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REVIEW 4 major objections 4 minor 46 references

Second-Order Conductivity Probes a Cascade of Singularities in a Moir\'e Superlattice

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read In twisted double bilayer graphene, the second-order nonlinear conductivity changes sign at every mid-band van Hove singularity while time-reversal symmetry is intact, reaching about 70 μm V−1 Ω−1, roughly ten times earlier extrinsic…

desk verdict A systematic experimental map of giant second-order conductivity in tDBLG, with a plausible but not fully anchored claim that NLER sign changes track Hall-identified van Hove singularities. read the letter →

arxiv 2507.05969 v1 pith:UGULA6TG submitted 2025-07-08 cond-mat.mes-hall

Tanweer Ahmed , Bao Q. Tu , Kenji Watanabe , Takashi Taniguchi , Marco Gobbi , Fèlix Casanova , Luis E. Hueso This is my paper · ORCID
classification cond-mat.mes-hall
keywords twisteddoublebilayergraphenevanHovesingularitiessecond-orderconductivitynonlinearelectricalresponseLifshitztransitionmoirésuperlatticeextrinsicscatteringHalleffect
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 sets out to show that the second-order nonlinear electrical response (NLER) of a moiré superlattice can locate van Hove singularities, band-structure points where the density of states diverges, without applying a magnetic field. In twisted double bilayer graphene, made by stacking two bilayer graphene crystals with a small relative twist, the authors tune the Fermi level through several superlattice bands on both sides of charge neutrality and observe that the second-order longitudinal and transverse voltages change sign close to every mid-band van Hove singularity, at non-integer fillings $n/n_s$, as well as at integer band fillings. Near the singularity in the second superlattice band the second-order conductivity reaches roughly 70 $\mu$m V$^{-1}$ Ω$^{-1}$, an order of magnitude larger than previously reported extrinsic nonlinear responses. Temperature-dependent scaling identifies disorder-mediated side-jump and skew scattering as the mechanisms, and the paper concludes that second-order conductivity is a zero-field probe of Fermi-surface reconstructions.

What carries the argument

The central object is the second-order conductivity tensor $\sigma^{2\omega}$, extracted from the second-harmonic voltages $V_{xx}^{2\omega}$ and $V_{xy}^{2\omega}$ using the channel geometry and first-order conductivity. The twist of the two bilayer graphene crystals breaks inversion symmetry and allows a nonlinear response with no magnetic field; the disorder-mediated side-jump and skew-scattering channels produce longitudinal and transverse components of comparable size. Sign changes in $\sigma^{2\omega}$ arise because the nonlinear response depends on derivatives of the Fermi distribution, which flip when the Fermi surface topology changes at a van Hove singularity. The paper identifies the mechanisms by fitting the generalized scaling law $R_s^2 V_{xy(x)}^{2\omega}/(V_{xx}^{\omega})^2 = \mathcal{C}_1 R_0^2 + \mathcal{C}_2 R_0 R_T + \mathcal{C}_3 R_T^2$, whose coefficients encode intrinsic, side-jump, and skew-scattering contributions.

What would settle it

Measure the density of states of the same tDBLG device with an independent probe, such as quantum capacitance or Shubnikov–de Haas oscillations, and check whether every NLER sign reversal at non-integer $n/n_s$ coincides with a van Hove singularity. The central claim is falsified if the nonlinear sign changes track the Hall sign changes but not the independently located singularities.

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Extended reading notes

Core claim

On its own terms, the discovery is that time-reversal-symmetric second-order conductivity is a sensitive probe of van Hove singularities in a moiré band structure. The experimental signature is a sign reversal and a local extremum of $\sigma^{2\omega}$ at values of $n/n_s$ that do not correspond to integer band fillings, together with additional sign changes at the integer fillings themselves. These non-integer positions coincide with sign reversals of the low-field Hall voltage measured at $B = 500$ mT, which the authors interpret as Lifshitz transitions where the Fermi surface changes topology. The effect appears across the whole cascade of mid-band singularities, and its magnitude reaches $|\sigma^{2\omega}_{yxx}| \approx 70$ μm V$^{-1}$ Ω$^{-1}$ near the second valence band, about ten times larger than earlier extrinsic nonlinear responses. The paper therefore claims that NLER can serve as a structural probe of Fermi-surface reconstructions and that tDBLG is a highly efficient nonlinear electrical platform.

