Two-dimensional and interface superconductivity

Scope

Two-dimensional geometry and interface location describe different properties. Weak out-of-plane dispersion does not alone establish a two-dimensional phase transition. An interface can support a superconducting region between constituents that are not superconducting separately. Charge redistribution, oxygen defects, strain, orbital structure and disorder can change together, so an enhanced transition does not identify one universal interface mechanism. R1 R2

Pair formation and macroscopic phase coherence need not coincide. Every temperature below retains its probe and criterion: a spectral gap, resistance onset, noise-floor zero, magnetic screening or BKT analysis. An ultrathin film may also have finite lateral size, nonuniform current paths and coupling to its substrate. These conditions matter when comparing it with an ideal phase model. R4 R6 R8

Mathematical assumptions

In the convention $F=(J_s/2)\int d^2r\,|\nabla\theta|^2$, the ideal BKT jump is $k_BT_{\mathrm{BKT}}=\pi J_s(T_{\mathrm{BKT}}^-)/2$. Here $J_s$ is the long-wavelength, renormalized total phase stiffness, with units of energy. It is not the bare pairing amplitude or a separately measured geometric contribution. Magnetic screening, finite size and interlayer coupling limit the length scales over which the logarithmic-vortex description applies. BCS-like amplitude formation and BKT phase ordering are not mutually exclusive microscopic pairing mechanisms. R6 R7

For a homogeneous local sheet response, $J_s=\hbar^2/(4e^2L_k)$ relates the same stiffness to sheet kinetic inductance. Combining it with the jump gives $L_k=\Phi_0^2/(8\pi k_BT_{\mathrm{BKT}})$, where $\Phi_0=h/(2e)$. Independent electron-density and pair-density conventions give the same conversion. At a hypothetical 0.188 K jump it predicts approximately 65.5 nH per square; this is a model conversion, not an inductance measured in Reyren's device. Finite-frequency response must not be silently identified with the asymptotic equilibrium stiffness. R6 R8

Experimental criteria

A convincing BKT comparison combines current–voltage behavior, an appropriate resistance-fluctuation regime and stiffness where available. An apparent cubic law over a chosen current interval is insufficient: the synthetic response $V=I+I^3$ has nearly cubic high-current behavior while retaining finite low-current resistance. Likewise, an activated resistor can mimic a linearized BKT plot in a narrow window. These checked counterexamples test logical uniqueness, not the validity of any cited experiment. Heating, current window, finite size and inhomogeneity need independent controls. R8

Reyren's 2007 LaAlO3/SrTiO3 measurements distinguish eight-unit-cell and fifteen-unit-cell LaAlO3 overlayers, with resistance reaching the noise floor below approximately 200 and 100 mK respectively at 100 nA. Those overlayer thicknesses are not measured superconducting-sheet widths. The field-dependent transition uses 50% of the 1 K resistance; extrapolated zero-temperature fields of 65 and 30 mT are therefore criterion-dependent estimates. R1

For the eight-unit-cell sample, the current–voltage exponent reaches three near 188 mK and the resistance-tail analysis yields about 190 mK. Figure 4 also shows an ohmic low-current regime attributed to finite size. Agreement between these analyses is informative without eliminating their assumptions. The paper's roughly 10 nm thickness bound relies on an oxygen-defect/carrier-profile scenario and bulk carrier requirements, rather than direct spatial imaging or a unique explanation of carrier origin. R1

Oxide interface controls

The Reyren specimens use TiO2-terminated SrTiO3, pulsed-laser growth and oxygen treatment during cooling. A two-unit-cell reference remains insulating within the reported measurement window. These controls constrain oxygen-vacancy interpretations but do not prove that defects are absent. Later electrostatic gating requires nonlinear capacitance integration and attention to conditioning history; a dome does not establish carrier density as the only variable or identify a unique quantum critical pairing interaction. R1 R9

In Gozar's author manuscript, I denotes insulating La2CuO4, M denotes metallic La1.55Sr0.45CuO4 and S denotes oxygenated superconducting La2CuO4+δ. Reversing I–M to M–I changes the characteristic transition from roughly 15 to 30 K; oxygenating M–I produces M–S near 50 K. The thickness-series figure uses a resistance midpoint. Its separate screening figure reports 33.2 K for S and 51.6 K for M–S, measured with 10 kHz mutual inductance. Screening and transport criteria must remain distinct. R2

