Topological transport in monolayer jacutingaite

Muhammad Sabieh Anwar; Muzamil Shah

REVIEW 3 major objections 7 minor 52 references

Topological transport in monolayer jacutingaite

T0 review · 3 major / 7 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read Monolayer jacutingaite, already predicted to be a large-gap Kane-Mele quantum spin Hall insulator, should reveal six distinct topological phases under electric and laser fields, each identifiable by its finite-frequency spin- and…

desk verdict A standard but useful finite-frequency optical conductivity calculation for jacutingaite; the core spectra are worth referee time, but the S-QHI Chern numbers and several internal references need correction before the results can be relied on. read the letter →

arxiv 2412.16965 v1 pith:BGISCXLF submitted 2024-12-22 cond-mat.mes-hall

Muzamil Shah , Muhammad Sabieh Anwar This is my paper · ORCID

classification cond-mat.mes-hall

keywords monolayerjacutingaitePt2HgSe3Kane-MelemodeltopologicalphasetransitionFloquetengineeringopticalconductivityspinHalleffectvalley

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

Monolayer jacutingaite (Pt2HgSe3) is predicted to be the first large-gap Kane-Mele quantum spin Hall insulator, and this paper asks whether its topological state can be read out and controlled optically. The authors study the low-energy Kane-Mele Hamiltonian under two knobs—a staggered sublattice potential from an electric field and an off-resonant circularly polarized laser treated by Floquet theory—and map the resulting phases: quantum spin Hall insulator, valley-spin-polarized metal, spin-polarized metal, photo-induced quantum Hall insulator, band insulator, and spin-polarized quantum Hall insulator. The central claim is that each phase has a distinct finite-frequency optical conductivity spectrum: the Kubo-formula longitudinal and Hall conductivities depend strongly on the topological state, the photon energies of intra- and interband transitions are set by the four spin-valley Dirac masses and can be tuned by the two fields, and doping can Pauli-block selected transitions. If correct, optical conductivity becomes a contactless way to identify and switch between topological phases in a single material.

What carries the argument

The load-bearing object is the four-band Kane-Mele Hamiltonian $\hat H_{\eta,s}=\hbar v_F(\eta k_x\sigma_x+k_y\sigma_y)+(\eta s\lambda_{\rm so}+\lambda_z+\eta\lambda_\omega)\sigma_z$ at the two valleys $K,K'$ and two spins. The single control parameter is the Dirac mass $\Delta_{\eta,s}=\eta s\lambda_{\rm so}+\lambda_z+\eta\lambda_\omega$: a phase transition occurs whenever one mass changes sign, and the spin/valley Chern numbers $C_{\eta,s}=(\eta/2)\,\mathrm{sgn}(\Delta_{\eta,s})$ label the phase. The optical calculation is carried by the Kubo formula, whose longitudinal and Hall components depend on $\Delta_{\eta,s}$ and on $M=\max(|\Delta_{\eta,s}|,2|\mu_F|)$; the Hall term is proportional to $\eta\Delta_{\eta,s}\tan^{-1}(\hbar\Omega/M)/\hbar\Omega$, which is what makes the transverse response valley- and spin-selective and hence phase-sensitive.

What would settle it

Measure the frequency-dependent $\sigma_{xx}(\omega)$ and $\sigma_{xy}(\omega)$ of a gated monolayer Pt2HgSe3 sample under circularly polarized drive and compare with the predicted resonance pattern: for example, in the K valley at $\lambda_z=0$, $\lambda_\omega=0$, the claim gives a spin-down interband edge at $\hbar\omega=0.5\lambda_{\rm so}$ and a spin-up edge at $1.5\lambda_{\rm so}$, with the Hall conductivity changing sign between them. If sweeping the gate voltage or laser intensity across the claimed phase boundary fails to move these edges according to $2|\Delta_{\eta,s}|$, or if spin mixing produces transitions the calculation forbids, the central claim would be refuted.

