Edelstein effect in optically driven monolayer jacutingaite Pt$_2$HgSe$_3$

Bui Dinh Hoi; Le Thi Thu Phuong; Nguyen Quang Bau; Ta Thi Tho

REVIEW 3 major objections 4 minor 28 references

Edelstein effect in optically driven monolayer jacutingaite Pt$_2$HgSe$_3$

T0 review · 3 major / 4 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Edelstein response pinpoints light-driven topological switch in Pt2HgSe3

desk verdict The paper's central 'spin' Edelstein discontinuity is actually a sublattice pseudospin response: the authors define σ as sublattice Pauli matrices but then use σ as the spin operator, so the headline result is not a physical spin effect. read the letter →

arxiv 2505.06144 v1 pith:MX2XBMEO submitted 2025-05-09 cond-mat.str-el

Nguyen Quang Bau , Ta Thi Tho , Le Thi Thu Phuong , Bui Dinh Hoi This is my paper · ORCID

classification cond-mat.str-el

keywords EdelsteineffectFloquetengineeringjacutingaitePt2HgSe3quantumspinHallinsulatortopologicalphasetransitionspin-orbitcouplingorbitalmagnetizationsemimetal

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

This paper claims that the spin and orbital Edelstein effects—electric-field-induced spin and orbital polarizations—can serve as experimental probes of light-induced topological phase transitions in monolayer jacutingaite Pt2HgSe3. In the effective low-energy Dirac model, circularly polarized light adds a valley-contrasting mass term that can cancel the intrinsic spin-orbit mass for one spin species in one valley, closing the gap and creating a spin-polarized semimetal. The paper identifies two universal transport signatures of this transition: a pronounced discontinuity in the interband spin Edelstein conductivity and a vanishing orbital Edelstein susceptibility. These signatures do not require computing Chern numbers, so they offer a direct, transport-based way to locate the topological boundary.

What carries the argument

The load-bearing objects are the spin-valley-resolved Dirac mass term $\Delta_{\zeta,s} = \zeta s \Delta_{\mathrm{so}} + \zeta \Delta_d$, the Kubo formula for the Edelstein conductivity tensor, and the orbital angular momentum operator defined through the Berry curvature (orbital magnetic moment). The argument works by evaluating the intraband and interband contributions separately: the interband spin response remains finite at charge neutrality and is discontinuous at the gap-closing point, while the orbital Edelstein response vanishes there because of symmetry and the structure of the orbital matrix elements. The Floquet high-frequency expansion (Eqs. A2–A4) supplies the light-induced mass $\Delta_d = e^2 A_0^2 v_F^2 / \omega_d$, which is the tunable knob for driving the system through the transition.

What would settle it

A direct time-dependent numerical simulation of the full driven Hamiltonian, without the high-frequency effective-mass approximation, could settle whether the gap actually closes at Δd/Δso = ±1 and whether the spin Edelstein conductivity really shows a discontinuity there; if the exact Floquet bands remain gapped at that point or the conductivity varies smoothly, the predicted signature would not survive.

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Extended reading notes

Core claim

The central discovery is that the transition from the quantum spin Hall insulating phase to a spin- and valley-selective semimetallic phase is encoded in the Edelstein response functions of the light-dressed Dirac Hamiltonian $H_{\zeta,s} = v_F(\zeta k_x \sigma_x + k_y \sigma_y) + (\zeta s \Delta_{\mathrm{so}} + \zeta \Delta_d)\sigma_z$. For each valley and spin species, the mass term $\Delta_{\zeta,s} = \zeta s \Delta_{\mathrm{so}} + \zeta \Delta_d$ vanishes when $\Delta_d/\Delta_{\mathrm{so}} = \pm 1$, closing the gap for exactly one spin flavor in one valley. At that critical point, the interband spin Edelstein conductivity develops a pronounced discontinuity, the intraband spin response changes sharply, and the orbital Edelstein susceptibility vanishes. The paper argues that these features are universal, valley-contrasting, and robust against doping, and that they provide a direct transport-based diagnostic of the photoinduced topological transition.