Load-bearing premise

The crucial assumption is that the sign reversals of the low-field Hall voltage at non-integer $n/n_s$ are van Hove singularities rather than artifacts of disorder, density inhomogeneity, or correlated states; if that assignment is wrong, the matching NLER sign changes do not prove the paper's central claim.

Editorial extensions

If this is right

  • If the central claim is right, van Hove singularities in moiré superlattices can be mapped from transport alone, without the magnetic field that the Hall method requires.
  • The near-equality of longitudinal and transverse second-order conductivities becomes a practical discriminator: comparable magnitudes indicate extrinsic mechanisms, while a purely transverse signal would point to a Berry-curvature-dipole origin.
  • The seventy-micron-ampere-per-volt-per-ohm figure implies that tDBLG tuned near a second-band van Hove singularity can act as a highly efficient rectifier at low temperature.
  • Because the sign-change loci track the displacement field $D$, the nonlinear response can chart how the band structure evolves when the superlattice is tuned.

Reading between the lines

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

  • My inference: the same zero-field protocol should generalize to any inversion-broken moiré stack with tunable mid-band van Hove singularities, such as twisted bilayer graphene or twisted transition-metal dichalcogenides, although the paper only demonstrates tDBLG.
  • My inference: because the nonlinearity is extrinsic, the absolute value of $\sigma^{2\omega}$ near a van Hove singularity will likely depend on impurity density and mobility, so the tenfold benchmark may need sample normalization before it becomes a material property.
  • My inference: an independent check would couple nonlinear transport with quantum capacitance or compressibility measurements on the same device; if the NLER sign reversals coincide with density-of-states peaks, the Hall-based vHS assignment would be confirmed rather than assumed.
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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 / 4 minor

Summary. This manuscript reports simultaneous first- and second-harmonic transport measurements in a twisted double bilayer graphene (tDBLG) device, with carrier density and displacement field tuned across several moiré bands. The central claim is that the second-order longitudinal and transverse conductivities (extrinsic NLER) change sign near mid-band van Hove singularities identified from Hall voltage sign reversals at non-integer n/n_s, and that the second-order conductivity reaches approximately 70 μmV^-1Ω^-1, an order of magnitude larger than previously reported extrinsic NLER values. The authors infer extrinsic side-jump and skew-scattering contributions from temperature-dependent scaling using Eq. (1).

Significance. If the central claim holds, the paper would establish second-order conductivity as a zero-field transport probe of Fermi-surface reconstructions and identify tDBLG as a highly efficient nonlinear electrical platform. The experimental protocol is careful in several respects: the quadratic current scaling (Fig. 2a,b), the probe-polarity reversal test (Fig. 2c,d), the temperature-dependent scaling analysis (Fig. 5), and the inclusion of a second device at a different twist angle (SI) together support an extrinsic electronic second-order signal rather than a thermal artifact. However, the vHS assignment relies entirely on Hall sign reversals at a single magnetic-field value, without independent verification; the twist-angle ambiguity between the abstract and the extracted value, and the absence of error bars on the headline conductivity, are significant gaps. The paper is a solid experimental contribution, but the load-bearing identification of vHSs needs to be strengthened or the claims need to be tempered before the central conclusion can be accepted.