Watch

Extended reading notes

Core claim

The paper's central discovery is that the spin- and valley-resolved optical conductivities of monolayer jacutingaite are topological phase markers. Working from the effective Hamiltonian with Dirac mass $\Delta_{\eta,s}=\eta s\lambda_{\rm so}+\lambda_z+\eta\lambda_\omega$, where $\eta$ is the valley index, $s$ the spin, $\lambda_{\rm so}$ the intrinsic spin-orbit coupling, $\lambda_z$ the staggered potential, and $\lambda_\omega$ the Floquet mass from the laser, the authors compute Berry curvature, spin/valley Chern numbers, density of states, and the finite-frequency Kubo conductivities $\sigma_{xx}$ and $\sigma_{xy}$. They show that the signs of the four masses determine six phases, and that the interband Hall response $\sigma_{xy}^{\rm inter}\propto (2\eta\Delta_{\eta,s}/\hbar\Omega)\tan^{-1}(\hbar\Omega/M)$ produces resonances at photon energies $2|\Delta_{\eta,s}|$ whose positions, signs, and number of peaks are characteristic of each phase. They further show that raising the chemical potential blocks some interband transitions by Pauli exclusion, leaving intraband Drude features in specific spin channels.

Load-bearing premise

The load-bearing premise is that jacutingaite's low-energy electrons are exactly described by a simple two-band model with only three energy offsets—spin-orbit, electric-field, and laser-induced—with no extra spin-mixing term, and that the laser is fast and weak enough to act only through one averaged offset; the paper's numeric check of that fast-and-weak condition mixes up wavelength and frequency units, so the condition is not actually demonstrated.

Editorial extensions

If this is right

The finite-frequency longitudinal and Hall conductivities can be used experimentally to distinguish QSHI, VSPM, SPM, BI, P-QHI, and S-QHI phases in the same monolayer without contacting edge states.
Tuning the electric field or the laser intensity continuously shifts the photon energies of the intra- and interband transition peaks, since these are set by combinations of $\lambda_z$, $\lambda_\omega$, and $\lambda_{\rm so}$.
Changing the chemical potential selectively Pauli-blocks some spin-down interband transitions, so the same sample can be switched between interband-dominated and Drude-dominated optical response.
The direction of the transverse spin and valley current can be controlled by choosing the photon energy, because the finite-frequency Hall conductivity changes sign at valley-specific resonances.
Circular dichroism, Faraday, and Kerr spectra derived from the computed conductivities should carry the phase information, offering magneto-optic and valleytronic probes in the THz range.

Reading between the lines

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

If these fingerprints survive in a real sample, optical conductivity would give a contactless phase diagram of jacutingaite, potentially easier than transport edge-state measurements in exfoliated flakes.
Because all results come from the Kane-Mele mass structure, the same finite-frequency signatures should appear—scaled by $\lambda_{\rm so}$—in other buckled Dirac materials, but jacutingaite's much larger gap should make them observable at more practical frequencies.
The paper's numerical justification for the off-resonant condition mislabels 500 nm light as 0.6 THz; taken at face value that drive is not off-resonant, so the cleanest test of the predictions would use genuinely THz radiation or a corrected estimate of $a\omega_0/v_F$.
Excitonic and other many-body corrections, absent from the single-particle Kubo calculation, could shift or split the predicted absorption edges, so the sharpest quantitative test may need to wait for measurements that include such effects.

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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,

The useful part of this paper is the finite-frequency, spin- and valley-resolved optical conductivity spectra for ML-jacutingaite under staggered potential plus off-resonant light. That specific set of curves is not in Vargiamidis et al. or Alipourzadeh et al., and the Kubo machinery is standard and independently referenced. The DOS and Pauli-blocking discussion is a reasonable extension. If you work on jacutingaite, this is a convenient source for where the interband peaks sit as a function of λz and λω.

The soft spots are real but mostly housekeeping, with one substantive one. Substantive: the S-QHI row of Table I cannot be obtained from the paper's own Chern-number definitions. Using Cη,s = (η/2)sgn(Δη,s) at the plotted point (λz=λso, λω=1.5λso), all four masses are nonzero — I checked; Δ−,− is 0.5λso, not zero, so the stress-test's gapless-point arithmetic doesn't hold. But C↑=1 and C↓=0 give Cs=0.5, and CK=1, CK′=0 give Cv=0.5, not the Cs=Cv=1 in the table. The text also says both Cv=0 and Cv=1 for this phase. So the S-QHI phase label is not pinned down. The optical spectra themselves are computed from the masses, so they aren't invalidated, but the claim that each topological phase has a distinct fingerprint needs the phase labels to be right.

Housekeeping: the 500 nm drive is called 0.6 THz; 500 nm is about 600 THz. The error is six orders of magnitude, though it actually works in the paper's favor — the off-resonant condition is even better satisfied. Figure cross-references are scrambled throughout; Figs. 3/6/8 captions and in-text mentions don't line up. These need a careful pass.