Load-bearing premise

The high-frequency Floquet expansion replaces the periodically driven system by the static effective mass Δd, and the paper locates the transition at Δd/Δso = ±1, where this mass is comparable to the intrinsic spin-orbit mass, without explicitly checking that the perturbative expansion remains valid at that drive strength.

Editorial extensions

If this is right

Tuning the drive amplitude or frequency lets one switch monolayer jacutingaite between the quantum spin Hall insulating phase and a spin-polarized semimetal without modifying the material itself.
The Edelstein response gives an all-electrical probe of the topological transition, since it can be read from transport measurements without extracting Chern numbers.
The signatures are valley-selective, so they reveal which valley and spin species undergo gap closing, enabling spin-valley resolved diagnostics.
The interband scattering time controls the magnitude and anisotropy of the spin Edelstein conductivity at the transition, so lifetime engineering can enhance the observable signal.

Reading between the lines

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

Because the proof uses a generic two-band Dirac Hamiltonian with a tunable mass, the same discontinuity and vanishing signatures should appear in other gapped Dirac materials with a photoinduced mass term, such as silicene or transition-metal dichalcogenides; this is an extrapolation beyond the paper's explicit claim.
The vanishing orbital Edelstein susceptibility at the transition may provide a Berry-curvature-sensitive observable that is experimentally easier to access than the anomalous Hall effect, but the paper does not make this connection explicitly.
If the high-frequency Floquet expansion fails quantitatively at the critical drive strength, the signatures could still survive but at a shifted drive amplitude, which would make the effect a useful empirical probe even if the precise mass formula changes.
A direct test could be performed by measuring current-induced spin polarization (e.g., via Kerr rotation) in a Pt2HgSe3 monolayer while sweeping the laser intensity across the predicted critical value.

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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

Quick take: the paper's headline result is not a spin Edelstein effect. The model is a spin-diagonal two-band Hamiltonian, so the true spin operator in each spin sector is s⊗I. It has no interband matrix elements. The interband 'spin' conductivity that produces the discontinuity in Figs. 2(d)-(f) is computed with sublattice Pauli matrices; it is a pseudospin coherence response. The intraband spin components are similarly momentum-dependent only because σ is treated as spin. So the central claim — a transport-accessible spin probe of the topological transition — does not follow.

What the paper does well: the algebra is clean, the Floquet derivation in Appendix A is standard, and the orbital Edelstein part, computed from the Berry curvature, is internally consistent. The two-band model for jacutingaite is reasonable, and the valley-contrasting gap-closing analysis is correct. If the 'spin' label were replaced by 'sublattice pseudospin', the calculation would be a minor but valid model study of pseudospin Edelstein responses.

The soft spots: first, the physical spin operator in the model is diagonal and constant, so all spin Edelstein components — intra and inter — are mislabeled. This is not a small oversight; it changes the observable. Second, as the reader noted, at Δd/Δso = ±1 the Floquet high-frequency expansion is not checked; the drive-induced mass is of the same order as the intrinsic SOC, so the effective Hamiltonian may not be valid there. That issue is real but secondary once the operator error is fixed.

Readership: people working on pseudospin or orbital Edelstein effects might find the formalism useful, but anyone interested in spin transport in jacutingaite should be wary. I would not cite this as a spin Edelstein result.

Recommendation: desk reject. The central observable is misidentified, so the paper's advertised finding cannot be salvaged without rewriting it as a pseudospin-Edelstein paper, which would be a much weaker result. A referee would catch this immediately.

