Dimensional crossover and emergence of novel phases in puckered PdSe$_2$ under pressure

Boby Joseph; Chumki Nayak; Kapildeb Dolui; Koushik Dey; Mainak Palit; Sanjoy Kr Mahatha; Soumik Das; Subhadeep Datta; Tanima Kundu

Dimensional crossover and emergence of novel phases in puckered PdSe$_2$ under pressure

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Compressing the layered semiconductor PdSe2 past 9 GPa produces a new octahedrally distorted phase whose flat bands explain its pressure-enhanced superconductivity.

desk verdict Solid high-pressure XRD study whose central new-phase claim is honest but underdetermined; worth refereeing, but the >9 GPa phase needs a hydrostaticity check before it becomes a result. read the letter →

arxiv 2501.13057 v2 pith:V3PFG6CQ submitted 2025-01-22 cond-mat.mtrl-sci

Tanima Kundu , Soumik Das , Koushik Dey , Boby Joseph , Chumki Nayak , Mainak Palit , Sanjoy Kr Mahatha , Kapildeb Dolui

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Subhadeep Datta

This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords PdSe2highpressuredimensionalcrossoverpyritemarcasitearsenopyriteflatbandssuperconductivity

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 shows that pressure does more than squeeze PdSe2: it changes the material's dimensionality and crystal symmetry in a sequence of three transitions. Below 2.3 GPa the puckered orthorhombic phase simply compresses; above that, the Jahn–Teller distortion is suppressed, the in-plane lattice expands, and the material metallizes. At 4.8 GPa interlayer $d_{z^2}$–$\pi^*$ hybridization drives a 2D-to-3D crossover into the cubic pyrite phase, and above 9 GPa a further transformation sets in, with the data fitting either an orthorhombic marcasite ($Pnnm$) or monoclinic arsenopyrite ($P2_1/c$) structure. The paper argues that flat bands made from Pd $d_{xz}$ or $d_{xy}$ orbitals in these high-pressure phases raise the electron–phonon coupling and account for the rise of $T_c$ from 2.4 K to 13.1 K reported in earlier transport measurements. A sympathetic reader would care because it turns a single material into a testbed for how structural distortion, dimensionality, and band topology cooperate under pressure.

What carries the argument

The central objects are three closely related anion-dimer crystal structures: pyrite ($Pa\bar{3}$) with symmetric, corner-sharing PdSe6 octahedra; marcasite ($Pnnm$) with edge-sharing octahedra arranged in uniform cation chains; and arsenopyrite ($P2_1/c$) with edge-sharing octahedra in alternating short and long chains. The mechanism that carries the argument is the pressure-induced distortion of the Pd $t_{2g}$ orbitals: octahedral compression breaks the degeneracy and lifts either the $d_{xz}$ or $d_{xy}$ orbital toward the Fermi level, creating flat bands, a sharp peak in $N(E_F)$, and, through the McMillan relation $T_c \propto \exp(-1/\lambda)$ with $\lambda \propto N(E_F)\langle g^2\rangle/\omega^2$, stronger superconductivity. The lower-pressure crossover is carried by the same orbital language: suppression of the Jahn–Teller singlet state transfers charge from $d_{z^2}$ to $d_{x^2-y^2}$, and interlayer $d_{z^2}$–$\pi^*$ hybridization converts square-planar PdSe4 units into octahedral PdSe6 units.

What would settle it

A high-pressure X-ray diffraction experiment on selenium-free PdSe2 using helium as the pressure medium, reaching 13 GPa and showing no peaks beyond those of the pyrite phase, would refute the new-phase claim; conversely, observing the $Pnnm$ or $P2_1/c$ reflections appear and grow with pressure would confirm it.

