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REVIEW 2 major objections 5 minor 53 references

Single spin-polarised Fermi surface in SrTiO$_3$ thin films

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Pith's one-line read Thin SrTiO3 films grown on niobium-doped substrates reduce the surface 2D electron gas to a single spin-polarised Fermi surface, a configuration that could host Majorana bound states.

desk verdict A credible growth-based route to a single helical Fermi surface on STO, with the Zeeman-gap interpretation still resting on crystal data rather than film data. read the letter →

arxiv 1908.07379 v2 pith:SYTYQSC2 submitted 2019-08-20 cond-mat.str-el cond-mat.mes-hall

Eduardo B. Guedes , Stefan Muff , Mauro Fanciulli , Andrew P. Weber , Marco Caputo , Zhiming Wang , Nicholas C. Plumb , Milan Radović
show 1 more author
J. Hugo Dil
This is my paper · ORCID
classification cond-mat.str-elcond-mat.mes-hall PACS 73.20.At71.70.Ej79.60.-i
keywords strontiumtitanatetwo-dimensionalelectrongasspin-polarisedFermisurfaceRashbaspin-orbitcouplingZeemangapMajoranaboundstatesangle-resolvedphotoemissionpulsedlaserdeposition
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper reports a way to control the band filling of the two-dimensional electron gas (2DEG) that forms at the surface of SrTiO3(001). By growing thin SrTiO3 films on niobium-doped SrTiO3 substrates, the authors lower the bottom of the main $d_{xy}$ band from the usual 230 meV to 80 meV below the Fermi level, so the Fermi level sits inside the spin gap at the surface Brillouin zone centre. Spin-resolved photoemission then shows exactly one helical, spin-polarised band. If correct, this gives a stable single-spiral Fermi surface in a superconducting material, which is the ingredient combination needed for Majorana bound states, and it also implies the 2DEG is confined within the top two unit cells of the film.

What carries the argument

The argument rests on two ingredients. The first is a growth-controlled chemical-potential shift: pulsed-laser-deposited homoepitaxial SrTiO3 films on Nb-doped substrates fix the $d_{xy}$ band bottom at 80 meV, far below the 230 meV filling of cleaved or annealed crystals. The second is the Rashba-Zeeman spin gap at the surface Brillouin zone centre, a spin gap that opens at $\bar{\Gamma}$ when spin-orbit and magnetic interactions combine, as previously measured for STO crystal surfaces. Placing the Fermi level inside that gap yields exactly one helical Fermi surface; the simultaneous fit of spin-integrated intensity and the three spin-polarisation components of the momentum distribution curve is the tool that establishes this single band. The Nb-doping level of the substrate moves the band bottom and thus selects how many bands cross the Fermi level.

What would settle it

A decisive test is to measure the spin-resolved dispersion of the 10 u.c. film across a range of binding energies down to the band bottom. If the spin splitting between the two $d_{xy}$ branches is smaller than 80 meV, or if a second spin-polarised branch is found crossing $E_F$, then the Fermi level is not in the Zeeman gap and the central claim is refuted.

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Extended reading notes

Core claim

For pulsed-laser-deposited SrTiO3 films between 3 and 20 unit cells (u.c.) thick on 0.5 wt% Nb-doped SrTiO3(001), the surface 2DEG consists of a single $d_{xy}$-derived parabolic band with a band bottom at 80 meV binding energy and an effective mass of $0.74\,m_e$; the heavier $d_{xz}$ and $d_{yz}$ bands are absent, and the state is purely two-dimensional in photon-energy scans. Spin-resolved angle-resolved photoemission on a 10 u.c. film resolves one band whose in-plane spin polarisation is perpendicular to the crystal momentum and reverses sign across the zone centre, matching a helical Rashba-like texture. Interpreting this through the Zeeman gap previously reported at the STO surface Brillouin zone centre, the authors conclude that the Fermi level for these films lies inside the gap, leaving a single spin-polarised Fermi surface. On 0.05 wt% Nb-doped substrates the band bottom moves back up to roughly 170 meV and a second inner band appears to be populated, showing that substrate doping tunes the filling. The authors further infer, from the thickness independence and from XPS of Sr 3d and Ti 3p core levels, that the 2DEG is confined to no more than two unit cells beneath the top TiO2 layer and that the amount of surface SrOx, rather than the Ti3+ fraction, tracks the band filling.

