{"id":"11d7ee5c-091c-43f9-8e21-cb2150ea6ea8","arxiv_id":"2607.17759","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A self-consistent loop between SCDFT and quasi-harmonically renormalized structures raises the predicted Tc of MgB2 from 36 K to 39 K and shifts the pressure turnaround to ~200 GPa.","lead":"The authors present a workflow that adds temperature-dependent lattice renormalization based on the quasi-harmonic approximation to superconducting density functional theory, then apply it to MgB2. Their predicted critical temperature rises from 36 K to 39 K at ambient pressure, matching experiment, and they predict a pressure turnover near 200 GPa.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"QHA-only 'anharmonic' correction is the load-bearing step; no explicit anharmonic benchmark separates thermal expansion from true phonon-phonon renormalization.","rationale":"The reader's weakest_assumption correctly identifies that QHA only includes thermal expansion and harmonic frequency shifts with volume, and omits explicit phonon-phonon anharmonicity. This is precisely the load-bearing concern: the paper's title and abstract promise 'anharmonic corrections,' but the implemented method is quasi-harmonic. The numerical agreement for MgB2 (39 K vs experimental 39 K) is encouraging but not probative for the general claim, because there are no explicit anharmonic benchmarks, no error bars, and no sensitivity analysis. A single SSCHA/TDEP comparison would settle whether the QHA geometry at 39 K is a sufficient proxy for anharmonicity in MgB2. The paper has real strengths: parameter-free SCDFT, a self-consistent iteration, and a physically plausible mechanism (DOS increase). Yet the overreach in terminology and the missing explicit anharmonic comparison justify the reader's CONDITIONAL verdict. My assessment does not change the verdict, so I recommend UNCHANGED: the paper should be accepted only after renaming/re-scoping the method and providing the explicit anharmonic check.","tokens_in":8517,"tokens_out":3833,"duration_ms":50363,"concrete_test":"Perform explicit anharmonic phonon calculations for MgB2 using SSCHA or TDEP at T=39 K and ambient pressure, and at the predicted high-pressure condition near the 200 GPa turnaround, using the same pseudopotentials, cutoffs, and k/q meshes. Compare the resulting phonon dispersions, DOS, Eliashberg function, and SCDFT Tc against the QHA-based values. If the explicit anharmonic renormalization changes lambda by more than ~0.02 or Tc by more than ~1 K, the QHA-based 'anharmonic correction' is not reliable; if it matches within noise, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The method's entire anharmonic content is the QHA in Eqs. (1)-(2): harmonic phonons evaluated at strained geometries, with the free energy minimized over symmetric strains. There is no cubic/quartic phonon-phonon interaction, no phonon self-energy, and no zero-point anharmonicity beyond the harmonic zero-point term. The central numerical claim—that ah-SCDFT raises MgB2 Tc from 36 K to 39 K and moves the pressure turnaround to ~200 GPa (Sections III B and III C)—is attributed to the QHA geometry change: increased DOS at EF and softening of the E2g modes. But this is exactly the part never benchmarked. The 3 K increase could be a thermal-expansion effect that any harmonic theory with temperature-dependent volume would produce, not a genuine anharmonic correction. Previous harmonic SCDFT already gives 36 K, so the improvement is modest and could be coincidental given the lack of error bars and sensitivity analysis. The pressure result is even more concerning: the turning point shifts from ~100 GPa (Singh) to ~200 GPa solely due to QHA geometry, with no experimental data at that pressure shown and no assessment of whether QHA remains valid under strong compression. Because the paper's novelty is a 'general approach ... with anharmonic corrections,' the absence of any explicit anharmonic benchmark means the central claim is not yet supported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a computational workflow, 'ah-SCDFT', that iterates between standard SCDFT superconductivity calculations on the 0 K harmonic geometry and a temperature-dependent equilibrium geometry obtained from the quasi-harmonic approximation (QHA) at the currently predicted critical temperature. The authors apply this to MgB2: the harmonic SCDFT gives Tc = 36 K, while using the QHA-renormalized geometry at 39 K raises Tc to 39 K, matching the experimental value. Under pressure, the same procedure yields a nonmonotonic Tc(P) with a turning point shifted from ~100 GPa (previous harmonic calculations) to ~200 GPa, and gives Tc = 20 K at 25 GPa in agreement with experiment. The paper claims this establishes a general, computationally inexpensive way to include anharmonic effects in first-principles superconductivity predictions.","tokens_in":8708,"tokens_out":4182,"duration_ms":47548,"significance":"If the claims