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Extended reading notes

Core claim

The paper's central claim is that PdSe2 follows a three-stage pressure pathway: the ambient puckered orthorhombic phase ($Pbca$) first expands in-plane and metallizes above 2.3 GPa as the Jahn–Teller distortion is suppressed; at 4.8 GPa interlayer $d_{z^2}$–$\pi^*$ orbital hybridization converts it into the three-dimensional cubic pyrite phase ($Pa\bar{3}$); and above roughly 9 GPa a novel phase appears, identified by Rietveld refinement as either orthorhombic marcasite ($Pnnm$) or monoclinic arsenopyrite ($P2_1/c$), both deriving from octahedral distortions in the Pd $d$ orbitals, specifically a splitting of the $t_{2g}$ manifold. In these high-pressure phases, nearly flat bands near the Fermi level, dominated by $d_{xz}$ in marcasite and $d_{xy}$ in arsenopyrite, enhance the electronic density of states and thereby the electron–phonon coupling, which the paper presents as the mechanism behind the experimentally observed increase of the superconducting transition temperature under pressure.

Load-bearing premise

The load-bearing premise is that the extra diffraction peaks appearing above 9 GPa come from a real second crystalline phase with one of the two candidate structures, rather than from non-hydrostatic stress or the residual selenium impurity.

Editorial extensions

If this is right

Above ~9 GPa, Rietveld refinement requires a second phase alongside pyrite, with the marcasite fraction reaching 22% and the arsenopyrite fraction 42% by 13.1 GPa.
The orthorhombic $Pbca$ phase coexists with pyrite only between 4.8 and 7.2 GPa, so the 2D-to-3D dimensional crossover is complete before the octahedrally distorted phase appears.
Calculated superconducting transition temperatures at 12 GPa are 5.6 K for pyrite, 6.8 K for marcasite, and 5.8 K for arsenopyrite, all within the experimentally observed range.
Phonon calculations find no imaginary modes at 12 GPa for any of the high-pressure phases, and enthalpy calculations place $P2_1/c$ and $Pnnm$ within 80 meV per formula unit of pyrite between 6 and 20 GPa, making thermal access to these phases plausible.
If the flat-band mechanism is right, the pressure-enhanced $T_c$ reported for PdSe2 is not a property of the pyrite phase alone but of the octahedrally distorted phases that appear above 9 GPa.

Reading between the lines

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

If the new phase is real, the same pressure pathway may appear in PdS2 and in Pt-based dichalcogenides, because their ambient structures share the same dimer-anion motif and similar Jahn–Teller-sensitive coordination.
The flat-band mechanism predicts that $T_c$ should track the phase fraction of marcasite or arsenopyrite, so simultaneous transport and diffraction measurements on the same sample could test the correlation directly.
A cleaner structural test would use helium as the pressure medium and selenium-free crystals: helium stays hydrostatic well past 10 GPa, removing the non-hydrostatic stress that can mimic a symmetry-lowering transition, and eliminating the residual Se diffraction lines that complicate the pattern.
The paper leaves open which of the two candidate phases actually forms; a texture-aware single-crystal or high-resolution powder study could discriminate $Pnnm$ from $P2_1/c$ by their distinct reflection conditions.

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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

The paper to know about: a careful synchrotron XRD, Raman, and DFT study of PdSe2 up to 13 GPa. The strongest new observations are the in-plane lattice expansion above 2.3 GPa and a much narrower Pbca-to-pyrite coexistence window (~2 GPa) than earlier reports, which is a genuine improvement in the experimental record. The refinements are transparent, with full structural tables and fit residuals, and the DFT work (enthalpy, phonons, electron-phonon) is thorough and properly caveated. The authors deserve credit for presenting the two candidate high-pressure phases, Pnnm and P21/c, as possibilities rather than a unique assignment.

The load-bearing claim, however, is the emergence around 9 GPa of a marcasite or arsenopyrite phase, and the current evidence does not uniquely establish it. Both models fit the minority-phase peaks with essentially equal Rwp, the phase fraction peaks at only 22% (Pnnm) or 42% (P21/c), and the DFT enthalpy keeps pyrite stable to 20 GPa, with the new phases 80 meV/f.u. higher. More seriously, the 4:1 methanol-ethanol medium freezes near 10 GPa, exactly where the new peaks appear, and the authors flag this only in the Raman discussion. Non-hydrostatic stress can split cubic peaks in ways that mimic a lower-symmetry second phase. The absence of any new Raman mode above 9 GPa is consistent with a stress-induced artifact, so the two-phase Rietveld fits carry the whole argument.