major comments (4)
  1. [Fig. 1f,g and Fig. 3c,d] The non-integer vHS positions are identified exclusively by sign reversals of V_H^ω at B = 500 mT, and the matching NLER sign changes are then presented as evidence for the vHS sensitivity. No independent verification of a vHS at each brown-arrow density is provided for sample A (no band-structure calculation, compressibility measurement, or quantum-oscillation map), and sample B at θ ≈ 1.44° does not validate the specific vHS sequence of sample A. Because single-field Hall sign reversals can also arise from density-dependent mobility contrasts, coexisting electron and hole pockets, or correlated states in multi-band tDBLG, the NLER-vHS correlation is not independently anchored. Please add a continuum-model calculation for the extracted twist angle, an independent density-of-states probe, or explicitly weaken the central claim to a correlation between two first-order transport signatures.
  2. [Abstract and Fig. 1d] The abstract states θ ≈ 0.7°, while the superlattice density n_s extracted from integer fillings gives θ ≈ 0.92°. Since predicted vHS fillings in tDBLG are strongly twist-angle dependent, this discrepancy is not a cosmetic detail: the paper never states which angle is used when comparing the observed non-integer sign reversals to any model. The authors should reconcile the two values or explain why the ambiguity does not affect the vHS identification.
  3. [Fig. 4c] The headline value |σ_yxx^2ω| ≈ 70 μmV^-1Ω^-1 near n/n_s ≈ -1.7 is reported without an uncertainty estimate and is taken from a single device. The extraction formula in Fig. 4 depends on sample geometry and first-order conductivity, so propagation of errors and a check on a second device with the same twist angle are needed before claiming a factor-of-ten enhancement over previous reports. At minimum, the authors should provide error bars and explicitly state the number of devices and contacts used for the quoted value.
  4. [Fig. 5 and Eq. (1)] The conclusion that the NLER is dominated by a combination of side-jump and skew scattering rests on fits of Eq. (1) with three free parameters at only two densities (n/n_s ≈ 0.7 and 1.9). While the temperature scaling is consistent with an extrinsic mechanism, the fitted coefficients alone cannot confirm the vHS identification; this part of the analysis should be presented as supportive evidence for the mechanism rather than as a proof of the vHS assignment.
minor comments (4)
  1. [Conclusion] The word 'exibiting' in the concluding paragraph should be corrected to 'exhibiting'.
  2. [Fig. 2] The notation V_xx(y)^2ω and V_xy(x)^2ω is confusing; please define a single notation for longitudinal and transverse second-harmonic voltages and use it consistently in the text and captions.
  3. [Reference [43]] Reference [43] is incomplete: it provides only the journal and article number without authors or a full title, and should be formatted consistently with the other references.
  4. [Fig. 3a,b] The claim that the locus of non-integer NLER sign changes 'closely match' the Hall sign reversals is made visually; a quantitative table or overlay of the extracted densities from V_H^ω and V_xx,yy^2ω would make the correspondence reproducible.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the NLER-vHS correlation is an empirical comparison of two independently measured observables.

full rationale

The paper's central claim is an experimental correlation, not a derivation that reduces to its own inputs. Van Hove singularities are identified from sign reversals of the Hall voltage at non-integer fillings, following external works [14,15], while the nonlinear response is measured separately as V_xx^2omega and V_xy^2omega under time-reversal-symmetric conditions. The paper then compares the loci of the two sets of sign changes and finds that they coincide. There is no equation or fitting procedure that constructs the NLER behavior from the Hall-derived vHS positions; the scaling-law fit in Eq. (1) extracts scattering-mechanism parameters and is not used to locate vHSs or to produce the reported conductivity magnitude. The self-citation [26] appears in a general list of NLER references alongside many independent external works [27-34], so it is not load-bearing. Concerns that the Hall sign reversals might not uniquely prove the existence of vHSs are external validation or interpretation questions, not circularity. The derivation chain is therefore self-contained with respect to the paper's empirical claims.

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

The central claim rests on the Hall-based identification of vHSs, the scaling law used for mechanism attribution, and the assumption of a uniform twist angle. The only fitted quantities are the scaling coefficients C1-C3, which support the mechanism discussion but not the main vHS detection claim.