Referee Report

3 major / 4 minor

Summary. The manuscript studies a two-band Dirac model for monolayer jacutingaite Pt2HgSe3 under irradiation by circularly polarized light. A high-frequency Floquet expansion maps the light to a valley-dependent mass term Δd added to the spin-orbit mass, so that Δd/Δso = ±1 closes the gap for one spin-valley flavor. Using Kubo linear response, the authors compute spin and orbital Edelstein susceptibilities and report that the interband spin susceptibility is discontinuous and the orbital susceptibility vanishes at the gap-closing point. They propose these features as a transport-based probe of the light-induced topological transition that does not require computing Chern numbers.

Significance. The idea of using current-induced polarization to detect light-induced band inversions is attractive, and the algebra connecting the mass term to the response is straightforward. However, the central spin Edelstein result relies on identifying the sublattice pseudospin Pauli matrices with the physical spin operator. Because the physical spin operator has no interband matrix elements in this model, the reported interband spin discontinuity is an artifact of that identification. The orbital Edelstein channel is physically well defined, but the claimed universal spin signature, which is the paper's main advertised result, is not a spin response. The paper is therefore not a sound basis for the stated spintronic conclusions; a reframing as a pseudospin Edelstein study would substantially weaken the experimental accessibility claims.

major comments (3)

[Sec. II.A, II.B, and Appendix B] Section II.A defines σ_i as Pauli matrices on the pseudospin (sublattice) space and s=±1 as the spin label. The Hamiltonian in Eq. (1) is block diagonal in s, so within each spin sector the physical spin operator is S_z=(ℏ/2)s I_2 and the in-plane spin operators have no matrix elements at all; consequently every interband matrix element O^spin_{mn} of the physical spin vanishes. Nevertheless, the Kubo evaluation in Appendix B, Eqs. (B1g)-(B1i), uses the sublattice Pauli matrices σ_i as the 'spin' operator, producing nonzero interband matrix elements. The interband spin Edelstein susceptibility in Eq. (8) and the discontinuity in Fig. 2(d)-(f) are therefore sublattice-pseudospin coherence responses, not responses of the electronic spin. Replacing O with the physical spin operator forces the interband term to zero and removes the headline signature claimed in the abstract and in Sec. IV.
[Appendix A and Eq. (A4)] Appendix A replaces the driven Hamiltonian by the static mass term Δd=e^2 A0^2 v_F^2/ω_d using the leading-order high-frequency expansion in Eq. (A2). The paper locates the transition at Δd/Δso=±1. At that point the dimensionless drive parameter is eA0 v_F/ω_d = sqrt(Δso/ω_d); the paper never specifies ω_d/Δso or verifies that this parameter is small. For a strong-SOC material such as jacutingaite with Δso on the scale of tens to hundreds of meV and off-resonant frequencies in the infrared-to-visible range, this ratio can be order one, in which case the truncation in Eq. (A2) is uncontrolled and higher-order Floquet corrections can shift or remove the gap closing. The predicted response signatures therefore do not necessarily describe the actual Floquet state at the nominal transition.
[Sec. III and Eq. (8)] The interband Kubo integrand for the pseudospin operator behaves as O(p)/(ε_n-ε_m)^2 ~ 1/k^2 at large momentum for all values of Δd, so after the d^2k integration it is logarithmically divergent in the absence of a cutoff. The paper uses a linearized Dirac Hamiltonian valid only near K and does not specify a momentum cutoff, a subtraction, or a regularization scheme. The finite discontinuity plotted in Fig. 2 is therefore cutoff-dependent and cannot be claimed as a universal signature unless the regularization is specified and shown not to affect the qualitative jump.

minor comments (4)

[Sec. III] The word 'vallyes' should be 'valleys' in the opening sentence of Sec. III.
[Author affiliation] The affiliation list contains 'Faculty of of Physics'; the duplicated 'of' should be corrected.
[Sec. II.B] The paper sets ℏ=kB=me=e=1 but leaves lifetimes in eV; the text should state how this unit system maps to physical SI units for the plotted quantities.
[Fig. 2 caption] The caption refers to Δd/Δso as the 'normalized sublattice asymmetry parameter', but Δd is a light-induced mass term rather than a sublattice asymmetry; the terminology should be revised for clarity.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the Edelstein conductivities are computed from the stated low-energy Hamiltonian; the claimed signatures are algebraic consequences of the mass-gap closure, not fitted inputs or self-citation chains.

