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REVIEW 4 major objections 5 minor 64 references

Magnetically induced Circular Photogalvanic Effect in Symmetric Two-dimensional Materials

T0 review · 4 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read A magnetic exchange field from a substrate can break inversion symmetry in the band dispersion of a centrosymmetric monolayer, generating a helicity-dependent circular photogalvanic effect without any lattice asymmetry.

desk verdict A creative mechanism for helicity-dependent currents in a centrosymmetric monolayer, but the in-plane configuration cancels between valleys; the paper's sign error undermines its central claim. read the letter →

arxiv 2608.09309 v1 pith:JLHFIRBZ submitted 2026-08-10 cond-mat.mes-hall

Peng Liu , Fanhao Jia , Ruixue Li , Yuan Li , Igor Zutic , Gaofeng Xu This is my paper · ORCID
classification cond-mat.mes-hall
keywords circularphotogalvaniceffectmagneto-circularmagneticproximityvalley-contrastphotocurrentcentrosymmetric2DmaterialSbHmonolayerBethe-Salpeterequationhelicity-dependent
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

Circular photogalvanic effect normally requires a material whose lattice lacks inversion symmetry; this paper proposes that a magnetic effect can do the same job in a structurally symmetric material. As a proof of principle, it studies a monolayer of SbH on a magnetic substrate, where staggered magnetic exchange fields from the substrate shift the energy bands at the two valleys so that circularly polarized light excites unbalanced currents. The paper shows the resulting photocurrent is tunable by the magnitude and direction of the substrate magnetization, and it computes the accompanying single-particle and excitonic optical absorption with a Bethe–Salpeter equation. If the mechanism holds, it removes the structural inversion-breaking requirement for helicity-dependent photocurrents and makes magnetic proximity a switch for valley-selective optoelectronic responses.

What carries the argument

The argument is carried by a four-band effective Hamiltonian $H_{\rm tot} = H_0 + H_{\rm ex} + H_U + H_R$ for the low-energy states at the $\pm K$ valleys of monolayer SbH. $H_0$ is the bare Dirac-type band structure with spin-orbit coupling $\lambda_{\rm SO}$; $H_{\rm ex}$ is the staggered magnetic exchange field $M_A$ ($M_B$) acting on the A (B) sublattice along the substrate magnetization direction; $H_U$ is a staggered sublattice potential; and $H_R$ is Rashba spin-orbit coupling. The load-bearing mechanism is the competition between the Zeeman splitting of the exchange field and the Rashba coupling, which shifts the bands perpendicular to the in-plane field and makes the integrand of the CPGE tensor $\beta_{ij}(\omega) = \sum_k (i\pi e^3 / \hbar^2 A)\,\partial_{k_i}E_{k,12}\,\Omega^v_j(k)\,\delta(\hbar\omega - E_{k,21})$ asymmetric in $k$-space. For the absorption side, the Bethe–Salpeter equation yields the exciton envelope functions and, through them, the circularly resolved absorption spectra.

What would settle it

Measure the helicity-dependent photocurrent in a centrosymmetric SbH monolayer on a magnetic substrate while rotating the in-plane magnetization: the theory predicts the current should follow the in-plane component of the exchange field, vanishing when the field is perpendicular to the current direction ($\theta = \pi/2$) and reversing sign when the field direction is reversed ($\theta = \pi$). Observing no such angular dependence, or no current when $M_A = M_B$, would falsify the proposed mechanism.

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Extended reading notes

Core claim

The paper's central claim is that a magnetic effect can effectively break the symmetry of the energy dispersion in a centrosymmetric material and thereby generate helicity-dependent photocurrents, an effect it names the magneto-circular photogalvanic effect (MCPGE). For monolayer SbH on a magnetic substrate, the substrate induces staggered exchange fields $M_A$ and $M_B$ on the two sublattices; with $M_A \gg M_B$ and a finite in-plane component, the bands at the $\pm K$ valleys shift in opposite directions perpendicular to the field. This breaks $k$-space inversion symmetry, so the resonant optical transition contour becomes asymmetric and the contributions from opposite momenta no longer cancel. Because the two valleys couple exclusively to opposite circular polarizations and carry opposite Berry curvature, a given helicity excites one valley and produces a net current. An out-of-plane field component further splits the valleys, yielding near-100% valley polarization, and the same physics appears in the excitonic absorption obtained from the Bethe–Salpeter equation.

