}(0)\sim116 T) reflects the intrinsic pairing strength of the interface rather than extrapolation or model limitations.

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