full rationale

The paper's derivation chain is self-contained. The model Hamiltonian is Eq. (1), H_{ζ,s}(k)=v_F(ζ k_x σ_x + k_y σ_y)+Δ_{ζ,s} σ_z, with Δ_{ζ,s}=ζ s Δ_so+ζ Δ_d (Eq. 2). The spin/orbital Edelstein tensors are evaluated from the Kubo formula, Eq. (8), with matrix elements listed from the eigenstates, Eqs. (5) and Appendix B. No parameter is fitted to reproduce the reported signatures; τ_intra and τ_inter are hand-set scattering times that change magnitudes but not the location or existence of the discontinuity, and the chemical potential values are stated sampling points. The gap-closure points Δ_d/Δ_so=±1 are read off from the mass term in Eq. (2), and the discontinuities and vanishing features in the Edelstein components are derived from the band eigenstates at those points; this is a mathematical consequence of the model, not an input. The Floquet effective mass Δ_d=e^2 A_0^2 v_F^2/ω_d (Eq. A4) comes from a standard high-frequency expansion cited to Refs. [24-28], none of which are authored by the present group, so there is no self-citation chain carrying the central claim. The spin operator is defined in Sec. II.B as \hat S_i=(ℏ/2) σ_i with σ_i acting on the pseudospin (sublattice) space; consequently the interband 'spin' Edelstein response is, by that definition, a pseudospin-coherence response rather than a physical spin response. That is a concern about operator misidentification or physical interpretation, not circularity: the paper states the definition explicitly and the calculation follows from it. Similarly, the validity of the high-frequency Floquet expansion at Δ_d ~ Δ_so is an assumption about the parameter regime, not a circular reduction. Therefore the circularity score is 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The calculation is self-contained once the Dirac Hamiltonian is assumed: the only hand-set numbers are the two relaxation times, no new entities are introduced. The main external inputs are the material-to-model mapping and the Floquet high-frequency approximation.

free parameters (2)

tau_intra = 0.25 eV
Intraband relaxation time used in Eq. 10; chosen uniformly, not from material data, and results are stated in arbitrary units.
tau_inter = 0.25 eV, varied up to about 1.5 eV
Interband relaxation time in the Kubo denominator; set to 0.25 eV then scanned in Fig. 4; no experimental justification is given.

assumptions (4)

domain assumption The two-band, spin-valley massive Dirac Hamiltonian Hζ,s = vF(ζkxσx + kyσy) + ∆ζ,sσz (Eq. 1) captures the low-energy electronic structure of monolayer jacutingaite.
The paper models Pt2HgSe3 only through a Dirac Hamiltonian with mass ∆ζ,s = ζs∆so + ζ∆d, relying on prior works for the mapping to the material; multi-orbital or remote-band effects are not included.
domain assumption The driven system is described by the static Floquet Hamiltonian with first-order correction [H_-1,H_+1]/ωd (Eq. A2), assuming weak amplitude and high frequency.
Used to justify the light-induced mass ∆d = e^2 A0^2 vF^2/ωd, but the transition is studied at ∆d/∆so ~ 1, where the perturbative condition is not checked.
standard math Kubo linear response with independent intraband and interband relaxation times (Eq. 8) gives the Edelstein conductivities.
The Kubo formula is standard; the paper assumes static limit, T about zero, and simple relaxation-time broadening.
domain assumption The orbital angular momentum is band-diagonal with L_z^± given by the Berry-curvature expression (Eq. 12), so interband orbital matrix elements vanish.
The statement ⟨u±|Lz±|u∓⟩ = 0 follows from treating Lz as diagonal in band index; a fully gauge-invariant orbital operator could have non-diagonal pieces, which this model excludes.