Load-bearing premise

The load-bearing premise is that the magnetic substrate produces staggered exchange fields with $M_A \neq M_B$ and with a finite in-plane component; if the exchange were uniform across the two sublattices or purely out-of-plane, the band shifts and the magneto-circular photogalvanic effect would vanish.

Editorial extensions

If this is right

  • Centrosymmetric 2D materials with magnetic proximity can host helicity-dependent photocurrents without any lattice inversion breaking, widening the material pool for circular photogalvanic devices.
  • The MCPGE current is tunable by the strength and direction of the substrate magnetization, including a current reversal when the in-plane field is reversed.
  • With an out-of-plane exchange-field component, valley polarization approaches ±100%, and linearly polarized light alone suffices to generate a nonzero injection current.
  • Excitonic absorption peaks follow the single-particle absorption and reverse their circular polarization after each band crossing, so the optical response can reveal band crossings induced by magnetic proximity.
  • The effect also adds an externally tunable contribution to photocurrents in non-centrosymmetric materials and can serve as an optical probe of magnetic proximity in 2D materials.

Reading between the lines

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

  • The staggered-exchange requirement suggests the mechanism should generalize to any buckled centrosymmetric monolayer in which a magnetic substrate couples differently to the two sublattices; functionalized bismuth and antimony monolayers, and possibly two-dimensional altermagnets, are natural candidates.
  • Because the current direction and magnitude are set by the exchange field direction and strength, MCPGE could serve as a non-invasive optical readout of magnetic ordering or magnetization reversal in van der Waals heterostructures.
  • If the exchange field can be switched electrically or by spin-orbit torque, the same structure becomes a helicity-controlled optoelectronic switch, and the valley-selective excitation could be extended to helicity-controlled terahertz emission in centrosymmetric Dirac semimetal films.
  • The calculation assumes ballistic injection-current generation; in real devices, disorder, finite temperature, and the dielectric environment will modify the magnitude, but the angular dependence and valley-contrast signatures should remain.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The manuscript proposes a magneto-circular photogalvanic effect (MCPGE) in a centrosymmetric monolayer SbH placed on a magnetic substrate. The authors use a four-band k·p Hamiltonian with staggered magnetic exchange, a staggered potential, and Rashba spin-orbit coupling; compute per-valley CPGE tensors from the standard injection-current formula in Eq. (4); and find that the exchange field shifts the valence-band isoenergy contours, producing β^K_ij = −β^{−K}_ij together with valley-contrast Berry curvature. They argue that valley-selective circular dichroism converts these opposite per-valley tensors into a helicity-dependent photocurrent. The paper also computes single-particle and excitonic absorption via a Bethe-Salpeter equation and discusses tunability with magnetization direction.

Significance. If correct, the proposal would broaden CPGE to magnetically proximitized centrosymmetric monolayers and offer a tunable, valley-selective photocurrent. The paper has clear strengths: it applies the standard CPGE tensor formula rather than fitting to a target, it presents explicit numerical maps of band shifts and Berry curvature, and it includes a BSE treatment of excitonic absorption. However, the central in-plane demonstration is internally inconsistent: the full-Brillouin-zone sum in Eq. (4) cancels exactly for the configuration shown in Fig. 2. The out-of-plane valley-split configuration in Fig. 3 could in principle support a nonzero effect, but the manuscript would need to be substantially reframed around that case. As written, the main claim is not established.

