Terahertz field-driven nonlinear Hall effect and other second order transport phenomena in two-dimensional tellurene

Chang Niu; E. M\"onch; J. Wunderlich; L. E. Golub; M. D. Moldavskaya; Peide D. Ye; S. D. Ganichev

REVIEW 2 major objections 5 minor 59 references

Terahertz field-driven nonlinear Hall effect and other second order transport phenomena in two-dimensional tellurene

T0 review · 2 major / 5 minor · reviewed 2026-07-13 · grok-4.5

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Pith's one-line read THz radiation drives gate-tunable second-order currents in 2D tellurene that decompose into nonlinear Hall, longitudinal and diagonal channels.

desk verdict Solid THz experiment that cleanly maps all three second-order channels in C1 tellurene onto LPGE; the data hold, the skew-dominance claim is only an estimate. read the letter →

arxiv 2607.09256 v1 pith:IMXOJRO2 submitted 2026-07-10 cond-mat.mes-hall cond-mat.mtrl-sci

M. D. Moldavskaya , L. E. Golub , E. Mönch , Chang Niu , Peide D. Ye , J. Wunderlich , S. D. Ganichev This is my paper · ORCID

classification cond-mat.mes-hallcond-mat.mtrl-sci

keywords nonlinearHalleffect2DtellureneterahertzphotogalvanicBerrycurvaturedipoleskewscatteringsidejumpgate-tunabletransportC1symmetry

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 shows that linearly polarized terahertz radiation generates dc currents in two-dimensional tellurene Hall bars that are quadratic in the ac electric field and depend on its orientation. The currents arise because the flakes have only C1 symmetry, so all second-order conductivity components are allowed. By rotating the field and measuring both along and perpendicular to the crystal c-axis, the authors resolve three transport channels—nonlinear Hall, nonlinear longitudinal and nonlinear diagonal—and prove they are exactly the same as the familiar linear photogalvanic contributions. Every channel reverses when the gate voltage switches the carriers from electrons to holes, grows by roughly two orders of magnitude upon cooling to 4.2 K, and strengthens as the radiation frequency is lowered. A combined phenomenological and semiclassical theory accounts for the data with three microscopic processes: skew scattering, side jumps and the Berry curvature dipole. The work therefore converts a contactless optical measurement into a practical probe of nonlinear transport that works from cryogenic temperatures up to room temperature.

What carries the argument

The equivalence between the six independent LPGE coefficients (J0, JL1, JL2 along a and c) and the three nonlinear-transport vectors (NLH, NLL, NLD) given by the linear relations in Eqs. (24)–(26). This identity converts a polarization scan of a photocurrent into a complete map of the second-order conductivity tensor.

What would settle it

Measure the same six current coefficients in a tellurene flake whose impurity density has been independently quantified (for example by residual-resistivity ratio or deliberate doping) and check whether the observed magnitude tracks the predicted 1/τ or 1/τ^{2} scaling of conventional versus coherent skew scattering.

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Extended reading notes

Core claim

Terahertz-driven dc currents in C1-symmetric 2D tellurene are second-order responses that decompose cleanly into nonlinear Hall, nonlinear longitudinal and nonlinear diagonal channels; these channels are identical to the linear photogalvanic contributions, are gate-tunable with opposite signs for electrons and holes, and are generated by the combination of skew scattering, side-jump and Berry-curvature-dipole mechanisms.

Load-bearing premise

The assignment of conventional skew scattering as the dominant microscopic source rests on an order-of-magnitude estimate that uses an unmeasured disorder strength, so the ranking of mechanisms is assumed rather than independently verified.