Verdict: conditional. The central derivation is standard and likely correct, and the finite-frequency spectra are a real extension. But as posted, the internal inconsistencies make it unreliable as a quantitative guide. It deserves a serious referee — the physics core is worth engaging — and the referee should ask for a corrected Chern-number table and a thorough consistency edit.

Recommendation: send to peer review, expect major revision.

Referee Report

3 major / 7 minor

Summary. The paper studies a low-energy Kane-Mele model for monolayer jacutingaite (Pt2HgSe3) in the presence of a staggered sublattice potential and an off-resonant circularly polarized laser field. It derives the four-band Dirac spectrum, computes Berry curvatures and Chern numbers, maps out a phase diagram with QSHI, VSPM, SPM, BI, P-QHI, and S-QHI phases, and uses Kubo formulas to obtain finite-frequency spin- and valley-resolved longitudinal and Hall conductivities. The authors claim that the optical conductivities provide distinct fingerprints of each topological phase and that the photon energies of intra- and interband transitions can be tuned by the external fields and by doping-induced Pauli blocking.

Significance. The paper addresses a timely and relevant problem: identifying observable finite-frequency optical signatures of the topological phases in a large-gap Kane-Mele material. The theoretical framework is standard, the spin-orbit coupling is taken from prior DFT work, and the Kubo expressions are based on established references; there is no fitting to experimental data and the calculations are reproducible in principle. The central claim that each phase has a distinct conductivity spectrum is plausible and would be useful for experimental proposals. However, the internal inconsistencies in the S-QHI Chern numbers, the incorrect numerical justification of the Floquet condition, and the missing definitions of the spin and valley Hall combinations undermine the reliability of the phase classification and of the interpretation of several figures. These issues are fixable within the manuscript's scope, but they must be addressed before the results can be accepted.

major comments (3)

[Section II, Table I, Eqs. (12)-(14)] The S-QHI row of Table I is not compatible with the paper's own Chern-number definitions. With C↑=1 and C↓=0, Eq. (13) gives Cs=(1−0)/2=0.5, and with CK=1 and CK′=0, Eq. (14) gives Cv=(1−0)/2=0.5, yet the table lists Cs=1 and Cv=1. The same conclusion follows from Eq. (12) at the representative S-QHI point (λz=λso, λω=1.5λso): the four masses are 3.5λso, 1.5λso, −1.5λso, and 0.5λso, which yields C↑=1, C↓=0, CK=1, and CK′=0, hence Cs=Cv=0.5 rather than 1. The text also contradicts Table I: the paragraph defining the S-QHI phase states C=Cv=0, while Table I gives Cv=1. Since Figs. 7-10 present the S-QHI curves as a distinct topological fingerprint, the phase label, the Chern numbers, and the boundary of this region must be recomputed or explicitly redefined before those curves can be interpreted. I note that the claim that this S-QHI point has a vanishing Dirac mass does not hold for the stated parameters: the smallest mass is 0.5λso, so the representative point is gapped; the inconsistency in Cs and Cv nevertheless stands.
[Section II, Eq. (7), off-resonant condition] The numerical example used to justify the off-resonant Floquet approximation is wrong by six orders of magnitude. Light of wavelength 500 nm has frequency about 600 THz, not 0.6 THz, and 0.6 THz corresponds to a wavelength of about 500 µm. With the quoted numbers a≈3 Å and vF≈10^5 m/s, the ratio aω0/vF is about 11 only if ω0 is the 600 THz value; for 0.6 THz the ratio is about 0.011, which violates the stated condition aω0≫ vF. Consequently, the claim that “these conditions are readily met in typical scenarios” and that “for THz radiation, this condition is even more strictly satisfied” is not supported. The estimate must be corrected, or the validity discussion must be restricted to optical frequencies.
[Section IV, Eqs. (23)-(24), Figs. 7-8] The paper never defines the “spin Hall” and “valley Hall” conductivities that are plotted in Figs. 7-8. Equations (23)-(24) define σxy for each valley and spin flavor, but it is not stated whether the figures show σxy^{η,s} separately, the spin Hall combination (σ↑−σ↓)/2, or the valley Hall combination (σK−σK′)/2. This ambiguity makes the sign discussion in the text, such as the statement that the first negative peak at 0.5λso is associated with spin-down and the positive peak with spin-up in the K (K′) valley, impossible to verify against Eq. (24). These signs are part of the claimed control of the transverse current direction, so the plotted quantities must be defined explicitly and the signs reconciled with the formula.