major comments (4)
  1. [Eq. (4), Fig. 2(h), and the text after Fig. 2(h)] The in-plane configuration shown in Fig. 2 yields a vanishing total CPGE, and the manuscript's valley-selection argument double-counts the helicity sign. In Eq. (4) the CPGE tensor is a sum over the full Brillouin zone. The manuscript states that, for in-plane exchange, the isoenergy contours at ±K are identical, ∂_{k_y}E_{12} is identical at the two valleys, and β^K_ij = −β^{−K}_ij. Summing the two valley contributions in Eq. (4) therefore gives β^K_ij + β^{−K}_ij = 0 identically. The subsequent argument that valley-selective circular dichroism produces a helicity-dependent current is not a valid rescue: writing s_j = [E×E*]_j, σ+ excitation gives j_i = β^K_ij s_j, while σ− excitation gives j_i = β^{−K}_ij(−s_j) = (−β^K_ij)(−s_j) = β^K_ij s_j. The two helicities thus produce the same current, not opposite currents. Since the full-BZ sum already vanishes, the in-plane configuration of Figs. 2(a)–2(h), which is the stated proof of principle, yields zero magneto-CPGE.
  2. [Eq. (2) and the definition of HU] The model is not a centrosymmetric electronic Hamiltonian, so the claim that magnetism overcomes the inversion-symmetry limitation is not demonstrated. Eq. (2) assumes staggered exchange fields with M_A ≠ M_B, and the Hamiltonian also contains HU = U σ_z. Both terms are odd under A↔B sublattice exchange, which is precisely the operation that realizes inversion for this buckled honeycomb structure. The text even states that the exchange 'breaks the symmetry between the two sublattices.' The abstract's claim that the limitation of inversion-symmetry breaking is overcome is therefore an input assumption, not a consequence derived from a centrosymmetric starting point. To support the central claim, the authors would need to start from an inversion-invariant Hamiltonian (for example, M_A = M_B and U = 0) or else explicitly reframe the work as CPGE controlled by an inversion-breaking magnetic proximity field.
  3. [Text near Fig. 3(b)] The statement that 'linearly polarized light is sufficient to induce a nonzero injection current' contradicts Eq. (3). The injection rate is proportional to [E×E*], which vanishes identically for linearly polarized light. The valley asymmetry shown in Fig. 3 makes β^K and β^{−K} unequal in magnitude, but a CPGE current still requires circular polarization or another chiral excitation. If this is a typo, it must be corrected; as written, it indicates a confusion between valley polarization and helicity selection. This issue is load-bearing because the paper's tunability discussion relies on it.
  4. [Eqs. (4), (5), and Figs. 2–4] The central numerical results are not reproducible from the information given. The values of ħv_F, λ_SO, λ_R, U, M_A, M_B, the assumed constant ratio M_A/M_B, the Lorentzian broadening Γ, and the dielectric parameters entering the BSE kernel are all omitted from the main text; only a reference to Supplemental Material [38] is given. The authors should provide the complete parameter set, the integration domain used for the per-valley β^τ tensors, and the dielectric screening model, either in the paper or in an accessible supplement. Without these inputs, Figs. 2–4 cannot be checked or reproduced.
minor comments (5)
  1. [Throughout] There is a typographical error in the word 'sufficient' in the paragraph after Fig. 3(b); it should be corrected.
  2. [Fig. 2 discussion] The sentence 'Since ±K valleys have opposite Berry curvatures, the net currents at the two valleys are in opposite directions' is only true for the per-valley tensors before the full-Brillouin-zone sum is taken; in the full sum of Eq. (4) these contributions cancel. The wording should be revised to avoid implying a nonzero total for the in-plane case.
  3. [Eqs. (4) and (6)] The CPGE calculation uses a two-band model while the absorption calculation uses the four-band Hamiltonian. The authors should clarify why the additional bands included in the absorption do not affect the low-frequency CPGE response, or estimate their contribution.
  4. [Fig. 3 and text] The paper states that 'a constant ratio M_A/M_B has been kept' when increasing M_A, but neither the ratio nor the absolute values of M_A and M_B are given. A quantitative estimate from a specific magnetic substrate would substantially strengthen the proposal.
  5. [References] Reference [38] is to Supplemental Material; if the supplement is not included with the submitted manuscript, the numerical details are effectively unavailable to the reader. The supplement should accompany the submission.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: MCPGE is a direct application of the standard CPGE formula to an explicit model Hamiltonian; symmetry-breaking inputs are assumed, not fitted, and self-citations are not load-bearing.

full rationale

The derivation is not circular. The MCPGE is computed by applying the standard CPGE injection-current formula (Eq. 4) to an explicit four-band Hamiltonian (Htot = H0 + Hex + HU + HR, Eqs. 1–2). The staggered exchange fields and staggered potential are model inputs motivated by magnetic proximity (Refs. 25, 26, 31) and Rashba SOC (Ref. 40); they are not fitted to any target CPGE value. The CPGE tensor, valley polarization, and absorption spectra are genuine outputs of a numerical evaluation, and the photon energy 0.29 eV is chosen to match the in-plane gap, which is a resonance condition, not a fit of the response. Self-citations (e.g., Refs. 7, 28, 31, 48) supply model forms and methods, but the cited results do not contain the CPGE result and are corroborated by independent external work (e.g., Refs. 25, 29, 32, 33, 35, 40), so they are not load-bearing circular support. The symmetry-breaking ingredient is admittedly placed in the Hamiltonian, but the paper's proposal is precisely that magnetic proximity can create effective inversion-symmetry breaking in a centrosymmetric lattice; this is an assumed physical mechanism, not a definitional identity with the predicted photocurrent. The cancellation objection for the in-plane configuration is a separate correctness concern about the total Brillouin-zone sum, not a circularity, and is therefore not reflected in this score.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The calculation is a model-based demonstration. Its quantitative output depends on parameter values not given in the main text and on the domain assumption that a substrate creates staggered magnetic exchange. These are inputs to the model rather than parameters fitted to reproduce the target CPGE, which keeps the circularity burden low but limits how strongly the numbers can be trusted.