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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 useful part of this paper is experimental and phenomenological. They drive 2D tellurene Hall bars with linearly polarized THz (0.6–2.54 THz), measure the dc current both along and perpendicular to the c-axis, and show that the polarization dependence decomposes into the six independent C1 coefficients (J0, JL1, JL2 for each direction). They then rewrite those coefficients as the NLHE, NLL and NLD channels and demonstrate the exact equivalence to the LPGE Stokes terms. Intensity is quadratic, the currents reverse with gate voltage across the CNP, grow by ~100× on cooling to 4.2 K, and rise as frequency drops. Two samples, room-temperature and cryogenic data, pulsed and cw sources—all consistent with the C1 forms (Eqs. 3–4) and the standard Boltzmann expressions for skew, side-jump and BCD (Eqs. 11, 15).

What is new is the simultaneous resolution of the three channels plus the explicit LPGE–transport dictionary under C1. NLHE itself and THz LPGE in tellurene were already reported (their Refs. 7, 23, 24). The NLD term is just the remaining independent piece required by C1; naming it is bookkeeping, not a discovery.

Soft spots are real but limited. The claim that conventional skew dominates rests on the order-of-magnitude ratio ~εF/(Nd|U|) with εF≈50 meV and no measured disorder strength; that is an assumption, not a result. They also never extract absolute second-order conductivities because the local |E| is not calibrated (refractive-index factor near the reststrahlen band is left open). Frequency dependence is therefore only qualitative. None of this breaks the central observations or the channel mapping.

Math and citations look standard and honest; self-cites are to their own prior THz work on the same material. The paper is for people who care about nonlinear transport or THz rectification in low-symmetry 2D systems. It deserves a serious referee. I would read it, cite the experimental decomposition, and not lean on the microscopic ranking until someone measures Nd or |U|.

Referee Report

2 major / 5 minor

Summary. The manuscript reports THz-driven second-order dc currents in C1-symmetric 2D tellurene Hall bars, measured along and perpendicular to the c-axis. Polarization, intensity, gate, temperature and frequency dependences are shown to match the six independent LPGE coefficients of Eqs. (3)–(4). These are rewritten as NLHE, NLL and NLD transport channels (Eqs. 23–26). A semiclassical Boltzmann theory supplies skew-scattering (Eq. 11), Berry-curvature-dipole (Eq. 15) and side-jump contributions; the data are argued to be consistent with all three, with conventional skew scattering suggested to dominate on the basis of an order-of-magnitude estimate after Eq. (20). Currents reverse sign across the charge-neutrality point and grow strongly on cooling and on lowering frequency.

Significance. The work cleanly demonstrates that contactless, polarization-resolved THz excitation can resolve the full set of second-order conductivities in a low-symmetry 2D semiconductor without a linear dc background, and that the same tensor underlies both nonlinear transport and LPGE. The experimental trends (gate sign reversal, T and ω dependence) are robust and the phenomenological mapping is transparent. If the microscopic assignment can be sharpened, the paper would provide a useful template for separating intrinsic and extrinsic nonlinear responses in other non-centrosymmetric 2D materials.

major comments (2)

Sec. V after Eq. (20): the claim that conventional skew scattering dominates rests on j_skew/j_BCD ∼ ε_F/(N_d|U|) with ε_F ≈ 50 meV and an unquantified assertion that the ratio exceeds unity. No independent estimate of N_d or |U| (or of the relative weight of coherent skew, side-jump and BCD) is supplied. Because the abstract and Sec. VI present this microscopic origin as a result rather than a plausible scenario, either a quantitative bound (mobility, residual resistivity, or disorder model) or a clear statement that the assignment remains an assumption is required.
Sec. VI and insets of Fig. 3: the observed rise of J/P_s with decreasing frequency is attributed to a frequency-dependent refractive-index factor near the reststrahlen band that converts P_s into |E|^2. Without a measured or calculated conversion factor, the microscopic prediction j ∝ σ(ω) cannot be tested. A short estimate of the Fresnel factor (or an explicit statement that the frequency trend is only qualitative) is needed to keep the comparison with Eqs. (11) and (15) load-bearing.

minor comments (5)