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Cite this review

Pith. "Pith review of Edelstein effect in optically driven monolayer jacutingaite Pt$_2$HgSe$_3$." pith.science (2026). https://pith.science/paper/MX2XBMEO

@misc{pith2026250506144,
  author       = {Pith},
  title        = {Pith review of: Edelstein effect in optically driven monolayer jacutingaite Pt$_2$HgSe$_3$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MX2XBMEO}},
  note         = {Machine review of arXiv:2505.06144}
}

abstract

The optical control of spin- and valley-selective gapless states in two-dimensional materials presents new opportunities for next-generation spintronic and valleytronic technologies. In this work, we study monolayer jacutingaite (Pt$_2$HgSe$_3$), a quantum spin Hall insulator with strong intrinsic spin-orbit coupling, under irradiation by circularly polarized light. The light-induced Floquet engineering gives rise to tunable topological phases, including transitions to spin- and valley-polarized semimetallic states. To probe these topological transitions, we employ the spin and orbital Edelstein effects -- non-equilibrium responses arising from spin-orbit interactions in systems lacking inversion symmetry -- without resorting to topological invariants such as Chern numbers. We identify universal signatures of the phase transitions encoded in the Edelstein response: a pronounced discontinuity in the spin Edelstein conductivity and a vanishing orbital Edelstein susceptibility mark the onset of the semimetallic regime. Furthermore, we investigate how the growth and suppression of the spin Edelstein responses across the topological phase transition depend on the interband scattering time. These findings establish the Edelstein effect as a sensitive and experimentally accessible probe of light-induced topological transitions in quantum materials.

Figures

Figures reproduced from arXiv: 2505.06144 by the authors.

**Figure 2.** FIG. 2. Spin and orbital Edelstein susceptibilities [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** FIG. 3. Edelstein response functions (in arbitrary units) in [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: FIG. 4. Interband spin Edelstein conductivity tensor [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Reviews of Modern Physics82, 3045 (2010)

2010

[2] [2]

Qi and S.-C

X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Reviews of Modern Physics 83, 1057 (2011)

2011

[3] [3]

Manzeli, D

S. Manzeli, D. Ovchinnikov, D. Pasquier, O. V. Yazyev, and A. Kis, 2d transition metal dichalcogenides, Nature Reviews Materials2, 17033 (2017)

work page 2017

[4] [4]

X. Xu, W. Yao, D. Xiao, and T. F. Heinz, Spin and pseudospins in layered transition metal dichalcogenides, Nature Physics10, 343 (2014)

2014

[5] [5]

Marrazzo, M

A. Marrazzo, M. Gibertini, D. Campi, N. Mounet, and N. Marzari, Prediction of a large-gap and switchable Kane-Mele quantum spin Hall insulator, Phys. Rev. Lett. 120, 117701 (2018)

work page 2018

[6] [6]

Marrazzo, M

A. Marrazzo, M. Gibertini, D. Campi, N. Mounet, and N.Marzari,Relativeabundanceof Z2 topologicalorderin exfoliable two-dimensional insulators, Nano Letters19, 8431 (2019)

work page 2019

[7] [7]

Marrazzo, N

A. Marrazzo, N. Marzari, and M. Gibertini, Emer- gent dual topology in the three-dimensional Kane-Mele Pt2HgSe3, Phys. Rev. Res.2, 012063 (2020)

work page 2020

[8] [8]

Cucchi, A

I. Cucchi, A. Marrazzo, E. Cappelli, S. Riccò, F. Y. Bruno, S. Lisi, M. Hoesch, T. K. Kim, C. Ca- cho, C. Besnard, E. Giannini, N. Marzari, M. Gib- ertini, F. Baumberger, and A. Tamai, Bulk and sur- face electronic structure of the dual-topology semimetal Pt2HgSe3, Phys. Rev. Lett.124, 106402 (2020)

work page 2020