Excited quantum Hall effect: enantiomorphic flat bands in a Yin-Yang Kagome lattice

Feng Liu; Gurjyot Sethi; Hang Liu; Yinong Zhou; Zhengfei Wang

REVIEW 3 major objections 4 minor 55 references

Excited quantum Hall effect: enantiomorphic flat bands in a Yin-Yang Kagome lattice

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper predicts that circularly polarized light photoexciting two enantiomorphic flat bands of opposite Chern numbers in a Yin-Yang Kagome lattice produces a transient quantized Hall conductivity $\sigma_{xy} = -2e^2/h$ without any…

desk verdict An interesting photoexcited-Hall proposal whose central quantized conductivity claim is asserted from a filled-LL analogy rather than derived from any non-equilibrium calculation. read the letter →

arxiv 1908.03689 v2 pith:LGD66MSN submitted 2019-08-10 cond-mat.mtrl-sci cond-mat.mes-hallquant-ph

Yinong Zhou , Gurjyot Sethi , Hang Liu , Zhengfei Wang , Feng Liu This is my paper · ORCID

classification cond-mat.mtrl-scicond-mat.mes-hallquant-ph

keywords excited-statequantumHalleffectflatbandsKagomelatticeChernnumbercircularlypolarizedlighttime-reversalsymmetryBerrycurvaturetopologicalinsulator

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 proposes an excited-state quantum Hall effect (EQHE) that needs no static magnetization: circularly polarized light lifts an electron out of one flat band into a partner flat band of opposite Chern number, and the resulting electron-hole pair behaves like two filled Landau levels. In the Yin-Yang Kagome lattice model, the two flat bands are enantiomorphic—their Berry curvatures are mirror images with Chern numbers of opposite sign—and they are gapped from the rest of the spectrum. The paper argues that photoexcitation breaks time-reversal symmetry on the spot, yielding a quantized Hall conductivity $\sigma_{xy} = -2e^2/h$ whose sign is set by the handedness of the light. If correct, this gives an optical switch for chiral edge currents, replacing the magnetic field or magnetization used in ordinary quantum Hall systems.

What carries the argument

The Yin-Yang Kagome lattice: a Kagome lattice with a two-atom dumbbell at every site, whose hopping parameters (intra-dumbbell $t_1$ and cross-dumbbell $t_3$) produce two sets of Kagome bands with opposite hopping signs. This yields two flat bands whose real-space wavefunctions are localized on a hexagonal plaquette with alternating phases, so destructive interference forbids hopping out of the plaquette. With spin-orbit coupling, the two flat bands acquire opposite Berry curvature distributions and opposite Chern numbers; the flatness and whole-Brillouin-zone Berry curvature make the inter-band photoabsorption strong and delta-function-like, enabling chirality-selective excitation.

What would settle it

Measure the Hall conductivity of a photoexcited Yin-Yang Kagome sample, such as bilayer nickel-bis(dithiolene), under a short circularly polarized pulse: if the transverse current is not quantized at $-2e^2/h$ during the excitation, or if it depends on disorder and relaxation rate, the assumed equivalence to filled Landau levels is wrong.

Watch

Extended reading notes

Core claim

The central claim is that a non-equilibrium, photoexcited state of a time-reversal-symmetric insulator can carry a quantized chiral Hall response. The setting is a Kagome lattice with two atoms per site, a 'dumbbell' basis, whose band structure contains two sets of Kagome bands with opposite signs of effective hopping. Under spin-orbit coupling, each flat band acquires a Chern number, and the two flat bands have opposite Chern numbers in each spin channel, forming an enantiomorphic pair. Because these flat bands are optically active across the entire Brillouin zone, right- and left-handed circularly polarized light selectively excite opposite spin channels, creating an electron in the upper flat band and a hole in the lower one. The authors argue that this electron-hole pair acts like two filled Landau levels, so the Hall conductivity is quantized to $\sigma_{xy} = -2e^2/h$, with the sign following the light handedness rather than a magnetization direction.

Load-bearing premise

The load-bearing premise is that the photoexcited electron-hole pair in the two flat bands behaves exactly like two filled Landau levels, so that the Hall conductivity is the sum of their Chern numbers; the paper assumes this mapping rather than deriving a non-equilibrium transport response.