Load-bearing premise

The paper assumes that the magnetic spin gap seen at the surface of SrTiO3 crystals is still present in the thin films and is larger than 80 meV; the authors do not measure this gap in the films and explicitly write that "a change in spin splitting cannot be excluded and requires experimental verification."

Editorial extensions

If this is right

  • Stable control of band filling: unlike the universal 230 meV filling seen on cleaved and annealed SrTiO3 crystals, films on Nb-doped substrates put the Fermi level where the experimenter chooses within the spin gap, with no gate voltage or surface contamination required.
  • A single helical Fermi surface exists for films of 3 to at least 20 u.c. on 0.5 wt% Nb-doped substrates; combined with the superconductivity of STO, this is a single-material platform for Majorana bound states.
  • The 2DEG does not extend beyond the top two unit cells, so its properties are governed by the surface termination and the film's dielectric response rather than the bulk vacancy concentration.
  • Changing the substrate Nb doping from 0.5 to 0.05 wt% shifts the band bottom from 80 meV to about 170 meV, showing the filling can be tuned across the spin-gap window.
  • The correlation between surface SrOx content and band filling suggests surface chemistry is an additional, possibly independent, tuning knob.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the Zeeman gap in the films has the same size as on crystals, there should be an intermediate Nb-doping level at which the Fermi level crosses the gap edge; mapping that crossover would turn the single-vs-double Fermi surface transition into a controlled phase boundary.
  • Direct SARPES of the full band dispersion, not just the Fermi level, could measure the film's spin splitting directly and test whether the gap is actually larger than the 80 meV band bottom.
  • The SrOx correlation suggests a testable extension: preparing adjacent regions of the same film with different SrOx coverage (e.g., by localised annealing or patterned growth) should produce regions with different band fillings on one substrate.
  • If the confinement to two unit cells is right, then the single-spiral regime should be independent of film thickness beyond 3 u.c. but disappear when the surface termination is changed to TiO2-rich; this is checkable with existing PLD and ARPES tools.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. The paper reports ARPES and spin-resolved ARPES studies of pulsed-laser-deposited SrTiO3 films grown on Nb-doped SrTiO3(001) substrates. The authors find that the surface 2DEG in these films has a much reduced dxy band filling compared with STO single crystals: the dxy band bottom lies at about 80 meV for films on 0.5 wt% Nb-doped substrates, and the heavy dxz/dyz bands are absent, resulting in a purely two-dimensional state. For these films the Fermi surface consists of a single band with a helical spin texture, which the authors interpret as the Fermi level lying inside the Zeeman gap at the surface Brillouin-zone centre. For films on 0.05 wt% Nb-doped substrates the band filling is larger (about 170 meV), and the authors report evidence for a second populated band. XPS data correlate the band filling with the amount of surface SrOx and suggest that the filling changes are related to the surface termination and possibly the dielectric response. The authors conclude that film growth on Nb-doped substrates provides a stable way to control the 2DEG filling and that the 0.5% films host a single spin-polarised Fermi surface relevant for Majorana physics.