free parameters (1)
  • Scaling coefficients C1, C2, C3 = Multiple values across fits, e.g. C1 around -9e-5 to 3e-4 V^-1, C2 around 2e-4 to -9e-3 V^-1, C3 around -2e-4 to 6e-2…
    Coefficients in Eq. (1) fitted to temperature-dependent R_s and V^2omega data at fixed densities. They are used to infer the relative contribution of intrinsic BCD, side-jump, and skew scattering, but they are not used to locate vHSs.
assumptions (4)
  • domain assumption Hall voltage sign reversals at non-integer n/n_s identify van Hove singularities and Lifshitz transitions.
    Used in Fig. 1f-g and when comparing V_H^omega with V^2omega. The interpretation follows prior literature (refs. 14, 15, 45) and is not independently validated within this paper.
  • domain assumption The nonlinear response follows the generalized scaling law Eq. (1) with R0 = R_s(T=0) and RT = R_s(T)-R0, with contributions from intrinsic BCD, side-jump, and skew scattering.
    Invoked in Fig. 5 to infer the dominant mechanism. The paper fits this form but does not test alternative scaling models or report goodness-of-fit metrics.
  • domain assumption Probe configuration reversals rule out thermal effects, so the measured V^2omega is an electronic nonlinearity.
    The argument in Fig. 2c-d assumes that switching current and voltage probes eliminates all thermal and thermoelectric artifacts, which is a standard but non-exhaustive check.
  • domain assumption The moire filling n_s = 4/A with A = sqrt(3)a^2/(2 theta^2) gives integer band fillings and theta = 0.92 degrees from the observed resistance maxima.
    Used to convert densities to band fillings and to infer the twist angle. It assumes a rigid, uniform twist angle without significant lattice relaxation or twist-angle disorder.

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Cite this review

Pith. "Pith review of Second-Order Conductivity Probes a Cascade of Singularities in a Moir\'e Superlattice." pith.science (2026). https://pith.science/paper/UGULA6TG

@misc{pith2026250705969,
  author       = {Pith},
  title        = {Pith review of: Second-Order Conductivity Probes a Cascade of Singularities in a Moir\'e Superlattice},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UGULA6TG}},
  note         = {Machine review of arXiv:2507.05969}
}
read the original abstract

Systems lacking inversion symmetry inherently demonstrate a nonlinear electrical response (NLER) to an applied electric bias, emerging through extrinsic mechanisms. This response is highly sensitive to the electronic band structure, which can be engineered with remarkable precision in moir\'e superlattices formed from atomically thin quantum materials. Moir\'e superlattices host complex Fermi surface reconstructions near van Hove singularities (vHSs) in the electronic density of states. However, the role of these reconstructions in shaping NLER remains insufficiently understood. In this work, we systematically explore NLER in moir\'e superlattices of twisted double bilayer graphene (tDBLG) by tuning the Fermi level across multiple moir\'e bands on both sides of the charge neutrality point. We observe sharp variations and sign reversals in the NLER appearing via extrinsic pathways near mid-band vHSs. The second-order conductivity close to the vHSs demonstrates a much higher value than previous reports of extrinsic NLER in any other material. Our results demonstrate that NLER can serve as a sensitive probe of Fermi surface reconstructions and establish tDBLG as a versatile and highly efficient platform for generating and controlling the nonlinear electrical response.

Figures

Figures reproduced from arXiv: 2507.05969 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: a(b) showsthe second-order longitudinal (transverse) conductivity extracted as 𝜎𝑥𝑥𝑥 2𝜔 (𝜎𝑦𝑥𝑥 2𝜔 ) = 𝜎 𝑉𝑥𝑥 2𝜔𝐿/𝑉𝑥𝑥 𝜔2 (𝜎 𝑉𝑥𝑦 2𝜔𝐿/𝑉𝑥𝑥 𝜔2 × 𝐿 2 /𝑊) [27] as a function of 𝑛 and 𝐷. Here L, W and σ are the length, and width of the channel and first order conductivity, respec…
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

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Works this paper leans on

46 extracted references · 40 canonical work pages

  1. [1]

    I. M. Lifshitz, Anomalies of electron characteristics of a metal in the high pressure region, Sov. Phys. JEPT 11, 1130 (1960)

    work page 1960

  2. [2]

    Van Hove, The Occurrence of Singularities in the Elastic Frequency Distribution of a Crystal, Phys

    L. Van Hove, The Occurrence of Singularities in the Elastic Frequency Distribution of a Crystal, Phys. Rev. 89, 1189 (1953)

    work page 1953

  3. [3]

    Bastien, A

    G. Bastien, A. Gourgout, D. Aoki, A. Pourret, I. Sheikin, G. Seyfarth, J. Flouquet, and G. Knebel, Lifshitz Transitions in the Ferromagnetic Superconductor UCoGe, Phys. Rev. Lett. 117, 206401 (2016)

    work page 2016

  4. [4]