Editorial extensions

If this is right

A single light pulse, with no external magnetic field or magnetic dopants, would create a chiral edge current in a two-dimensional insulator, and flipping the light handedness would reverse the current.
The photocurrent is predicted to be quantized at $\sigma_{xy} = -2e^2/h$ as long as the electron-hole pair resides in the flat bands, giving a robust transport signal largely independent of band details.
The mechanism extends Hall physics from ground states to excited states, and the flat-band photoabsorption is much stronger than valley Hall because it involves the whole Brillouin zone rather than isolated valleys.
The paper identifies concrete candidate realizations: bilayer Kagome lattices such as nickel-bis(dithiolene) and sp2-bonded hexagonal molecular lattices built from triangular graphene flakes, whose band structures already show the enantiomorphic flat bands.

Reading between the lines

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

If the quantized response survives relaxation, a time-resolved Hall measurement under a short circularly polarized pulse should show a prompt Hall voltage that persists only for the excited-state lifetime; that would directly test the paper's mechanism.
The enantiomorphic flat-band pair could be recreated in photonic, cold-atom, or phononic lattices, where the same two-band, opposite-Chern-number structure might yield an optical-control Hall analogue without electronic spin.
With interactions, the flat bands would amplify correlation effects, so photoexcited states may host fractional-like or excitonic Hall responses; the paper leaves that territory unexplored.
A non-equilibrium transport calculation that includes disorder and relaxation is the missing quantitative check: if the Hall conductance is not exactly $-2e^2/h$ in that calculation, the paper's mapping from Chern numbers to an excited-state response would need revision.

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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 reader and the stress-test note land on the same spot, and I think they are right. The paper has a clear, explicit tight-binding model with analytic wavefunctions, Berry curvature plots, and consistent ground-state spin Hall plateaus. It also honestly acknowledges that the Yin-Yang Kagome lattice is the same as the previously studied hexagonal star lattice, so the structural novelty is modest. The genuinely new idea—using circularly polarized light to excite between two opposite-Chern flat bands and claiming a quantized, switchable Hall response—is worth taking seriously as a proposal.

But the central quantitative claim, sigma_xy = -2 e^2/h, is not supported by the presented calculation. The paper says the enantiomorphic flat bands "behave like" two filled Landau levels, and that is the whole argument. In a real photoexcited state you do not get two filled bands. A single photon or even a weak pump creates an electron in the upper band and a hole in the lower band with occupation per k of order 1/N, not 1. For a clean noninteracting system, the Hall conductance of a partially occupied band is the occupation-weighted integral of the Berry curvature, which gives -(e^2/h)(C_upper - C_lower)/N, i.e., it vanishes in the thermodynamic limit. To get the claimed quantization you would need complete population inversion of both flat bands—one electron per unit cell promoted—and no relaxation. The paper never specifies pump intensity, steady-state occupation, dephasing, or provides any Kubo, Floquet, or edge-transport calculation. The k-independence of the optical matrix element does not fix this; it just delocalizes the pair in k-space without changing the occupation per k.

The photo-absorption spectrum being delta-function-like is also not enough. That peak is a joint density-of-states feature, not a Hall response. The Berry curvature distribution being uniform in the BZ is necessary for a quantized response only if the band is fully occupied, which is exactly the assumption at issue.

I want to stress that the paper is not incoherent or dishonest. The band-structure and ground-state calculations are fine, and the authors were upfront about the lattice equivalence. The problem is that the headline effect is a hypothesis, not a result. The paper is for people working on topological flat bands, valleytronics, and non-equilibrium Hall effects; they will find the setup thought-provoking, but the conclusion should be read with caution.

A serious referee could usefully push the authors to either derivate the excited-state Hall response properly—say, with a Floquet or time-dependent transport calculation—or reframe the paper as a proposal and specify the conditions under which quantization might hold. I would not desk-reject it; the idea is interesting enough to merit referee time, but it should not be accepted in its current form.

Referee Report

3 major / 4 minor

Summary. Zhou et al. propose an 'excited-state quantum Hall effect' (EQHE) in a two-sub-lattice Kagome model ('Yin-Yang Kagome lattice') that hosts two enantiomorphic flat bands of opposite Chern numbers in each spin channel. Circularly polarized light is argued to selectively excite one spin channel, creating a non-equilibrium state whose Hall conductivity is quantized as σ_xy = -2 e^2/h, with the sign controlled by light handedness. The paper derives the tight-binding band structure, real-space wavefunctions, Berry curvatures, ground-state spin Hall conductivities, and interband absorption, and it discusses candidate material realizations in bilayer Kagome and sp2 hexagonal lattices.