minor comments (7)

[Table I] Table I contains two identical QSHI rows; the duplicate should be removed.
[Fig. 9] The labels in Fig. 9 do not match the phase definitions: panel (d) is labeled “SPM” for λz=0, λω=0.5λso, although SPM is defined at λω=λso, and panel (f) is labeled “S-QHI” for λz=0, λω=0.5λso, although S-QHI is defined at λz=λso, λω=1.5λso.
[Section IV] The figure references in Section IV are inconsistent: the longitudinal conductivity spectra described as Figs. 6(a)-(d) are actually in Fig. 7, and the imaginary longitudinal conductivity described as Fig. 8(c)-(d) is in Fig. 7(c)-(d); Fig. 6 is the phase diagram.
[Fig. 8 caption] The caption of Fig. 8 reuses subplot labels (c) and (d) and refers to the imaginary parts as panels (c)-(d) when they are actually panels (e)-(f); this should be corrected.
[Table II] Table II contains apparent parameter errors: the P-QHI row gives transition energies 0.5λso and 2.5λso, which correspond to (λz,λω)=(0,1.5λso) rather than the listed (1,1), and the QSHI row (0,0) should have a single spin-degenerate interband threshold at 2λso rather than a spin-down threshold at λso.
[Section IV] The text states that the charge-neutral case has µF=0 and then says that the simulations use µF=λso; this contradiction should be resolved.
[Throughout] There are numerous typographical errors, including “spintronics pprogram”, “and and”, and the malformed inequality “| ±λz ± λω = 0| > λso”; these should be corrected in a thorough revision.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular derivation: the optical conductivities are computed from an externally parameterized Kane-Mele Hamiltonian via standard Kubo formulas; the self-citations are non-load-bearing.

full rationale

The paper's central claim is that spin- and valley-resolved optical conductivities depend on the topological phase. The model Hamiltonian in Eq. (8) contains only externally set inputs: the spin-orbit coupling lambda_so = 81.2 meV is taken from prior DFT work [21], and lambda_z and lambda_omega are tunable field parameters. The effective Dirac masses Delta_{eta,s} are not fitted to any conductivity data. The topological phases are labeled by Chern numbers obtained from the standard formula C_{eta,s} = (eta/2) sgn(Delta_{eta,s}) in Eq. (12), and the conductivities are computed from the Kubo formulas in Eqs. (19)-(24), which are cited to several sources, including but not limited to the authors' prior work [46,48]. The resulting spectra are explicit functions of the same masses, so the phase dependence of the spectra follows from the Hamiltonian; this is derivation, not circularity. No parameter is fitted to the predicted conductivity, no prediction is statistically forced by fitting a subset of the data, and no uniqueness theorem from the authors' own prior work is invoked to forbid alternative choices. The self-citations [46,48] supply standard formulas for Berry curvature and Kubo conductivity and are corroborated by independent references [49,50], so they are not load-bearing. The paper's apparent internal inconsistencies, such as the S-QHI row of Table I giving C_up = 1 and C_down = 0 while Eq. (13) would give C_s = 0.5, are correctness concerns about the phase classification, not circular reductions of the derivation. Therefore the circularity score is low.

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

The paper rests on the standard Kane-Mele low-energy model with parameters from prior DFT, a standard Floquet expansion, and Kubo formulas from earlier works. No data is fitted; lambda_z, lambda_omega, Gamma, and mu_F are swept control parameters. The main hidden assumptions are the neglect of Rashba coupling and higher bands, and the validity of the off-resonant approximation.

free parameters (4)

staggered potential lambda_z = swept from 0 to 2*lambda_so
External electric field knob; not fitted but central to the phase diagram and optical spectra.
optical field strength lambda_omega = swept from 0 to 1.5*lambda_so (signed by helicity)
Off-resonant circularly polarized light amplitude; control parameter in the Floquet Hamiltonian.
broadening Gamma = 0.002*lambda_so (Fig. 6) or 10^-3*lambda_so (Figs. 7, 8, 10)
Phenomenological dissipation chosen by hand; sets linewidths only, not peak positions.
chemical potential mu_F = 0, 0.6*lambda_so, 1.6*lambda_so in different figures
Doping level, chosen by hand for the Pauli-blocking study; controls intraband weight and blocking.

