Open issues of the annealing-tuned phase diagram of single-layer FeSe/SrTiO$_3$: interfacial doping mechanism, the insulating N phase, the two-dimensional character of the 65 K transition, direct superconductivity confirmation, and the overdoped regime

A 2013 angle-resolved photoemission study of one-unit-cell FeSe films on SrTiO$_3$ (He et al., Nature Materials 12, 605–610) mapped an annealing-controlled phase diagram: a low-doping phase (N phase) whose electronic structure resembles antiferromagnetic parent iron pnictides competes with a superconducting phase (S phase), and a superconducting gap that closes near 65 K signals superconductivity far above the 8 K of bulk FeSe. The paper explicitly left open five issues: the microscopic mechanism by which mild vacuum annealing changes the carrier concentration; the crystal structure and intrinsic properties of the N phase; whether the transition is true three-dimensional long-range order or two-dimensional physics such as a Kosterlitz–Thouless transition; direct transport and magnetic-susceptibility confirmation; and exploration of the overdoped regime. What remains open is the quantitative microscopic decomposition of annealing-induced doping and the N-to-S conversion, the atomic and electronic structure of the insulating N phase, and the quantitative reconciliation of the roughly 65–100 K pairing scale with the much lower phase-coherence temperature.

Background

In iron-based superconductors, superconductivity is usually obtained by doping carriers into a parent compound that shows antiferromagnetic order, and the transition temperature $T_c$ traces a dome-shaped function of doping. Bulk FeSe is an exception among the parents in that it shows no static antiferromagnetic order and superconducts only near 8 K. In 2012, molecular beam epitaxy (MBE, a technique that deposits films one atomic layer at a time in ultrahigh vacuum) was used to grow one-unit-cell (1-UC) FeSe films on the (001) surface of SrTiO$_3$, and scanning tunneling spectroscopy found a superconducting-like gap of roughly 20 meV (Wang et al., 2012), an order of magnitude larger than expected from bulk FeSe. Angle-resolved photoemission spectroscopy (ARPES, which measures the band dispersion and Fermi surface of a crystal by ejecting electrons with photons and analyzing their energy and emission angle) then showed that in the monolayer all the bands near the Brillouin-zone center $\Gamma$ sink below the Fermi level, leaving only electron pockets near the zone corner $M$. He et al. (2013) tuned the carrier concentration of this monolayer by a mild post-growth vacuum annealing procedure carried out in many small steps, measuring the electronic structure after each step. They identified two competing phases: the N phase at low doping, whose momentum-resolved spectra near $M$ (a hole-like band and 'strong spots' of spectral weight) resemble the antiferromagnetic parent compounds BaFe$_2$As$_2$ and SrFe$_2$As$_2$ while, unlike those parents, having no Fermi crossing near $\Gamma$; and the S phase, an electron-doped phase with an electron-like Fermi surface near $M$ that develops a gap. The gap was extracted from symmetrized energy distribution curves (EDCs, photoemission spectra mirrored about the Fermi level so that gap opening appears as a dip), follows a Bardeen–Cooper–Schrieffer (BCS)-like temperature dependence, opens along the entire Fermi surface without shifting the Fermi momentum, and closes near 65±5 K at the strongest annealing, with $2\Delta/k_B T_c \approx 6$–$7$ indicating strong coupling. This 65 K is an electronic indication — a gap-closing temperature from photoemission — not a thermodynamic transition temperature, and the paper says so. The authors posed five open issues, quoted in the problem statement. Several terms used below: the Meissner effect is the expulsion of magnetic field by a superconductor, detectable as diamagnetic screening; a Berezinskii–Kosterlitz–Thouless (BKT) transition is the topological unbinding of vortex–antivortex pairs by which a strictly two-dimensional superconductor develops phase coherence instead of conventional three-dimensional long-range order; exchange bias is a shift of a ferromagnet's hysteresis loop caused by coupling to an adjacent antiferromagnet, used here as indirect evidence of antiferromagnetism; X-ray photoemission spectroscopy (XPS) measures core-level binding energies and work functions; scanning transmission electron microscopy with electron energy loss spectroscopy (STEM-EELS) maps atomic-scale composition and chemistry in cross section.

Problem Statement

As stated by its source (He et al., Nature Materials 12, 605–610 (2013)), the problem is to resolve the five issues that the annealing-tuned phase diagram of single-layer FeSe on SrTiO$_3$ left open: (1) determine the microscopic mechanism by which mild vacuum annealing raises the carrier concentration, discriminating among Se-vacancy formation, oxygen depletion of the SrTiO$_3$ surface with interfacial charge transfer, and atomic rearrangement at the FeSe–SrTiO$_3$ interface; (2) determine the detailed crystal structure and intrinsic physical properties of the low-doping N phase, including its magnetic order, its degree of insulating character, and its relation to the antiferromagnetic parent compounds of the iron pnictides; (3) decide whether the superconductivity of the monolayer is governed by true three-dimensional long-range order or by two-dimensional physics such as a Kosterlitz–Thouless transition, and identify the concrete role of the SrTiO$_3$ substrate and interface in stabilizing the superconducting state; (4) confirm superconductivity by direct resistivity and magnetic-susceptibility (Meissner) measurements, reported as under way but technically difficult; and (5) extend the phase diagram to higher (overdoped) carrier concentrations and establish whether $T_c$ can be increased further, noting that the strongest annealing conditions destabilize the film. The task is to resolve the surviving core of these questions: (i) A quantitative microscopic decomposition of annealing-induced carrier doping and the N-to-S phase conversion in 1-UC FeSe/SrTiO$_3$, giving the relative roles of SrTiO$_3$ oxygen vacancies, Se vacancies, and Se diffusion into the substrate (all three candidate channels are in scope); (ii) the atomic and electronic structure of the insulating N phase, whose magnetic order is so far established only indirectly (exchange bias) and whose crystal structure is undetermined; and (iii) the quantitative account of how the pairing scale (the 65 K gap-closing temperature, and gaps persisting up to and above 100 K on doped substrates) relates to the much lower BKT-like phase-coherence temperature of roughly 30–55 K measured by transport, i.e. the dimensionality and fluctuation physics of the superconducting transition in this monolayer. The other parts of the source's five issues are not addressed here.

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