Significance. The proposal is conceptually interesting: if the quantized response holds, it would provide an optically switchable topological charge Hall effect without intrinsic magnetization, distinct from the valley Hall effect. The explicit lattice model with analytic wavefunctions and the internally consistent ground-state Chern and spin-Hall calculations are strengths. However, the central quantitative claim—the quantization of the photoexcited Hall conductivity—is not established by the presented calculation; it rests on an analogy to filled Landau levels that requires a fully inverted band, a condition neither stated nor justified. The paper's model and ground-state topology are useful contributions, but the excited-state response needs a proper derivation.

major comments (3)

[Paragraph beginning 'Effectively the enantiomorphic FBs behave like...' and Fig. 1(d)] The central claim of a quantized Hall conductivity σ_xy = -2 e^2/h is asserted without derivation. In a noninteracting band, a completely occupied band of Chern number C contributes C e^2/h, but a partially occupied band contributes (e^2/h) ∫ d²k/(2π) f(k) Ω(k). For a single photoexcited electron-hole pair in a finite system of N unit cells, the occupation difference is O(1/N), giving a contribution of order e^2/(hN), not -2 e^2/h. The quantization requires a full spin-selective inversion (one promoted electron per unit cell), which is not stated or derived. The authors should specify the pump intensity/pulse area needed to achieve such an inversion and provide a Kubo or time-dependent transport calculation for the resulting excited Slater determinant.
[Paragraph beginning 'Consequently, the CPL photoexcitation breaks instantaneously the TRS...' and Fig. 3(d)] The paper assumes that the photoexcited electron-hole state retains the equilibrium Hall quantization without performing a non-equilibrium transport calculation. The delta-function-like absorption peak and k-independent optical matrix element only show that transitions occur at all k-points; they do not determine the steady-state occupation of the upper band or the Hall response under continuous illumination. The authors should clarify whether EQHE is a transient response after a coherent π-pulse or a steady-state effect under cw pumping, and justify quantization in the chosen regime, including the roles of relaxation and dephasing.
[Fig. 1(d) and abstract] The phrase 'an electron and a hole occupying two LLs' suggests a single electron-hole pair, but a single pair does not yield a quantized Hall conductivity. If the intended scenario is a coherent full inversion of one spin channel (one electron-hole pair per unit cell), the manuscript should state this explicitly and reconcile the language throughout; if not, the numerical claim of σ_xy = -2 e^2/h is incorrect as stated. This ambiguity is load-bearing for the main conclusion.

minor comments (4)

[Fig. 2(b) caption] The caption reads 'obtained with t1, t2 = 0, t3 = 0.3t1', which is ambiguous; presumably t2 = 0 and t1 is the energy unit. Please rephrase.
[Reference [13]] Reference [13] contains an apparent OCR artifact 'Tworzyd/suppress lo' and should be corrected to 'Tworzydło'.
[Fig. 4(a) text] The text 'exhibiting Ying-Yang Kagome band' uses 'Ying-Yang' inconsistently with 'Yin-Yang' used elsewhere in the paper.
[Abstract] The phrase 'each supporting originally a helical topological insulating state' is imprecise: the helical topological insulator is a property of the gapped ground state, not of a single flat band.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found: the band structure and Chern numbers are derived from an explicit tight-binding Hamiltonian, and the claimed Hall response is an extrapolation of standard band topology rather than a restatement of the input.

full rationale

The central derivation chain starts from an explicit tight-binding Hamiltonian (Eq. 1) with specified hoppings t1, t2, t3 and spin-orbit coupling lambda; the Yin-Yang flat bands, their wavefunctions, bandwidths, gaps, and Chern numbers are all computed from that Hamiltonian rather than assumed. The self-citations present (refs. 21, 46, 47) are used for a spin-Hall-conductivity calculation and for possible artificial-lattice realizations, and neither is load-bearing for the EQHE claim. The step from opposite Chern numbers to sigma_xy = -2 e^2/h is an application of the standard TKNN/Chern-number relation; whether that relation remains valid for a photoexcited, partially occupied flat-band state is a physical validity question for which no Kubo or non-equilibrium transport calculation is given, but this is a derivation gap, not circularity, because the conclusion is not identical to the input by definition and no fitted parameter is relabeled as a prediction.