hold, the proposed workflow is practically useful: it requires no empirical μ*, uses widely available QHA codes and SCDFT implementations, and the fixed-point iteration between Tc and lattice geometry is a clear and easily implemented idea. The reproducible pipeline (QUANTUM ESPRESSO, thermo_pw, superconducting toolkit) and the explicit convergence criterion are strengths. However, the significance is currently limited by the mismatch between the title/abstract claim of 'anharmonic corrections' and the actual content of Eqs. (1)-(2), which is the quasi-harmonic approximation. The numerical improvement over harmonic SCDFT is modest (3 K) and is presented without error bars or sensitivity analysis. The pressure prediction at ~200 GPa is not benchmarked against experiment or explicit anharmonic calculations. The central idea is defensible, but the paper overstates its novelty and the evidence for it.","major_comments":[{"comment":"The anharmonic content of the proposed method is the quasi-harmonic approximation (QHA): Eq. (2) is the harmonic phonon free energy summed over phonon wavevectors and branches, with no cubic/quartic anharmonic terms, no phonon self-energy, and no explicit phonon-phonon interaction. The geometry at T_cn is obtained by minimizing this harmonic free energy over symmetric strains, which is thermal expansion within the QHA, not a calculation of anharmonic corrections. The abstract and Introduction claim 'systematically incorporates anharmonic corrections' and 'explicitly integrates anharmonic corrections into SCDFT'; these statements are not supported by Eqs. (1)-(2). The method should be described as SCDFT with a QHA-renormalized lattice, or the authors must benchmark the QHA against explicit anharmonic calculations (e.g., SSCHA) and show that the missing phonon-phonon terms are small for Mg","section":null},{"comment":"The central numerical demonstration is a 3 K increase of Tc from 36 to 39 K caused by the QHA-renormalized geometry. No numerical uncertainty or sensitivity analysis is reported. SCDFT with the Sanna2020 kernel is already accurate to a few K for many materials, and the difference between 36 and 39 K is comparable to typical methodological error. The attribution 'in excellent agreement with experiment' therefore requires error bars or a sensitivity study (pseudopotentials, k/q grids, exchange-correlation functional, QHA strain sampling). Without this, the 39 K result may be coincidental. At minimum, the paper should report the convergence of Tc with respect to numerical settings and the effect of using different pseudopotentials, since the Methods section itself uses SG15 for superconductivity and PseudoDojo for geometry.","section":null},{"comment":"The pressure claim—the turning point shifts from ~100 GPa (Singh) to ~200 GPa—is made without any experimental data above 40 GPa and without validating the QHA equation of state against measured lattice constants under pressure. The text also states MgB2 becomes structurally unstable above 340 GPa from imaginary phonons, but this is not connected to any experimental structural transition. Given that the method is intended to resolve discrepancies among prior reports, the authors should compare their computed P-V/V0 curve to experiment and assess QHA validity under strong compression (e.g., anharmonic frequency shifts versus volume, or explicit anharmonic calculations at representative pressures). Otherwise, the 'turning point' is a prediction that is currently untestable from the data shown.","section":null}],"minor_comments":[{"comment":"Equation (2) is garbled in the manuscript: the equals sign is missing and the sum over modes and the plus sign separating zero-point and thermal parts are unclear. Please rewrite it cleanly.","section":null},{"comment":"Reference [41] is cited as 'Ma et al.' but the first author is Y. Wang. Please correct the citation to match the reference list.","section":null},{"comment":"The x-axis label is missing and the definition of T_cn (n=0,1,2,...) is not stated. Please add an axis label and define the iteration index.","section":null},{"comment":"The data availability statement says the data are not publicly available because it is 'not technically feasible'—this is unusual for a computational paper. Please deposit the relevant input/output files or provide a more specific justification.","section":null},{"comment":"The title and abstract use 'an-harmonic' with a hyphen inconsistently; the standard term 'anharmonic' should be used throughout. Also, phrases such as '12^3 Monkhorst-Pack k-point mesh' should be written as 12×12×12 for clarity.","section":null}],"recommendation":"major_revision","confidential_remarks":"The paper's core workflow—iterating SCDFT with QHA-renormalized geometries—is a reasonable and potentially useful idea, but the current manuscript overstates the method by calling QHA an 'anharmonic correction.' I recommend major revision rather than rejection because the numerical model can be fixed by reanalysis, renaming, or adding explicit benchmark calculations. The pressure claim needs stronger validation. I would ask the authors to either rename the method to 'SCDFT with QHA lattice renormalization' or add a quantitative estimate of omitted phonon-phonon interactions."