Significance. The experimental data are of high quality and the paper introduces a promising growth-based route to tune the filling of the STO surface 2DEG. The thickness-independence study over 3–20 unit cells, the direct spin-resolved observation of a helical texture in the films, and the XPS correlation with surface SrOx are valuable additions to the field. The paper is also honest about its limitations, explicitly flagging the need for spin-splitting verification. However, the central claim that the Fermi level lies inside the Zeeman gap, and hence that the 0.5% films host a single helical Fermi surface relevant for Majorana physics, depends on an unmeasured parameter: the size (and even existence) of the Zeeman gap in these PLD-grown films is not directly established by the present data. This makes the headline result conditional on an external measurement whose reproducibility is debated.

major comments (2)
  1. [Section II.A, Fig. 4] The central conclusion that the Fermi level lies inside the Zeeman gap for the 0.5 wt% Nb-substrate films is not directly measured. The spin gap Δ is taken from Ref. [18] on STO single crystals and assumed to be unchanged in the PLD-grown films; the paper itself states in Section II.A that "a change in spin splitting cannot be excluded and requires experimental verification." Because an inner spin-split branch would have a small Fermi wave vector (roughly 0.05 Å⁻¹ for Δ just below 80 meV) and could be masked by the 70 meV energy resolution of the COPHEE SARPES and the strong incoherent spectral weight below 150 meV, the observation of a single band in the spin-resolved MDC does not by itself place the Fermi level inside the gap. This assumption is load-bearing for the Majorana-platform claim in Section III and for the title/abstract statement of a single spin-polarised Fermi surface.
  2. [Section II.B and Appendix Sec. 5] The evidence that the 0.05 wt% Nb-substrate film hosts two occupied bands relies on a four-peak fit to low-resolution COPHEE data and on unresolved or broad spectral weight in the high-resolution ARPES data; the authors acknowledge in Section II.B that this "requires further investigation." Since this film is one of only two substrate dopings used to demonstrate substrate-controlled band filling, the abstract's claim that band filling "can be controlled" by the substrate doping is stronger than the present evidence. A more systematic doping series or a clearly resolved second band in the 0.05% film would be needed to fully support the claim of controlled, monotonic tuning of the 2DEG filling.
minor comments (5)
  1. [Fig. 3 caption] The caption describes "The 2DEG on 10 u.c. film grown on highly-doped substrate," but panels (a-c) are for 3, 5, and 20 u.c. films; this appears to be a typo and should be corrected.
  2. [Appendix Sec. 1] The appendix contains leftover text from a thesis ("6.2. Ba x Sr1°x TiO3 Thin Films" and "6.2.1 Film preparation") that is not part of the paper and should be removed.
  3. [Sec. II.C] The word "spectromiscroscopy" should be "spectromicroscopy."
  4. [Appendix Sec. 3] The sentence "Along (a) ΓX and (b) ΓX" should read "Along (a) ΓX and (b) ΓM."
  5. [Fig. 1] The labels "b) SrTiO3 thin film" and "b) SrTiO3 single crystal" appear to be interchanged; the schematic in panel (b) shows the film structure and should be labelled accordingly.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the single-Fermi-surface claim rests on direct ARPES/SARPES data, with the Zeeman-gap interpretation imported from external prior work and explicitly flagged as needing verification.

full rationale

The paper's central claims are direct experimental observations: the dxy band bottom, Fermi wave vector, absence of heavy bands, number of bands crossing EF, and helical spin polarization are all measured by ARPES/SARPES on PLD-grown films. The interpretation that EF lies inside the Zeeman gap combines the measured 80 meV band bottom with the Rashba+Zeeman model from external SARPES on STO crystals (ref. 18), but the gap is not fitted here and is not defined in terms of the conclusion. The authors explicitly acknowledge the assumption: 'a change in spin splitting cannot be excluded and requires experimental verification' (Sec. II A). Ref. 18 is independent, externally falsifiable prior work, even though some authors overlap, and its disputed status is openly discussed (ref. 21, Appendix Sec. 6). No equation in the paper reduces the predicted result to an input by construction, and no fitted parameter is renamed as a prediction. Concerns about the unmeasured Zeeman gap in PLD films are external validity or robustness issues, not circularity.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The paper's central claims rest on several unverified assumptions: the persistence of the crystal Zeeman gap in films, the rigid-band-shift picture, and the inference of 2 u.c. confinement from thickness independence. The only numbers fitted to data are the band parameters, which are outcomes rather than free inputs. No invented entities are introduced.