Assumptions & free parameters 3 free parameters · 3 assumptions · 1 invented entities

The central model is built from three hand-chosen hopping and SOC ratios and depends on two unproven domain assumptions: uniform chirality-selective optical coupling across the whole Brillouin zone, and persistence of quantized Hall response in a non-equilibrium photoexcited state. No new particles, forces, or conserved quantities are introduced.

free parameters (3)

t3/t1 ratio = 0.3
Chosen in Fig. 2(b) to produce the two enantiomorphic flat bands; the central model sets t2=0 and t3=0.3t1.
t2/t1 ratio = 0
Set to zero in the main model; the authors state it does not affect the band structure qualitatively over a wide parameter range.
SOC strength lambda/t1 = 0.0375
Used in Fig. 3(a) to open the four topological gaps; the EQHE discussion is presented at this value.

assumptions (3)

domain assumption A non-interacting tight-binding Hamiltonian with spin-conserving SOC captures the relevant physics of the proposed lattice.
Interactions, disorder, phonons, and exciton effects are omitted; some of the listed implications, such as flat-band ferromagnetism and fractional QHE, would require interactions.
ad hoc to paper A circularly polarized photon can excite an electron between the two flat bands across the entire Brillouin zone with a delta-function-like peak.
The paper assumes uniform optical activity from localized flat-band wavefunctions but does not show explicit light-matter matrix elements or a many-body excitation calculation.
ad hoc to paper The non-equilibrium photoexcited electron-hole state retains the equilibrium Chern-number Hall quantization.
The claim sigma_xy = -2 e^2/h rests on this assumption; no Kubo, Floquet, or time-dependent transport calculation is provided, and clean partially filled bands do not automatically exhibit quantized Hall conductance.

invented entities (1)

Yin-Yang Kagome lattice model
purpose: Provides two enantiomorphic flat bands with opposite hopping signs and opposite Chern numbers for the proposed EQHE.
The model is admitted to be a re-labeling of the known hexagonal star lattice, and no experimental realization is shown; the DFT candidate materials are suggestive but not independently confirmed.

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Cite this review

Pith. "Pith review of Excited quantum Hall effect: enantiomorphic flat bands in a Yin-Yang Kagome lattice." pith.science (2026). https://pith.science/paper/LGD66MSN

@misc{pith2026190803689,
  author       = {Pith},
  title        = {Pith review of: Excited quantum Hall effect: enantiomorphic flat bands in a Yin-Yang Kagome lattice},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LGD66MSN}},
  note         = {Machine review of arXiv:1908.03689}
}

read the original abstract

Quantum Hall effect (QHE) is one of the most fruitful research topics in condensed-matter physics. Ordinarily, the QHE manifests in a ground state with time-reversal symmetry broken by magnetization to carry a quantized chiral edge conductivity around a two-dimensional insulating bulk. We propose a theoretical concept and model of non-equilibrium excited-state QHE (EQHE) without intrinsic magnetization. It arises from circularly polarized photoexcitation between two enantiomorphic flat bands of opposite chirality, each supporting originally a helical topological insulating state hosted in a Yin-Yang Kagome lattice. The chirality of its edge state can be reversed by the handedness of light, instead of the direction of magnetization as in the conventional quantum (anomalous) Hall effect, offering a simple switching mechanism for quantum devices. Implications and realization of EQHE in real materials are discussed.

Figures

Figures reproduced from arXiv: 1908.03689 by the authors.

**Figure 2.** FIG. 2. Creation of the enantiomorphic FBs in a Yin-Yang [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 4.** FIG. 4. (a,b) An AA stacking bilayer Kagome lattice (left) [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

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Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

(b) The quantized spin Hall conductivity ( σ s xy) within the energy window of the SOC gaps

0375t1). (b) The quantized spin Hall conductivity ( σ s xy) within the energy window of the SOC gaps. (c) Plots of Berry curvatures (Ωz) in the ﬁrst BZ for the two FBs in (a), which are the mirror image of each other due to the opposite Chern number. (d) The inter-FB photo-absorption spectrum of the right-handed CPL (σ +) for the spin-down channel. The sa...

work page

[2] [2]

K. v. Klitzing, G. Dorda, and M. Pepper, Physical Re- view Letters 45, 494 (1980)

work page 1980

[3] [3]

D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Physical review letters 49, 405 (1982)

1982

[4] [4]

R. B. Laughlin, Physical Review Letters 50, 1395 (1983)

1983

[5] [5]

F. D. M. Haldane, Physical Review Letters 50, 1153 (1983)

1983

[6] [6]

F. D. M. Haldane, Physical review letters 61, 2015 (1988)

1988

[7] [7]

C. L. Kane and E. J. Mele, Physical review letters 95, 226801 (2005)

work page 2005

[8] [8]

B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Science 314, 1757 (2006)

2006