Keep four distinct kinds of length-scale evidence separate:

• Deposited thickness: Gozar increases the upper layer in half-unit-cell steps. The transition plateaus after approximately two unit cells in the thickness series. This constrains a characteristic interfacial length scale; it is not a direct image of a superconducting boundary. One LSCO unit cell along the growth direction is approximately 1.3 nm in this paper.
• Screening-current model: The M–S response is decomposed into contributions with extrapolated transitions near 40 and 50 K. Interpreting their low-temperature current amplitudes as thickness weights gives $d_1/d_2\approx20$ and $d_1+d_2=20$ unit cells, hence $d_2\approx20/21\approx0.95$ unit cells. This is the paper's approximate one-unit-cell inference, expressed arithmetically, not a measurement with two-decimal precision. Current conversion also assumes a London response, a typical penetration depth near 2000 Å and an empirical temperature dependence.
• Chemical interface width: Error-function fits to the La EELS profile give rms widths of $1.2\pm0.4$ nm at M–I and $0.8\pm0.4$ nm at substrate–M. These set upper bounds on cation mixing within the structural measurement and fit. They neither measure the superconducting-sheet width nor establish perfectly abrupt chemistry or the absence of oxygen defects.
• Layer-selective suppression: Logvenov's original abstract describes Zn substitutions used as markers to locate interface superconductivity within a single CuO2 plane in bilayers with three-unit-cell constituent layers. The deposited block thickness, chemical profile width and inferred active plane are different quantities. This remains an abstract-level check: Zn concentration, layer-index calibration, transport criteria and the full spatial profile have not been re-extracted from the original methods here.

The thickness evidence supports localization under the stated preparation and models. It does not make current amplitude a unique thickness meter or show that every microscopic interface has the same profile. Complete Gozar final-version comparison, raw-data reconstruction and Logvenov full-methods review remain open. R2 R3

FeSe spectra and annealing

He and colleagues' 2012 author version, associated with the 2013 journal article, follows annealing-dependent electronic phases in single-layer FeSe/SrTiO3. Figure 3 extracts gaps from symmetrized energy-distribution curves and compares them with BCS-form temperature fits. Sequence 10 has an approximately 10 meV gap closing around 40 K; sequence 15 reaches roughly 19 meV and 65 ± 5 K. The latter is an ARPES gap scale, not a measured zero-resistance temperature. R4

The inferred electron count assumes two degenerate electron sheets, and the observed band evolution is not a simple rigid shift. Annealing may alter selenium or oxygen content and atomic configuration; later annealing also degrades sample quality. The selected author text describes direct single-layer transport and magnetic measurements as still underway. A BCS-shaped fit is compatible with a superconducting interpretation but does not independently demonstrate global phase coherence. R4

Lee's later replica-band study supports coupling between FeSe electrons and a substrate-related phonon, while its estimated pairing enhancement depends on the assumed background interaction. Its 58 ± 7 K fitted gap closing belongs to that specimen and analysis, not to He's annealing sequence. Replica bands alone do not partition every contribution to the pairing kernel. See multiband pairing for the source-specific model limitations. R5

Limits and disputes

A superconducting single layer establishes sufficiency under its preparation and measurement conditions, not that interlayer coupling is universally irrelevant. Interface records should not be merged with bulk, transient or high-pressure records. Complete scientific acceptance remains open: selected original passages and figures, inherited named checks and model arithmetic are documented, while full supplements, final-author comparisons, raw-data reanalysis and independent replication are incomplete. R1 R2 R3 R4

Discovery implications

Separate thickness, termination, oxygen history, strain and electrostatics in a controlled comparison. Report the current and frequency window, temperature criterion, sample variation and structural uncertainty. A useful mechanism should predict which intervention changes a gap and which changes phase stiffness, with observations that can distinguish competing explanations. Keep those outcomes separate in prose, search filters and exported evidence. R4 R5 R8 R9

Related topics

Continue with BKT transitions, transport evidence, electrostatic gating, multiband pairing, and geometric stiffness.

Material cases

Values describe individual reports, not a ranking. Unknown means the checked source did not supply the field at this review scope.