free parameters (3)
  • dxy band bottom energy (0.5% films) = 80 meV
    Fitted from ARPES dispersions; the claim that EF lies inside the Zeeman gap depends on comparing this value with the gap size from [18].
  • dxy band bottom energy (0.05% films) = 170 meV
    Fitted from ARPES dispersions; used to argue for two populated bands on the low-doped film, though the inner band is not fully resolved.
  • dxy effective mass = 0.74 me
    Parabolic fit to the dispersion; not directly load-bearing for the central claim but used to compare with the single-crystal value.
assumptions (4)
  • domain assumption The 2DEG on STO films has the same Rashba-Zeeman spin structure as the crystal surface 2DEG, with a Zeeman gap at the zone centre large enough to contain the Fermi level when band filling is 80 meV (from Santander-Syro et al. Nat. Mater. 2014 [18]).
    Used in the discussion to interpret the single observed band as the sole helical Fermi surface with EF inside the Zeeman gap; the gap is not directly measured in this work.
  • domain assumption The band filling difference between crystals and films corresponds to a rigid shift of the dxy band, so the spin splitting (Rashba parameter) is unchanged.
    Explicitly stated in Sec. II A: 'applying a rigid upwards energy shift would lead to a single spin-polarized Fermi surface'; the authors acknowledge a change in spin splitting cannot be excluded and requires verification.
  • domain assumption Absence of the heavy dxz/dyz bands at hν = 85 eV in films indicates they are unoccupied, not simply not probed.
    Used to conclude the 2DEG is purely dxy-derived; they also use photon-energy scans and polarization dependence.
  • domain assumption The similarity of Fermi surfaces for 3, 5, and 20 u.c. films implies the 2DEG is confined to the top 2 u.c. or less.
    Inference from thickness independence; no direct depth profiling is performed.

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Pith. "Pith review of Single spin-polarised Fermi surface in SrTiO$_3$ thin films." pith.science (2026). https://pith.science/paper/SYTYQSC2

@misc{pith2026190807379,
  author       = {Pith},
  title        = {Pith review of: Single spin-polarised Fermi surface in SrTiO$_3$ thin films},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SYTYQSC2}},
  note         = {Machine review of arXiv:1908.07379}
}
abstract

The 2D electron gas (2DEG) formed at the surface of SrTiO$_3$(001) has attracted great interest because of its fascinating physical properties and potential as a novel electronic platform, but up to now has eluded a comprehensible way to tune its properties. Using angle-resolved photoemission spectroscopy with and without spin detection we here show that the band filling can be controlled by growing thin SrTiO$_3$ films on Nb doped SrTiO$_3$(001) substrates. This results in a single spin-polarised 2D Fermi surface, which bears potential as platform for Majorana physics. Based on our results it can furthermore be concluded that the 2DEG does not extend more than 2 unit cells into the film and that its properties depend on the amount of SrO$_x$ at the surface and possibly the dielectric response of the system.

Figures

Figures reproduced from arXiv: 1908.07379 by the authors.

Figure 1
Figure 1. FIG. 1. The spin-polarised 2DEG on SrTiO [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. 3D Fermi surface mapping of state at SrTiO [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The 2DEG on 10 u.c. film grown on highly-doped substrate. (a) Fermi surface, (b) band structure and (c) 2D curvature [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Spin-polarisation of single band at Fermi level. (a) Electron dispersion of 10 u.c. STO film grown on 0.5 wt% Nb:STO [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. The 2DEG on film grown on low-doped substrate. (a) Fermi surface in the k [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. XPS analysis of PLD-grown STO films. (a) Ti 3p core-level measured at normal emission (NE) and 45 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 6
Figure 6. Figure 6: – (a-c) RHEED oscillations of the film growth of 3 uc (a), 5 uc (b) and 20 uc (c) FIG. A1. RHEED oscillations of the film growth of (a) 3 u.c., (b) 5 u.c. and (c) 20 u.c. STO on 0.5 wt% Nb:STO(001) [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

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