    Shi et al., Enhanced superconductivity accompanying a Lifshitz transition in electron-doped FeSe monolayer, Nat

    X. Shi et al., Enhanced superconductivity accompanying a Lifshitz transition in electron-doped FeSe monolayer, Nat. Commun. 8, 14988 (2017)

    work page 2017

  5. [5]

    Liu et al., Evidence for a Lifshitz transition in electron-doped iron arsenic superconductors at the onset of superconductivity, Nat

    C. Liu et al., Evidence for a Lifshitz transition in electron-doped iron arsenic superconductors at the onset of superconductivity, Nat. Phys. 6, 419 (2010)

    work page 2010

  6. [6]

    H. Zhou, L. Holleis, Y . Saito, L. Cohen, W. Huynh, C. L. Patterson, F . Yang, T. Taniguchi, K. Watanabe, and A. F . Young, Isospin magnetism and spin-polarized superconductivity in Bernal bilayer graphene, Science 375, 774 (2022)

    work page 2022

  7. [7]

    A. K. Geim and K. S. Novoselov, The rise of graphene, Nat. Mater. 6, 183 (2007)

    2007

  8. [8]

    A. H. Castro Neto, F . Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Rev. Mod. Phys. 81, 109 (2009)

    work page 2009

Show all 46 references
  1. [9]

    McCann and M

    E. McCann and M. Koshino, The electronic properties of bilayer graphene, Rep. Prog. Phys. 76, 056503 (2013)

    2013

  2. [10]

    Varlet, D

    A. Varlet, D. Bischoff, P . Simonet, K. Watanabe, T. Taniguchi, T. Ihn, K. Ensslin, M. Mucha-Kruczyński, and V . I. Fal’ko, Anomalous Sequence of Quantum Hall Liquids Revealing a Tunable Lifshitz Transition in Bilayer Graphene, Phys. Rev. Lett. 113, 116602 (2014)

    2014

  3. [11]

    A. M. Seiler, N. Jacobsen, M. Statz, N. Fernandez, F . Falorsi, K. Watanabe, T. Taniguchi, Z. Dong, L. S. Levitov, and R. T. Weitz, Probing the tunable multi-cone band structure in Bernal bilayer graphene, Nat. Commun. 15, 3133 (2024)

    2024

  4. [12]

    Brihuega, P

    I. Brihuega, P . Mallet, H. González-Herrero, G. Trambly de Laissardière, M. M. Ugeda, L. Magaud, J. M. Gómez- Rodríguez, F . Ynduráin, and J.-Y . Veuillen, Unraveling the Intrinsic and Robust Nature of van Hove Singularities in Twisted Bilayer Graphene by Scanning Tunneling M...

    2012

  5. [13]

    G. Li, A. Luican, J. M. B. Lopes dos Santos, A. H. Castro Neto, A. Reina, J. Kong, and E. Y . Andrei, Observation of Van Hove singularities in twisted graphene layers, Nat. Phys. 6, 109 (2010)

    2010

  6. [14]

    S. Wu, Z. Zhang, K. Watanabe, T. Taniguchi, and E. Y . Andrei, Chern insulators, van Hove singularities and topological flat bands in magic-angle twisted bilayer graphene, Nat. Mater. 20, 488 (2021)

    2021

  7. [15]

    Xu et al., Tunable van Hove singularities and correlated states in twisted monolayer–bilayer graphene, Nat

    S. Xu et al., Tunable van Hove singularities and correlated states in twisted monolayer–bilayer graphene, Nat. Phys. 17, 619 (2021)

    2021

  8. [16]

    Moriya, K

    R. Moriya, K. Kinoshita, J. A. Crosse, K. Watanabe, T. Taniguchi, S. Masubuchi, P . Moon, M. Koshino, and T. Machida, Emergence of orbital angular moment at van Hove singularity in graphene/h-BN moiré superlattice, Nat. Commun. 11, 5380 (2020)

    2020

  9. [17]

    Dutta, A

    R. Dutta, A. Ghosh, S. Mandal, K. Watanabe, T. Taniguchi, H. R. Krishnamurthy, S. Banerjee, M. Jain, and A. Das, Electric Field Tunable Superconductivity with Competing Orders in Twisted Bilayer Graphene near Magic-Angle, arXiv:2402.11649

    arXiv

  10. [18]

