Interplay between band structure and Hund's correlation to increase T$_{c}$ in FeSe

Dimitar Pashov; Francois Jamet; Mark van Schilfgaarde; Swagata Acharya

REVIEW 3 major objections 5 minor 45 references

Interplay between band structure and Hund's correlation to increase T$_{c}$ in FeSe

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read FeSe superconductivity is controlled by the dxy band position and Hund's coupling J.

desk verdict A serious computational study that plausibly identifies dxy proximity and Hund's J as key controls on FeSe superconductivity, but the headline interface result hangs on an untested Se height. read the letter →

arxiv 1908.08136 v2 pith:QUBUNEQX submitted 2019-08-21 cond-mat.str-el cond-mat.supr-con

Swagata Acharya , Dimitar Pashov , Francois Jamet , Mark van Schilfgaarde This is my paper · ORCID

classification cond-mat.str-elcond-mat.supr-con

keywords FeSeHund'smetalsuperconductingpairinggluedxyorbitalspinfluctuationsdynamicalmean-fieldtheoryEliashbergequationSrTiO3substrate

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 asks what controls the superconducting critical temperature Tc in FeSe, from bulk crystals (Tc ≈ 9 K) to a monolayer on SrTiO3 (Tc up to about 75 K). It argues that two conditions must hold simultaneously: the iron dxy band must sit near the Fermi level, and the Hund's exchange J must be large enough to make the metal strongly incoherent. Under those conditions, low-energy spin fluctuations near the antiferromagnetic ordering vector become intense and supply the superconducting pairing glue. The claim is supported by parameter-free calculations that scan J and the Fe–Se bond length, and it explains why a free-standing monolayer should not superconduct while the same monolayer on SrTiO3 should.

What carries the argument

The central machinery is QSGW++, a four-tier chain: QSGW (quasiparticle self-consistent GW) builds the one-particle Hamiltonian and captures nonlocal charge correlations; DMFT (dynamical mean-field theory) with a continuous-time quantum Monte Carlo impurity solver adds local spin fluctuations; a Bethe-Salpeter equation constructed from the DMFT local vertex and nonlocal bubbles yields the spin and charge susceptibilities; and the linearized Eliashberg equation turns those susceptibilities into the leading superconducting eigenvalue λ. The load-bearing ingredients for the paper's conclusion are the orbital-resolved mass renormalization 1/Z and scattering rate Γ, the intensity and dispersion of Im χ(q,ω) at q = (1/2,1/2), and the cRPA-derived values of U and J for each geometry.

What would settle it

Measure the selenium height in the FeSe/SrTiO3 interface with sub-0.01 Å precision (for example by surface-extended X-ray absorption fine structure or low-energy electron diffraction) and recompute the dxy band position at that height. If dxy sits more than about 100 meV below the Fermi level in the actual interface, the predicted λ = 0.34 would drop toward the monolayer value, falsifying the claim that dxy proximity is what restores superconductivity.

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Extended reading notes

Core claim

Using a four-tier ab initio method that combines quasiparticle self-consistent GW with dynamical mean-field theory, a Bethe-Salpeter treatment of two-particle response, and an Eliashberg solution of the pairing instability, the paper finds that the superconducting eigenvalue λ is controlled by the interplay of band structure and Hund's correlation. The Fe dxy orbital is the most strongly renormalized and incoherent of the five d orbitals, and it dominates the pairing glue as long as it lies near the Fermi energy. The glue itself is the imaginary part of the spin susceptibility Im χ(q,ω) concentrated near the antiferromagnetic wavevector (1/2,1/2): when J is raised from the ab initio 0.60 eV to 0.68 eV, the susceptibility sharpens and λ jumps from 0.067 to 0.9. Conversely, when the Fe–Se bond length is shortened so that dxy drops well below EF, the system becomes a coherent Fermi liquid with negligible spin fluctuations and λ ≈ 0. The same mechanism differentiates the two monolayer cases: in free-standing M-FeSe the dxy band is pushed about 300 meV below EF and λ = 0.002, while on SrTiO3 it returns to within 50–100 meV of EF, incoherence is restored, and λ = 0.34—five times the bulk value.