The Nonlinear Diagonal (NLD) current is introduced as a new effect (Eqs. 23, 26–27). A one-sentence comparison with existing literature on second-order diagonal responses would help readers place the terminology.
Figs. 5 and 7: several panels multiply J_L2 by 10 for visibility; the factor should be stated uniformly in every caption that uses it.
Notation for the six coefficients switches between J^{c,a}_{0,L1,L2} and C_{NLL,NLH,NLD}; a compact table mapping the two bases would improve readability of Sec. VI.
Sample #B shows a slight offset of the current-inversion point from U_G = 0 (Fig. 5f); the mixed-carrier explanation is plausible but could be supported by a brief two-carrier estimate.
A few typographical issues remain (e.g., “CONSIDERA TION”, “TECHNIQUE”, missing spaces in figure labels).

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: C1 phenomenology, Boltzmann-derived microscopic channels, and algebraic NLH/NLL/NLD↔LPGE mapping are independent of the data fits; self-citations supply only device/context background.

full rationale

The derivation chain is self-contained. Phenomenological forms (Eqs. 3–4) follow directly from the C1 point group under normal-incidence linear polarization and contain six independent coefficients by construction of the symmetry; they are not fitted to produce the claim. The microscopic expressions for skew-scattering (Eq. 11), BCD (Eq. 15) and side-jump currents are obtained by standard iteration of the Boltzmann equation with asymmetric scattering and anomalous velocity; the only free parameters are the usual scattering times and dimensionless asymmetry factors Ξ, Λ ≪ 1. The mapping (Eqs. 23–26) that equates the three transport channels (NLH, NLL, NLD) to the three LPGE Stokes components is pure linear algebra on the same second-rank response tensor and does not introduce new dynamical content. Polarization curves are fitted only to extract the six coefficients J_L1,L2,0 for subsequent comparison with gate, temperature and frequency trends; those trends are then checked against the independent high-frequency asymptotics of Eqs. 11 and 15. The order-of-magnitude estimate that conventional skew scattering dominates (after Eq. 20) is an assumption, not a circular prediction. Self-citations (Refs. 23, 42) document prior device fabrication and related LPGE observations but are not invoked as uniqueness theorems or as the sole support for any load-bearing step. Consequently the central claim—that the observed THz dc currents are second-order responses decomposable into the three channels and arising from the three standard mechanisms—does not reduce to its own inputs.

Assumptions & free parameters 3 free parameters · 4 assumptions · 1 invented entities

The central claim rests on standard semiclassical transport assumptions plus the experimental assertion of C1 symmetry for the substrate-supported flakes. No new particles or forces are introduced. Free parameters are the six independent second-order coefficients extracted from polarization fits and the unmeasured disorder strength that decides which microscopic channel dominates.

free parameters (3)

Six independent LPGE/second-order coefficients J^{c,a}_{0,L1,L2}
Extracted by fitting polarization curves (Eqs. 3-4) for each gate voltage, temperature and frequency; they are the phenomenological amplitudes that encode the microscopic mechanisms.
Disorder strength N_d |U| entering the skew-to-BCD ratio
Appears in the estimate after Eq. 20; never measured, yet used to argue that conventional skew scattering dominates.
Frequency-dependent refractive-index factor converting P_s to |E|^2
Invoked in Sec. VI to explain the observed frequency rise of J/P_s; not independently measured for 2D tellurene.

assumptions (4)

domain assumption Substrate-supported 2D tellurene has point-group symmetry C1, allowing all six in-plane second-order coefficients.
Stated in Sec. II and used to write Eqs. 3-4; justified by prior work (Ref. 23) and by the observation of all polarization harmonics.
domain assumption THz photon energy lies below the gap and carrier energies, so absorption is Drude-like free-carrier absorption treatable by the semiclassical Boltzmann equation.
Sec. V opening paragraphs; standard for meV THz radiation in semiconductors.
domain assumption Parabolic dispersion and degenerate statistics at the Fermi surface.
Used to obtain the closed-form skew-scattering current (Eq. 11).
standard math Standard expressions for Berry curvature dipole, side-jump accumulation and anomalous distribution.
Taken from the semiclassical literature (Refs. 25, 50, 51) and specialized to 2D.