free parameters (6)
  • lambda_SO (effective on-site spin-orbit coupling) = not stated in main text
    Enters H0 in Eq. (1); controls the gap and Berry curvature scale relevant for the MCPGE.
  • lambda_R (Rashba spin-orbit coupling) = not stated in main text
    Enters HR; competition with Zeeman splitting produces the in-plane band shifts that generate the photocurrent.
  • U (staggered potential) = not stated in main text
    Introduced in HU=U sigma_z as a small substrate-induced sublattice potential; contributes to effective inversion breaking.
  • MA and MB (magnetic exchange amplitudes) = not stated in main text; constant ratio MA/MB kept
    Staggered exchange drives the MCPGE; the assumption MA >> MB is used to justify that conduction bands are nearly unshifted.
  • Gamma (Lorentzian broadening) = not stated in main text
    Replaces the delta functions in Eqs. (4) and (6); affects line shapes and magnitudes of the computed response.
  • Dielectric parameters for the BSE kernel = not stated in main text
    The Coulomb kernel K_tau in Eq. (5) requires dielectric screening inputs that are not given in the main text.
assumptions (5)
  • domain assumption The magnetic substrate induces staggered exchange fields with MA not equal to MB and a nonzero in-plane component on the SbH monolayer.
    Introduced in Eq. (2) and Fig. 1; if the exchange were uniform, the sublattice symmetry breaking and the resulting MCPGE would vanish.
  • domain assumption The CPGE injection-current formula of Eq. (4) remains valid when inversion symmetry is broken by magnetic exchange rather than by lattice structure.
    The paper cites Refs. [10,35,42] for this formula but does not derive its magnetic generalization.
  • domain assumption Only the lower conduction band and higher valence band contribute to the photocurrent at the chosen photon energy.
    Stated just before Eq. (4); the absorption calculation later uses a four-band model, so the photocurrent calculation is knowingly reduced.
  • domain assumption Valley-contrast circular dichroism survives the in-plane exchange field, with K coupled to sigma+ and -K to sigma-.
    Used to argue that a single helicity excites one valley, so the opposite valley currents do not cancel.
  • domain assumption The SbH monolayer remains structurally centrosymmetric when placed on the magnetic substrate.
    Required for the 'symmetric material' framing of the abstract; the model includes only electronic symmetry breaking.

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Pith. "Pith review of Magnetically induced Circular Photogalvanic Effect in Symmetric Two-dimensional Materials." pith.science (2026). https://pith.science/paper/JLHFIRBZ

@misc{pith2026260809309,
  author       = {Pith},
  title        = {Pith review of: Magnetically induced Circular Photogalvanic Effect in Symmetric Two-dimensional Materials},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JLHFIRBZ}},
  note         = {Machine review of arXiv:2608.09309}
}
read the original abstract

Photocurrents that depend on the helicity of the incident light can be generated in both bulk and low-dimensional materials lacking inversion symmetry, known as the circular photogalvanic effect (CPGE). We propose that by employing a magnetic effect, the limitation on the inversion symmetry broken materials can be overcome, such that helicity-dependent photocurrent can be generated in a symmetric material, i.e., a magneto-circular photogalvanic effect (MCPGE). As a proof of principle, we elucidate the mechanism of such an MCPGE through an effective Hamiltonian of a monolayer SbH on a magnetic substrate with an adjustable magnetization. Moreover, the associated response in optical absorption is analyzed, both single-particle and excitonic, through a Bethe-Salpeter equation to describe the Coulomb interaction in excitons. Our result broadens the mechanism of CPGE and opens new opportunities for optoelectronic devices.

Figures

Figures reproduced from arXiv: 2608.09309 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic of an atomic ML on a magnetic sub [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a)-(d) Isoenergy contours showing shifts of conduction (solid) and valence bands (dashed) at the [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) Evolution of band-edge energies with [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Absorption spectra of a ML SbH with magnetization [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

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