Load-bearing premise

The entire distinction between the superconducting interface (λ = 0.34) and the non-superconducting monolayer (λ = 0.002) rests on the assumed selenium height above the iron plane—1.39 Å for the free monolayer and 1.40 Å on SrTiO3, taken from an external structure optimization; if the real height differs by a few hundredths of an Ångström in the direction that pushes dxy below the Fermi level, the predicted enhancement collapses.

Editorial extensions

If this is right

Because the superconducting eigenvalue λ jumps from 0.067 to 0.9 when J is tuned from 0.60 to 0.68 eV, materials that modestly increase Hund's coupling—by reducing screening—could gain an order of magnitude in Tc.
A free-standing FeSe monolayer is predicted to be a non-superconducting good metal with dxy about 300 meV below EF; placing it on SrTiO3 restores dxy proximity and raises λ fivefold to 0.34.
The pairing instability is dominated by the intra-orbital dxy–dxy channel, so the superconducting gap should be largest on dxy-dominated Fermi-surface sheets, as the paper notes is observed.
Compressing the Fe–Se bond length pushes dxy below EF, suppresses spin fluctuations, and eliminates superconductivity, making the collapsed phase of FeSe a coherent Fermi liquid with λ ≈ 0.

Reading between the lines

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

The paper's two-knob picture suggests a screening rule for other Hund's metals: an orbital with strong Hubbard correlations that sits near EF, plus a large J from reduced screening, is the recipe for high Tc; strain or pressure that moves that orbital away from EF will kill pairing even if J grows.
Because the same method predicts λ = 0.34 from spin fluctuations alone, the gap to the experimental 75 K could be closed by additional mechanisms, such as electron-phonon coupling at the SrTiO3 interface; a combined calculation including phonons is a direct test of whether spin fluctuations are sufficient.
A testable extension of the logic: electron-dope or strain bulk FeSe to move dxy closer to EF without changing J; the paper's mechanism predicts Tc should track the dxy proximity, which could be checked by ARPES plus specific-heat measurements across a doping series.
The monolayer result implies that simply isolating an FeSe layer is not enough to enhance Tc; the substrate's role is to undo the monolayer's downward shift of dxy, so interface design should focus on orbital alignment rather than only on doping or electron-phonon coupling.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Colleague—

This paper is worth a serious referee. The headline claim is concrete: in FeSe, high Tc requires the Fe dxy band near the Fermi level, and once that condition is met, Hund's J amplifies spin fluctuations that provide the pairing glue. The QSGW++ approach (QSGW+DMFT+BSE+Eliashberg) is state-of-the-art, and the internal trends are consistent: λ rises steeply with J up to a maximum, then falls; pushing dxy below EF collapses λ. The orbital-resolved decomposition identifying dxy as the dominant pairing channel is a genuinely new result, and the benchmark against neutron data in earlier work gives some confidence in the susceptibility.

What the paper does well: it is transparent about its own sensitivity. The authors state flat-out that the Se height is 'critical' and that DFT cannot be trusted for it, and they acknowledge that the calculated λ is extremely sensitive to J and h. That candor helps, but it also highlights the main weakness.

The soft spot is load-bearing. The entire contrast between M-FeSe/STO (λ=0.34) and the free-standing monolayer (λ=0.002) rests on the interface h being 1.40 Å, taken from Mandal et al.'s DFT+DMFT relaxation. The paper does not test how λ for the interface varies with h. Given bulk FeSe's λ drops from 0.067 to 0.003 when h is reduced from 1.463 to 1.27 Å, a few hundredths of an Ångström in h could plausibly shift dxy below EF and eliminate the claimed five-fold enhancement. This is not a minor technicality; it is the quantitative foundation of the paper's central comparison.

Two more points. First, the paper repeatedly refers to Tc but actually computes the superconducting eigenvalue λ. The connection to Tc is never spelled out, so claims like 'eight-fold increment in Tc' are not strictly derived. Second, the references are sloppy: 'Mondal' should be 'Mandal', and refs [44] and [46] are duplicated. Minor, but in a paper whose results hinge on an external structural input, getting that citation right matters.

On circularity: I do not see a serious problem. U and J are cRPA outputs, not fits to Tc, and the J-scan is presented as a sensitivity study. The fact that the method comes from the same group is not a flaw by itself.