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a legitimate but modest methodological step. The authors iterate SCDFT and a quasi-harmonic free-energy minimization to get a temperature-renormalized geometry, and they show it moves MgB2's Tc from 36 K to 39 K, with a pressure turnaround near 200 GPa. The fixed-point loop is clean, there is no fitted μ*, and the 36 K harmonic value matches prior SCDFT work.\n\nWhat's new: applying QHA geometry renormalization inside the SCDFT loop for MgB2, and specifically the pressure-dependence result. That appears to be new and resolves a disagreement between earlier calculations.\n\nThe main weakness is terminology and scope. QHA is not a full anharmonic treatment; it gives thermal expansion and volume-dependent harmonic frequencies, not phonon-phonon self-energy or linewidths. Calling that 'anharmonic corrections' is an overstatement, and the paper doesn't benchmark against explicit anharmonic calculations like SSCHA or self-consistent phonons. So the general claim is conditioned on whether thermal expansion alone captures the relevant anharmonicity for MgB2. That may be true—MgB2 is not strongly anharmonic—but the paper doesn't show it. Also no error bars or sensitivity analysis, and the data are not public.\n\nThe self-consistency is not circular; no parameter is fit to the target Tc. Some might worry the 3 K increase is a volume effect any temperature-dependent QHA would produce—which is exactly the point, but then it's not a universal correction.\n\nThis paper is for people doing SCDFT or first-principles superconductivity predictions. It deserves a serious referee: the method is clear, the demonstration is concrete, but the authors should be pushed to either re-name the approach as quasi-harmonic SCDFT or add a benchmark separating QHA from explicit anharmonicity. I'd send it to review with that expectation.","headline":"A useful fixed-point extension of SCDFT with QHA-derived thermal geometries; the MgB2 numbers are plausible, but the 'anharmonic' label oversells what is a quasi-harmonic correction.","tokens_in":9335,"tokens_out":1873,"would_cite":true,"duration_ms":21610,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper introduces ah-SCDFT, a self-consistent scheme that adds anharmonic lattice corrections to superconducting density functional theory, and shows that for MgB2 it raises the predicted critical temperature from 36 K to 39 K, matching","keywords":["superconductivity","anharmonic effects","quasi-harmonic approximation","superconducting density functional theory","MgB2","electron-phonon coupling","critical temperature","high pressure"],"falsifier":"Measure or fully anharmonically calculate the temperature dependence of the strongly coupled in-plane boron phonons in MgB2 near the A point between 0 K and 39 K; if the softening and the accompanying density-of-states increase are absent or much smaller than the quasi-harmonic prediction, the Tc enhancement to 39 K is not caused by the mechanism claimed. Equivalently, a high-pressure experiment mapping Tc between 100 and 250 GPa that finds no turning point near 200 GPa would falsify the pressure claim.","tokens_in":8302,"feed_emoji":"❄️","tokens_out":4417,"duration_ms":47876,"temperature":0.7,"pith_summary":"This paper introduces a general recipe for adding anharmonic corrections to first-principles superconductivity calculations, called ah-SCDFT. Instead of computing the superconducting critical temperature only at the zero-temperature geometry, the method re-optimizes the crystal structure at the predicted Tc using a quasi-harmonic free-energy minimization, then repeats the superconducting calculation on the renormalized lattice until the temperature stops changing. Applied to MgB2, the iteration raises Tc from 36 K to 39 K, the experimental value, by increasing the electronic density of states at the Fermi level and softening the strongly coupled phonon branches. Under pressure, the same procedure predicts a nonmonotonic Tc with a turning point near 200 GPa, which the authors argue reconciles previously conflicting theoretical results. The paper's aim is to make quantitative superconductivity prediction routine for materials where anharmonicity matters.","feed_headline":"Lattice renormalization lifts MgB2's Tc to 39 K, matching experiment","feed_subtitle":"A self-consistent loop between geometry and critical temperature adds anharmonic corrections to first-principles superconductivity predictio","key_machinery":"The load-bearing object is a self-consistent iteration loop: (1) compute Tc with standard superconducting density functional theory at the 0 K harmonic geometry; (2) at that temperature, minimize the