That said, the paper is not careless. It acknowledges the ambiguity in the abstract and conclusions, and the supporting data are presented so that a referee can test the claims. The 2.3 GPa expansion and the narrowing of the phase-coexistence window are solid and likely reproducible. The flat-band/electron-phonon story is plausible but rests on the reality of the new phase.

Recommendation: send it to peer review. A good referee should push for a hydrostaticity check (e.g., helium or neon medium) or at least a careful peak-shape analysis at 9-11 GPa before the new phase is treated as established. The experimental observations alone merit publication; the novel-phase claim needs to be either hardened or explicitly downgraded to a tentative suggestion.

Best, [Your name]

Referee Report

4 major / 5 minor

Summary. The paper reports a combined synchrotron powder XRD, Raman, and DFT study of PdSe2 under pressure up to 13.1 GPa. It identifies three pressure regimes: (i) a Jahn-Teller distorted orthorhombic Pbca phase that undergoes in-plane lattice expansion and metallization above 2.3 GPa; (ii) a 2D-to-3D dimensional crossover near 4.8 GPa to a cubic pyrite Pa-3 phase, with the Pbca phase coexisting until about 7 GPa; and (iii) an alleged new phase above about 9 GPa, assigned as either marcasite (Pnnm) or arsenopyrite (P21/c), coexisting with pyrite in minority fractions. DFT with RSCAN+MBD places pyrite as the enthalpy ground state up to 20 GPa and the two candidate phases within 80 meV/f.u. of it. Orbital-projected band structures and DFPT electron-phonon calculations are used to propose a flat-band-enhanced superconductivity mechanism, with estimated Tc values of 5.6-6.8 K at 12 GPa. The central novel claim is the existence and identity of the high-pressure phase, which underpins the flat-band interpretation.

Significance. If the high-pressure phase is real and correctly assigned, the paper extends the PdSe2 phase diagram beyond the previously reported pyrite stability and offers a structural explanation for the pressure-enhanced Tc reported by ElGhazali et al. The study has genuine strengths: the diffraction data are processed with Rietveld refinement with reasonable Rwp values; the DFT search is not circular, since the candidate structures and their enthalpy and band structures are computed independently of the refinement; phonon stability is checked; and the low-pressure phase evolution is internally consistent. The manuscript is honest in presenting two candidate space groups rather than a single assignment. However, the novel-phase claim is currently not uniquely established, and the superconductivity mechanism is only qualitatively connected to the observed Tc, so the significance is conditional pending a unique structural identification or a clear reframing of the central claim.

major comments (4)