Bottom line: the qualitative mechanism—dxy proximity plus Hund's coupling controls spin-fluctuation pairing—is plausible and well supported by the trends. The quantitative interface claim needs a robustness check on h. Send it to peer review; ask for an h-scan for the interface, an error bar on U and J, and an explicit statement of the λ-to-Tc mapping. A good referee will see the value and push for the missing analyses. For anyone working on FeSe or Hund's metals, this paper is worth reading.

Referee Report

3 major / 5 minor

Summary. The paper uses a combined QSGW+DMFT+BSE+Eliashberg (QSGW++) framework with cRPA-derived U and J to study superconductivity in bulk FeSe, a free-standing monolayer (M-FeSe), and a monolayer on SrTiO3 (M-FeSe/STO). The central claim is that the superconducting pairing eigenvalue lambda is controlled by two conditions: the Fe 3dxy orbital must lie close to the Fermi level, and the Hund's coupling J must be large enough to produce incoherent 'bad metal' behavior. The authors show that bulk FeSe has strong low-energy spin fluctuations near q=(1/2,1/2), that these fluctuations are dominated by dxy, and that small increases in J strongly enhance lambda. They then argue that in M-FeSe the dxy band is pushed below EF, killing the spin fluctuations and reducing lambda to 0.002, whereas in M-FeSe/STO the substrate restores dxy near EF, giving lambda=0.34, which they interpret as explaining the high observed Tc. They also study reduced Se height and electron doping as controlled perturbations around the ab initio reference.

Significance. If the central claim holds, the paper provides a unified orbital-specific mechanism for superconductivity across bulk, monolayer, and interface FeSe: Hund's coupling and the proximity of dxy to EF control the intensity of low-energy antiferromagnetic spin fluctuations, which in turn control the pairing eigenvalue. The work has notable strengths: the cRPA values of U and J are not fitted to Tc; the J-scan is presented explicitly as a sensitivity study rather than a fit; the computed Im chi(q,omega) is benchmarked against inelastic neutron scattering in a companion study; and the orbital-resolved dxy dominance of the pairing glue is a concrete, falsifiable prediction consistent with ARPES and STM observations. The qualitative picture is coherent and internally consistent. However, the quantitative claims, especially the 'five-fold enhancement' for M-FeSe/STO, are fragile because lambda is extremely sensitive to the Se height h and to J, and no uncertainty or robustness analysis is provided for the interface geometry.

major comments (3)

[Main text (paragraph 'We consider 5-ML slab...') and Fig. 2(d)] The central contrast between M-FeSe/STO (lambda=0.34) and free-standing M-FeSe (lambda=0.002) rests on the Se height h being 1.40 Å vs 1.39 Å, both taken from Ref. [44], but no sensitivity analysis is performed for the interface. The paper itself states about h: 'Its value is critical, as we have seen in the bulk case, and we cannot rely on DFT for it.' The bulk h-scan already shows the danger (Table II: h=1.463 Å gives lambda=0.067; h=1.27 Å gives lambda=0.003). A shift of a few hundredths of an Ångström in M-FeSe/STO, in the direction that pushes dxy below EF, could reduce lambda by more than an order of magnitude and erase the qualitative distinction between the interface and the monolayer. Please add a controlled sweep of h for M-FeSe/STO (and ideally for M-FeSe) around the adopted values, using the same cRPA U,J and QSGW++ pipeline, or provide an error estimate for h from the DFT+DMFT relaxation.
[Fig. 2(f) and Table II] The quantitative values of lambda are extremely sensitive to J: bulk FeSe goes from lambda=0.067 at J=0.60 eV to lambda=0.9 at J=0.68 eV (Table II and Fig. 2(f)). The cRPA J values are quoted without uncertainty (J=0.60, 0.67, 0.69, 0.71 eV for the four systems), and a 0.01-0.02 eV uncertainty in the interface J would change the reported M-FeSe/STO lambda=0.34 by a large factor. The qualitative trend (larger J increases low-energy Im chi and lambda up to a maximum) is supported, but the headline quantitative claim 'five times larger than bulk' is not robust unless accompanied by a J-sensitivity grid for the interface or an error estimate on cRPA J. Please either provide such a grid or soften the quantitative claim to a qualitative statement.
[Main text, paragraph on M-FeSe/STO results] The calculation fails to suppress the dxz,yz hole pockets that are absent in ARPES; the paper states this suppresses lambda by only 6%, but the supporting calculation is not shown. If the Fermi surface topology is wrong, the spin susceptibility and Eliashberg eigenvalue could be affected beyond 6%. Please document how the 6% estimate was obtained (e.g., by explicitly removing those pockets or shifting bands) and show the resulting chi(q,omega) and lambda for that modified Fermi surface.