    R. Su, M. Kuiri, K. Watanabe, T. Taniguchi, and J. Folk, Superconductivity in twisted double bilayer graphene stabilized by WSe2, Nat. Mater. 22, 1332 (2023)

    2023

  11. [19]

    Knüppel, J

    P . Knüppel, J. Zhu, Y . Xia, Z. Xia, Z. Han, Y . Zeng, K. Watanabe, T. Taniguchi, J. Shan, and K. F . Mak, Correlated States Controlled by Tunable van Hove Singularity in Moiré WSe2, arXiv:2406.03315

    arXiv

  12. [20]

    Liu, J.-B

    Y.-W. Liu, J.-B. Qiao, C. Yan, Y . Zhang, S.-Y . Li, and L. He, Magnetism near half-filling of a Van Hove singularity in twisted graphene bilayer, Phys. Rev. B 99, 201408 (2019)

    2019

  13. [21]

    Sodemann, Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materials, Phys

    I. Sodemann, Quantum Nonlinear Hall Effect Induced by Berry Curvature Dipole in Time-Reversal Invariant Materials, Phys. Rev. Lett. 115, (2015)

    2015

  14. [22]

    Isobe, S.-Y

    H. Isobe, S.-Y . Xu, and L. Fu, High-frequency rectification via chiral Bloch electrons, Sci. Adv. 6, eaay2497 (2020)

    2020

  15. [23]

    Z. Z. Du, H.-Z. Lu, and X. C. Xie, Nonlinear Hall effects, Nat. Rev. Phys. 3, 744 (2021)

    2021

  16. [24]

    Z. Z. Du, C. M. Wang, S. Li, H.-Z. Lu, and X. C. Xie, Disorder-induced nonlinear Hall effect with time- reversal symmetry, Nat. Commun. 10, 3047 (2019)

    2019

  17. [25]

    Ramos et al., Unveiling Intrinsic Bulk Photovoltaic Effect in Atomically Thin ReS2, Nano Lett

    M. Ramos et al., Unveiling Intrinsic Bulk Photovoltaic Effect in Atomically Thin ReS2, Nano Lett. 24, 14728 (2024)

    2024

  18. [26]

    Ahmed, H

    T. Ahmed, H. Varshney, B. Q. Tu, K. Watanabe, T. Taniguchi, M. Gobbi, F . Casanova, A. Agarwal, and L. E. Hueso, Detecting Lifshitz Transitions Using Nonlinear Conductivity in Bilayer Graphene, Small 21, 2501426 (2025)

    2025

  19. [27]

    P . He, G. K. W. Koon, H. Isobe, J. Y . Tan, J. Hu, A. H. C. Neto, L. Fu, and H. Yang, Graphene moiré superlattices with giant quantum nonlinearity of chiral Bloch electrons, Nat. Nanotechnol. 17, 378 (2022)

    2022

  20. [28]

    J. Duan, Y . Jian, Y . Gao, H. Peng, J. Zhong, Q. Feng, J. Mao, and Y . Yao, Giant Second-Order Nonlinear Hall Effect in Twisted Bilayer Graphene, Phys. Rev. Lett. 129, 186801 (2022)

    2022

  21. [29]

    Ma et al., Observation of the nonlinear Hall effect under time-reversal-symmetric conditions, Nature 565, 337 (2019)

    Q. Ma et al., Observation of the nonlinear Hall effect under time-reversal-symmetric conditions, Nature 565, 337 (2019)

    2019

  22. [30]

    He and H

    Z. He and H. Weng, Giant nonlinear Hall effect in twisted bilayer WTe2, Npj Quantum Mater. 6, 1 (2021)

    2021

  23. [31]

    Huang et al., Giant nonlinear Hall effect in twisted bilayer WSe2, Natl

    M. Huang et al., Giant nonlinear Hall effect in twisted bilayer WSe2, Natl. Sci. Rev. 10, nwac232 (2023)

    2023

  24. [32]

    Huang et al., Intrinsic Nonlinear Hall Effect and Gate-Switchable Berry Curvature Sliding in Twisted Bilayer Graphene, Phys