[IV (Figs. 4-5, SM Tables IV-V)] The existence of the allegedly new phase above 9 GPa is load-bearing and is not uniquely established. The manuscript presents Pnnm and P21/c as two equally valid refinements of the same data, with comparable Rwp values (for example, Rwp = 7.8% for Pnnm and 7.4% for P21/c at 11.1 GPa in SM Tables II, IV and V), and the new phase is a minority component (maximum 22% for Pnnm and 42% for P21/c). No single-phase pyrite model with anisotropic strain broadening is reported, nor is the contribution of the known ~1.4% Se impurity to the extra reflections quantified. The absence of any new Raman mode above 9 GPa further weakens independent confirmation of a symmetry-lowering transition. Because the flat-band and enhanced-Tc mechanism is anchored to this phase, the paper must either uniquely identify the phase, or demonstrate statistically that one candidate is preferred over the other, or re-frame the central claim as a conditional scenario.
[IV (XRD and Raman), SM Fig. S16] The 4:1 methanol-ethanol mixture is used as the pressure medium for both XRD and Raman up to 13.1 GPa. This medium is known to become non-hydrostatic near its glass transition around 10 GPa at room temperature, which is exactly the pressure range where the alleged new reflections appear (8.8-9.2 GPa). The manuscript acknowledges this possibility only in the Raman FWHM discussion (the passage beginning 'Although anhydrostatic pressure condition at higher pressure may be a possible issue...') and not in the XRD phase-fraction analysis. Non-hydrostatic stress can broaden or split cubic reflections and produce apparent coexistence with a lower-symmetry phase. The authors should test whether a pyrite-only model with strain broadening can fit the data above 9 GPa, and ideally repeat the experiment with a more hydrostatic medium such as helium.
[Fig. 6 and associated text] The DFT enthalpy diagram (Fig. 6) shows that pyrite remains the lowest-energy phase up to 20 GPa, with P21/c and Pnnm less than 80 meV/f.u. higher. The manuscript attributes the experimental stabilization of these phases to unquantified room-temperature thermal fluctuations. This is a load-bearing gap because the claimed new phase is not predicted to be thermodynamically stable at the pressures where it is reported. A vibrational free-energy estimate, which could be obtained from the phonon dispersions already presented in SM Fig. S14, is needed before the phase diagram in Fig. 8 can be presented as an experimental fact.
[III and IV (Tc estimates)] The superconducting-temperature estimates use a hand-set Coulomb pseudopotential mu* = 0.1 and give Tc = 5.6 K for pyrite, 6.8 K for marcasite, and 5.8 K for arsenopyrite at 12 GPa. These values are very close to one another, and the differences are comparable to the typical sensitivity of the Allen-Dynes formula to mu*; hence the claim that flat bands in the new phases enhance Tc relative to pyrite is not supported by the numbers alone. In addition, the comparison is made with the experimental Tc of 13.1 K observed at 23 GPa, whereas the calculation is at 12 GPa. A mu* sensitivity analysis and a calculation at the same pressure as the experimental point are required, or the claim should be restricted to qualitative trends.

minor comments (5)

[Abstract and Section IV] The statement 'Beyond 2.3 GPa ... metallization' is based on the calculated band structure at 2 GPa (Fig. 1(f)), not on transport data reported in this work; please clarify that this is a theoretical prediction.
[Section IV, Raman paragraph] The phrase 'anhydrostatic pressure condition' appears to be a typo for 'non-hydrostatic pressure condition'.
[Fig. 4(b) vs SM Table II] The Rwp values in the main text and SM tables are not fully consistent; for example, the Pnnm fit at 11.1 GPa is listed as Rwp = 8.39% in Fig. 4(b) but as Rwp = 7.8% in SM Table II. Please harmonize or explain the difference.
[Fig. 7] The insets showing the flat bands are small; please enlarge them or plot the bands along a path that clearly displays the dispersion near the Fermi level.
[Fig. 8] The phase diagram marks the calculated Tc range at 12 GPa with a single circular symbol; please specify whether this represents all three calculated structures or only the high-pressure phases.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the structural phase identifications rest on independent Rietveld fits against database-derived candidate structures, and the calculated Tc values are not fitted to or derived from the experimental superconductivity data.

full rationale

The paper's derivation chain is self-contained and does not reduce to its own inputs. The high-pressure phases (marcasite Pnnm and arsenopyrite P21/c) are identified by Rietveld refinement of the observed synchrotron XRD patterns against candidate crystal structures taken from the OQMD and Materials Project databases and from well-known mineral prototypes (pyrite, marcasite, arsenopyrite), not by constructing the candidates from the measured pattern. The DFT enthalpy calculations in Fig. 6 are independent of the experimental diffraction data and in fact find pyrite (Pa-3) lowest in energy up to 20 GPa, with P21/c and Pnnm slightly higher; the paper explicitly attributes their experimental appearance to room-temperature thermal fluctuations, which is a physical hypothesis, not a circular consequence of the fit. The superconducting Tc estimates are obtained from Allen-Dynes McMillan theory with a fixed, conventionally chosen mu* = 0.1, producing Tc values of 5.6 K (pyrite), 6.8 K (marcasite), and 5.8 K (arsenopyrite) at 12 GPa; these are not equal to, nor fitted to, the experimental values of 2.4 K at 7 GPa and 13.1 K at 23 GPa reported by ElGhazali et al., so there is no fitted-input-called-prediction reduction. The flat-band and electron-phonon interpretation is post hoc in the sense that it explains already-reported superconductivity, but it is grounded in independently computed band structures and phonons for the candidate phases, not derived from the Tc values themselves. The only self-citations are to the authors' previous work for sample synthesis and characterization (ref. [4]) and for a PDMS transfer technique (ref. [32]); these are provenance and experimental-method references, not load-bearing evidence for the central structural or superconducting claims. Finally, concerns about the 4:1 methanol-ethanol pressure medium freezing near 10 GPa and the ambiguity between the two candidate space groups are correctness or robustness risks, not circularity: the authors do not define the new phase in terms of the predicted Tc or derive the phase from the same fit parameters used to assert it. Accordingly, no circular step meeting the required quote-and-reduction standard is present, and the circularity score is 0.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central structural claims rest on DFT energetics and Rietveld fits; the free parameter mu* enters the Tc estimate. The assumptions are the standard transferability of DFT to this material, hydrostaticity of the pressure medium up to 13 GPa, and that the minority-phase fits represent genuine new phases.