minor comments (5)

[References] Reference [44] is spelled 'Mandal' in the reference list but 'Mondal' in the main text (two occurrences); please unify the spelling.
[References] Several references have incomplete bibliographic data or nonstandard formatting: [9] 'L. Sponza and et al', [10] lacks volume/page/article number, [13] 'E. Gull and et al.', and [46] appears twice. Please bring them into journal style.
[Tables I and II] The units 'A0' in Tables I and II should be 'Å', and the M-FeSe J value in Table I is given as 0.7 rather than 0.70 eV; please make the precision consistent with the other entries.
[Abstract] The sentence 'Our study opens a paradigm for a unified understanding what controls Tc' is missing a preposition; it should read 'understanding of what controls Tc'.
[Figure 2 caption] In the caption of Fig. 2, the phrase 'while in (b) and (c)dxy is pushed far below EF : and the system has properties similar to a normal Fermi liquid' contains a colon and spacing error; please correct the punctuation.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the calculated λ values are outputs of QSGW+DMFT+BSE with cRPA-derived U and J; the J excursions are an explicit sensitivity study, and the Se-height inputs are taken from an external DFT+DMFT structure calculation.

full rationale

The paper's derivation chain is self-contained rather than circular. The interaction parameters U and J are obtained from constrained RPA starting from the QSGW one-particle Hamiltonian, and the superconducting eigenvalues λ for bulk FeSe, the monolayer, and the STO interface are computed outputs of the DMFT+BSE+Eliashberg machinery. The paper does not fit U, J, or any parameter to the target λ or Tc; instead it varies J and the Fe-Se height around the ab initio point as an explicit parametric sensitivity study. The authors cite their own previous work to establish the method's fidelity, including benchmarks against neutron scattering and superconductivity in other Hund's metals, but the central FeSe claims are computed here and are not obtained by importing the conclusion through a self-citation. The acknowledged sensitivity of the interface result to the assumed Se height h=1.40 Å is a structural-robustness concern and a limitation, not circularity, because h is an externally supplied input rather than a quantity defined by or fitted to the pairing eigenvalue. No step in the paper reduces by construction to its own inputs, and therefore the appropriate circularity score is 0.

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

The central claim relies on the accuracy of the QSGW++ theory, the structural geometries (especially Se height) taken from an external calculation, and the cRPA-derived U and J values. The J-scan introduces a free parameter, but the key ab initio predictions (lambda_bulk=0.067, lambda_M-FeSe=0.002, lambda_STO=0.34) are computed, not fitted to Tc. The main circularity risk is that the same authors' earlier work provides the method and the FeSe spin-susceptibility benchmark (Ref 25), so the method is not independent of the target material.

free parameters (3)

Hund's coupling J (scan variable) = 0 to 1 eV; ab initio reference 0.60 eV (bulk), 0.67-0.71 eV for monolayer/interface from cRPA
The paper's primary parametric study treats J as a free parameter and finds lambda is extremely sensitive to it; the peak lambda at J=0.68 eV is used to argue small excursions in J cause large changes in Tc.
Se height h (structural input) = 1.39 Å (M-FeSe), 1.40 Å (M-FeSe/STO), from Ref [44]
Taken from an external DFT+DMFT relaxation, not computed here; the entire bulk-vs-monolayer-vs-interface comparison hinges on h-dependent dxy band position.
Doping potential shift ΔV and background charge Q = ΔV = -0.1 eV with Q=0.155e; ΔV=-0.2 eV with Q=0.211e
Ad hoc parameterization of electron doping in bulk FeSe by shifting the dxy potential and adding uniform background charge; used to demonstrate dxy proximity matters.

assumptions (4)

domain assumption The QSGW+DMFT+BSE+Eliashberg (QSGW++) framework accurately captures the superconducting pairing kernel for FeSe.
The entire paper uses this four-tier ab initio method (Section 'In this work...'); its accuracy for FeSe is asserted with benchmarks in the authors' earlier work, not independently validated in this text.
domain assumption The local DMFT vertex with nonlocal bubble diagrams is sufficient for spin-fluctuation-mediated pairing.
The BSE is constructed by computing the local vertex from the two-particle Green's function by DMFT and combining it with nonlocal bubble diagrams (Section 2); whether nonlocal vertex corrections are negligible is not established.
domain assumption The linearized Eliashberg equation in the BCS low-energy approximation determines the relative superconducting instability.
They solve Eliashberg equations in the BCS low energy approximation (Section 'How do these striking changes...') but never present the mapping from lambda to Tc.
domain assumption Structural parameters from Ref [44] are correct for the monolayer and interface.
h is predicted in Ref [44] and fixed; authors state 'we cannot rely on DFT for it', so the assumption is load-bearing.