    M. Huang et al., Intrinsic Nonlinear Hall Effect and Gate-Switchable Berry Curvature Sliding in Twisted Bilayer Graphene, Phys. Rev. Lett. 131, 066301 (2023)

    2023

  25. [33]

    Datta, S

    S. Datta, S. Bhowmik, H. Varshney, K. Watanabe, T. Taniguchi, A. Agarwal, and U. Chandni, Nonlinear Electrical Transport Unveils Fermi Surface Malleability in a Moiré Heterostructure, Nano Lett. 24, 9520 (2024)

    2024

  26. [34]

    Sinha et al., Berry curvature dipole senses topological transition in a moiré superlattice, Nat

    S. Sinha et al., Berry curvature dipole senses topological transition in a moiré superlattice, Nat. Phys. 18, 765 (2022)

    2022

  27. [35]

    K. Kang, T. Li, E. Sohn, J. Shan, and K. F . Mak, Nonlinear anomalous Hall effect in few-layer WTe2, Nat. Mater. 18, 324 (2019)

    2019

  28. [36]

    Suárez-Rodríguez et al., Odd Nonlinear Conductivity under Spatial Inversion in Chiral Tellurium, Phys

    M. Suárez-Rodríguez et al., Odd Nonlinear Conductivity under Spatial Inversion in Chiral Tellurium, Phys. Rev. Lett. 132, (2024)

    2024

  29. [37]

    P . He, H. Isobe, D. Zhu, C.-H. Hsu, L. Fu, and H. Yang, Quantum frequency doubling in the topological insulator Bi2Se3, Nat. Commun. 12, 698 (2021)

    2021

  30. [38]

    Y . Cao, V . Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P . Jarillo-Herrero, Unconventional superconductivity in magic-angle graphene superlattices, Nature 556, 43 (2018)

    2018

  31. [39]

    K. Roy, T. Ahmed, H. Dubey, T. P . Sai, R. Kashid, S. Maliakal, K. Hsieh, S. Shamim, and A. Ghosh, Number- Resolved Single-Photon Detection with Ultralow Noise van der Waals Hybrid, Adv. Mater. 30, 1704412 (2018)

    2018

  32. [40]

    Ahmed, K

    T. Ahmed, K. Roy, S. Kakkar, A. Pradhan, and A. Ghosh, Interplay of charge transfer and disorder in optoelectronic response in Graphene/hBN/MoS2 van der Waals heterostructures, 2D Mater. 7, 025043 (2020)

    2020

  33. [41]

    Shen et al., Correlated states in twisted double bilayer graphene, Nat

    C. Shen et al., Correlated states in twisted double bilayer graphene, Nat. Phys. 16, 520 (2020)

    2020

  34. [42]

    Y . Wang, J. Herzog-Arbeitman, G. W. Burg, J. Zhu, K. Watanabe, T. Taniguchi, A. H. MacDonald, B. A. Bernevig, and E. Tutuc, Bulk and edge properties of twisted double bilayer graphene, Nat. Phys. 18, 1 (2022)

    2022

  35. [43]

    Phys. Rev. B 99, 235406 (2019) - Band Structure and Topological Properties of Twisted Double Bilayer Graphene, https://journals.aps.org/prb/abstract/10.1103/PhysRev B.99.235406

    2019 doi

  36. [44]

    Cao et al., Correlated insulator behaviour at half- filling in magic-angle graphene superlattices, Nature 556, 80 (2018)

    Y . Cao et al., Correlated insulator behaviour at half- filling in magic-angle graphene superlattices, Nature 556, 80 (2018)

    2018

  37. [45]

    F . K. de Vries et al., Kagome Quantum Oscillations in Graphene Superlattices, Nano Lett. 24, 601 (2024)

    2024

  38. [46]

    Suárez-Rodríguez, B

    M. Suárez-Rodríguez, B. Martín-García, W. Skowroński, K. Staszek, F . Calavalle, A. Fert, M. Gobbi, F . Casanova, and L. E. Hueso, Microscale Chiral Rectennas for Energy Harvesting, Adv. Mater. 36, 2400729 (2024)

    2024

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.