free parameters (1)

effective screened Coulomb repulsion mu* = 0.1
Hand-set in the Allen-Dynes McMillan equation (Computational Details) to compute Tc; a standard but non-universal parameter that directly affects the claimed Tc values (5.6-6.8 K) and the flat-band superconductivity interpretation.

assumptions (4)

domain assumption DFT with RSCAN/PBE functionals and MBD dispersion correctly describes the relative enthalpies and band structures of the four PdSe2 phases.
Used throughout Computational Details and Figs. 6-7 to identify stable phases and flat bands; not independently benchmarked here beyond standard functional tests.
domain assumption The 4:1 methanol-ethanol mixture provides hydrostatic conditions up to 13.1 GPa.
Pressure medium loaded in both experiments; freezing near 10 GPa is acknowledged only in the Raman section but not in the XRD structural analysis where the 9-13.1 GPa phase fractions are extracted.
ad hoc to paper Rietveld phase fractions and two-phase fits uniquely reflect genuine phases rather than artifacts of stress gradients or the ~1.4% Se impurity.
The high-pressure XRD refinements use two coexisting phases (Pa-3 + Pnnm or Pa-3 + P21/c) and report phase fractions up to 42%; the paper attributes previous wide coexistence to local pressure gradients, but does not quantify stress effects in its own data.
domain assumption The Jahn-Teller distortion model and singlet-triplet crossover, taken from prior literature [12, 18], applies to PdSe2 under compression.
Used to explain the 2.3 GPa in-plane expansion and metallicity; not directly measured (no magnetic susceptibility or transport in this work).

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Pith. "Pith review of Dimensional crossover and emergence of novel phases in puckered PdSe$_2$ under pressure." pith.science (2026). https://pith.science/paper/V3PFG6CQ

@misc{pith2026250113057,
  author       = {Pith},
  title        = {Pith review of: Dimensional crossover and emergence of novel phases in puckered PdSe$_2$ under pressure},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/V3PFG6CQ}},
  note         = {Machine review of arXiv:2501.13057}
}

abstract

We investigate the pressure-driven structural and electronic evolution of PdSe$_2$ using powder X-ray diffraction, Raman spectroscopy, and first-principles calculations. Beyond 2.3 GPa, suppression of the Jahn-Teller distortion induces in-plane lattice expansion and metallization. Around 4.8 GPa, the interlayer $d_{z^2}-\pi^*$ orbital hybridization drives the dimensional crossover, facilitating the transformation from the 2D distorted to a 3D undistorted pyrite phase. At $\sim$ 9 GPa, a novel phase emerges, characterized by octahedral distortions in the $d$ orbitals of Pd. Structural analysis suggests the presence of marcasite ($Pnnm$) or arsenopyrite ($P2_1/c$) phase with orthorhombic and monoclinic configurations, respectively. Furthermore, the observed phonon anomaly and electronic structure modifications, including the emergence of flat bands in the high-pressure phases, elucidate the fundamental mechanisms underlying the previously reported exotic superconductivity with an enhanced critical temperature. These results highlight the pivotal role of dimensional crossover and structural transitions in tuning the electronic properties of puckered materials, providing pathways for novel functionalities.

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