quasi-harmonic Helmholtz free energy over symmetric strains to obtain a thermally expanded, phonon-renormalized geometry; (3) recompute Tc on this new geometry; repeat until consecutive Tc values differ by less than 0.01 K. The quasi-harmonic approximation used here includes thermal expansion and volume-dependent harmonic phonon frequencies, but not explicit phonon-phonon interactions.","core_discovery":"The central claim is that the temperature-dependent equilibrium geometry, generated by minimizing the Helmholtz free energy (electronic total energy plus harmonic phonon free energy) over strained lattices, is sufficient to capture the anharmonic lattice renormalization that matters for superconductivity in MgB2. Iterating between superconducting density functional theory and this renormalized geometry converges at Tc = 39 K, versus 36 K for the 0 K harmonic geometry. The mechanism is identified: the renormalized lattice raises the electronic density of states at the Fermi level and softens the strongly coupled in-plane boron phonon modes near the A point, increasing the electron-phonon coup","pith_inferences":["The term 'anharmonic' in this scheme really means quasi-harmonic thermal renormalization; explicit anharmonic phonon-phonon interactions and zero-point anharmonicity are left out, so if those effects are substantial the agreement at 39 K could be fortuitous rather than systematic.","The same iteration could be applied to materials that are dynamically unstable in the harmonic approximation, where the 0 K starting geometry is ill-defined; the method as stated may need a self-consistent phonon starting point to generalize.","A sharper test would be to run the loop on a superconductor like H3S, where anharmonicity reportedly changes Tc substantially, and compare the quasi-harmonic-only result to fully anharmonic calculations.","If the thermal renormalization explanation holds, temperature-dependent lattice constant measurements on MgB2 should show the same expansion and phonon softening used in the calculation, a straightforward experimental check."],"forward_implications":["If the renormalization loop is correct, harmonic-only SCDFT systematically underestimates Tc in materials with soft phonons or sizable thermal expansion, and the error is fixable without new physics.","The method transfers directly to other phonon-mediated superconductors, including hydrides under pressure where anharmonic effects are known to be large, at modest extra cost.","The predicted pressure dependence for MgB2 implies that the nonmonotonic Tc(p) is real but occurs at pressures beyond the previously claimed 100 GPa turning point, offering a target for high-pressure experiments.","The mechanism (DOS increase plus phonon softening) makes concrete predictions for temperature-dependent phonon spectra and electronic structure that can be tested by neutron scattering or angle-resolved photoemission.","Since the loop converges in a few iterations, the anharmonic correction can be added to any existing SCDFT workflow without algorithmic changes."],"fun_headline_variants":["Anharmonic SCDFT reproduces MgB2's 39 K Tc","Geometry self-loop lifts MgB2's Tc to 39 K","ah-SCDFT nails MgB2's Tc at 39 K","Anharmonic lattice renormalization matches MgB2's Tc","Self-consistent geometry captures anharmonicity for MgB2"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"Everything rests on the assumption that quasi-harmonic free-energy minimization (thermal expansion plus harmonic phonon frequencies at each volume) captures the anharmonic effects that matter for superconductivity, while leaving out explicit phonon-phonon interactions and zero-point anharmonicity.","fun_headline_variants_meta":{"raw":{"variants":["Anharmonic SCDFT reproduces MgB2's 39 K Tc","Geometry self-loop lifts MgB2's Tc to 39 K","ah-SCDFT nails MgB2's Tc at 39 K","Anharmonic lattice renormalization matches MgB2's Tc","Self-consistent geometry captures anharmonicity for MgB2"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001649,"raw_usage":{"total_tokens":6354,"prompt_tokens":678,"completion_tokens":5676,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":422,"completion_tokens_details":{"reasoning_tokens":5583}},"tokens_in":422,"tokens_out":5676,"duration_ms":41469,"temperature":1.0,"reasoning_tokens":5583,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-01T17:03:11.411545+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure or fully anharmonically calculate the temperature dependence of the strongly coupled in-plane boron phonons in MgB2 near the A point between 0 K and 39 K; if the softening and the accompanying density-of-states increase are absent or much smaller than the quasi-harmonic prediction, the Tc enhancement to 39 K is not caused by the mechanism claimed. Equivalently, a high-pressure experiment mapping Tc between 100 and 250 GPa that finds no turning point near 200 GPa would falsify the pressure claim.","supporting_citations":[],"review_version":1}