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Cite this review

Pith. "Pith review of Interplay between band structure and Hund's correlation to increase T$_{c}$ in FeSe." pith.science (2026). https://pith.science/paper/QUBUNEQX

@misc{pith2026190808136,
  author       = {Pith},
  title        = {Pith review of: Interplay between band structure and Hund's correlation to increase T$_c$ in FeSe},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QUBUNEQX}},
  note         = {Machine review of arXiv:1908.08136}
}

abstract

FeSe is classed as a Hund's metal, with a multiplicity of $d$ bands near the Fermi level. Correlations in Hund's metals mostly originate from the exchange parameter \emph{J}, which can drive a strong orbital selectivity in the correlations. The Fe-chalcogens are the most strongly correlated of the Fe-based superconductors, with $d_{xy}$ the most correlated orbital. Yet little is understood whether and how such correlations directly affect the superconducting instability in Hund's systems. By applying a recently developed high-fidelity \emph{ab initio} theory, we show explicitly the connections between correlations in $d_{xy}$ and the superconducting critical temperature $T_{c}$. Starting from the \emph{ab initio} results as a reference, we consider various kinds of excursions in parameter space around the reference to determine what controls $T_{c}$. We show small excursions in $J$ can cause colossal changes in $T_{c}$. Additionally we consider changes in hopping by varying the Fe-Se bond length in bulk, in the free standing monolayer M-FeSe, and M-FeSe on a SrTiO$_{3}$ substrate (M-FeSe/STO). The twin conditions of proximity of the $d_{xy}$ state to the Fermi energy, and the strength of $J$ emerge as the primary criteria for incoherent spectral response and enhanced single- and two-particle scattering that in turn controls $T_{c}$. Using constrained RPA, we show further that FeSe in monolayer form (M-FeSe) provides a natural mechanism to enhance $J$. We explain why M-FeSe/STO has a high $T_{c}$, whereas M-FeSe in isolation should not. Our study opens a paradigm for a unified understanding what controls $T_{c}$ in bulk, layers, and interfaces of Hund's metals by hole pocket and electron screening cloud engineering.

Figures

Figures reproduced from arXiv: 1908.08136 by the authors.

**Figure 2.** e). These signatures suggest that M-FeSe/STO is more correlated than the both the bulk and free standing monolayer. The leading instability from the Eliashberg equation survives but the second (dx2−y2 ) instability gets suppressed. Experimentally, the superconducting gap of FeSe/STO show maxima on the bands with dxy character [40]. Also in surface doped bulk FeSe where superconductivity enhances, the appearance of… view at source ↗

**Figure 3.** FIG. 3. Fermi surfaces are shown in the Γ-M (z=0) plane for both bulk FeSe and monolayer FeSe/STO from DFT+DMFT, [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (4 more)

**Figure 4.** Figure 4: FIG. 4. Color weighted QS [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: FIG. 5. We compute the net local moment and it’s evolution with J. Orbitally resolved single-particle scattering rate (Γ) and [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: FIG. 6. Energy and momentum resolved spin susceptibility Im [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: FIG. 7. Spectral function [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

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K. Haule, Physical Review B 75, 155113 (2007)

2007

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

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The more incoherent the A(k, ω) is the more intense is the Im χ(q = ( 1 2, 1 2, 0),ω )

is directly related to the presence of the Fe-d xy state at Fermi energy and its incoherence. The more incoherent the A(k, ω) is the more intense is the Im χ(q = ( 1 2, 1 2, 0),ω ). suppressed and diﬀused relative to the ab initio case (compare Fig. 6( a) to Fig. 6( d)). This results in Tc decreasing from 9 K to 6 K. These parametric studies isolating the...

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