assumptions (4)

domain assumption ML-jacutingaite low-energy bands are well described by the Kane-Mele Hamiltonian (Eq. 1) with SOC lambda_so and no Rashba coupling.
Invoked in Section II; based on Refs. [21,40]; neglects additional bands, trigonal warping, and Rashba spin-orbit coupling.
domain assumption The off-resonant Floquet expansion (Eqs. 5-7) is valid, requiring a*omega_0 >> v_F and A << 1 and |E| < hbar*omega_0/2.
Used to obtain effective Hamiltonian (Eq. 8); the paper's numerical check mistakenly calls 500 nm light 0.6 THz, so the condition is not cleanly established.
standard math Kubo formulas (Eqs. 20-24) from Refs. [48,50] give the longitudinal and Hall optical conductivities at T=0 for each massive Dirac cone.
Taken from prior literature without derivation; standard linear response for the two-band Dirac model.
domain assumption Spin is conserved in optical transitions (no Rashba term), so interband transitions couple only same-spin bands.
Used in Section IV to assign spin labels to transitions and Pauli blocking.

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Cite this review

Pith. "Pith review of Topological transport in monolayer jacutingaite." pith.science (2026). https://pith.science/paper/BGISCXLF

@misc{pith2026241216965,
  author       = {Pith},
  title        = {Pith review of: Topological transport in monolayer jacutingaite},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BGISCXLF}},
  note         = {Machine review of arXiv:2412.16965}
}

abstract

Monolayer-jacutingaite (Pt2HgSe3) has been predicted to be the first large-gap Kane-Mele quantum spin Hall insulator. Materials in the jacutingaite family undergo topological phase transitions (TPTs), i.e., from a topologically non-trivial to a semimetallic phase and further to the normal insulating phase when exposed to electric fields and off-resonance, high-frequency and high-intensity laser irradiation. In this article, we investigate the rich tapestry of topological phases in this unique material in the presence of an appropriate choice of off-resonance circularly polarized laser fields and staggered sublattice potentials. The interplay of these stimuli with large spin-orbit coupling, due to the buckled structure of jacutingaite materials, results in the emergence of quantum spin Hall insulator, valley-spin-polarized metal, spin-polarized metal, photo-induced quantum Hall insulator, anomalous quantum Hall insulator and band insulator phases. By analyzing the band structures, we compute Berry curvatures in different topological regimes for the $K$ and $K'$ valleys. Furthermore, by using the Kubo formula, we calculate the spin-valley resolved longitudinal and Hall conductivities as a function of photon energies showing that the conductivities exhibit a strong topological state dependence. The photon energy of the intraband and interband optical transitions can be tuned by varying the electric and optical fields. Finally, we demonstrate that by modulating the chemical potential, some of the allowed optical transitions become Pauli blocked due to the optical selection rules

Figures

Figures reproduced from arXiv: 2412.16965 by the authors.

**Figure 1.** FIG. 1. Schematic of ML-jacutingaite subjected to an external electric and off-resonant circularly polarized optical fields. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** FIG. 2. The phase diagram of the monolayer of jacutingaite as a function of [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** FIG. 3. Band structure of jacutingaite in distinct topological phases at the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: FIG. 4. Berry curvature of jacutingaite in distinct topological phases at the [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]

**Figure 5.** Figure 5: FIG. 5. The low-energy electronic density of states of jacutingaite at the [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

**Figure 6.** Figure 6: FIG. 6. Phase diagram of (a) longitudinal conductivity, (b) transverse Hall conductivity, for ML-jacutingaite in the [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]

**Figure 7.** Figure 7: FIG. 7. Longitudinal conductivity of jacutingaite as a function of normalized incident photon energy in distinct topological [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

**Figure 8.** Figure 8: FIG. 8. Transverse Hall conductivity of jacutingaite as a function of normalized incident photon energy in distinct topological [PITH_FULL_IMAGE:figures/full_fig_p012_8.png]

**Figure 9.** Figure 9: FIG. 9. Band structure of jacutingaite in distinct topological phases at the [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]

**Figure 10.** Figure 10: FIG. 10. Longitudinal conductivity of jacutingaite as a function of normalized incident photon energy in distinct topological [PITH_FULL_IMAGE:figures/full_fig_p014_10.png]

Discussion (0). Continue with ORCID to comment.

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