invented entities (1)

Nonlinear Diagonal (NLD) current
purpose: To complete the set of six linearly independent second-order responses allowed by C1 symmetry and to make J_L1 and J_L2 independent.
Defined in Sec. VI (Eqs. 23, 26-27) as the sum of the two terms proportional to S and S imes z-hat; it is a convenient re-labeling of already-allowed tensor components rather than a new physical object.

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Pith. "Pith review of Terahertz field-driven nonlinear Hall effect and other second order transport phenomena in two-dimensional tellurene." pith.science (2026). https://pith.science/paper/IMXOJRO2

@misc{pith2026260709256,
  author       = {Pith},
  title        = {Pith review of: Terahertz field-driven nonlinear Hall effect and other second order transport phenomena in two-dimensional tellurene},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IMXOJRO2}},
  note         = {Machine review of arXiv:2607.09256}
}

abstract

We study terahertz field-driven second-order nonlinear electron transport phenomena, including the nonlinear Hall effect (NLHE), in two-dimensional tellurene flakes. The dc current excited by linearly polarized terahertz (THz) radiation in Hall bar samples is investigated in directions both along and perpendicular to the $c$-axis of tellurene. As expected for second-order transport phenomena, the current scales as the square of the in-plane electric field of the radiation $\bf E$, and depends on its orientation. The current results from a combination of three contributions, including the NLHE, the Nonlinear Longitudinal (NLL) and Nonlinear Diagonal (NLD) currents. We established the equivalence between NLH, NLL, and NLD transport currents and Linear photogalvanic effect (LPGE) contributions induced by the absorption of linearly polarized and unpolarized THz radiation. All contributions can be controlled by a gate voltage and have opposite signs for electron and hole conductivity. The magnitude of the current increases drastically when the samples are cooled from room temperature to 4.2 K. It also increases with decreasing radiation frequency. These results are well described by the developed phenomenological and microscopic theories. We show that the THz radiation-induced electric current originates from microscopic mechanisms such as skew scattering, side jump, and the Berry curvature dipole.

Figures

Figures reproduced from arXiv: 2607.09256 by the authors.

**Figure 2.** (a) Azimuth angle dependence of the photocur [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 4.** Dependencies of the photocurrent J on the radiation intensity I = P/S ∝ E 2 . The data are obtained for frequencies f = 2.02 (upper panel) and 1.07 THz (lower panel) and several effective gate voltages. Solid lines show fits after J ∝ E 2 . dashed, dot-dashed and dotted lines, respectively. It is seen that for some effective gate voltages the contribution ∝ J c L2 is substantial and can even dominate, see, e.g., … view at source ↗

Figures from the paper (5 more)

**Figure 5.** Figure 5: Panels (a)-(e): Dependencies of the normalized photocurrent [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: Dependencies of the normalized photocurrent [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: Dependencies of the normalized photocurrent [PITH_FULL_IMAGE:figures/full_fig_p008_7.png]

**Figure 8.** Figure 8: Microscopic mechanism of the photocurrent for [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

**Figure 9.** Figure 9: Different contributions to the LPGE current for two polarization directions. Three currents correspond to the NLH, [PITH_FULL_IMAGE:figures/full_fig_p010_9.png]

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Pith tools

Reviewed July 13, 2026 · model on record in the stance chip above.

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of Eq. (3). Figure 2(b) shows a color map of the polarization dependent current contributionJ c −J c 0 as a function of the azimuth angleαand effective gate voltageU G. The figure shows that, for all gate voltages, the polarization dependence of the current in sample #A is determined by the first term of Eq. (3). The same result has been obtained for lowe...

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