Pith. sign in

REVIEW 2 major objections 1 minor 45 references

Rectified voltages in tellurium flakes are directly proportional to surface lone-pair polarization.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

A minimal three-component lattice model links linear and nonlinear transport coefficients in tellurium to the second and first moments of surface lone-pair polarization.

T0 review reviewed 2026-06-28 challenge →

load-bearing objection The paper links quantum-geometric transport coefficients in tellurium to moments of surface lone-pair polarization through a minimal lattice model, with the central claim resting on how faithfully that model captures the inversion-odd potential. the 2 major comments →

arxiv 2605.31197 v1 pith:BYCXDSQS submitted 2026-05-29 cond-mat.mes-hall

Surface lone-pair polarization probed by quantum-geometric transport in tellurium

Nathanael N. Batista , Wendel S. Paz , Manuel Su\'arez-Rodr\'iguez , Pierpaolo Fontana , Victor Velasco , Marcus V. O. Moutinho , Chang Niu , Peide D. Ye
show 5 more authors
Marco Gobbi F\`elix Casanova Luis E. Hueso Caio Lewenkopf Marcello B. Silva Neto
This is my paper
classification cond-mat.mes-hall
keywords telluriumlone pair polarizationquantum geometric transportsurface polarizationnonlinear transportBloch wave packetspolar texture
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

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 shows that quantum-geometry transport can probe surface lone-pair polarization in trigonal tellurium. This polarization creates an inversion-odd dipolar component in the crystal potential that shifts Bloch wavepacket centers and adds quantum-geometric corrections to carrier velocity. Linear transport coefficients respond to the second moment of this polarization field while nonlinear coefficients respond to the first moment. As a result, rectified voltages scale directly with the surface polarization. The mechanism is captured in a minimal three-component lattice model that describes the polar texture.

Core claim

Stereochemically active lone pairs produce surface polarization in trigonal tellurium that is revealed by quantum-geometry transport. The polarization appears as an inversion-odd dipolar component of the crystal potential, shifting the center of mass of Bloch wavepackets and producing quantum-geometric corrections to their velocity. A minimal three-component lattice model describes this lone-pair polar texture, with linear and nonlinear transport coefficients probing the second and first moments of the net polarization field respectively. Rectified voltages in tellurium flakes are directly proportional to the surface lone-pair polarization.

What carries the argument

Minimal three-component lattice model describing the lone-pair polar texture and its inversion-odd dipolar potential, which induces quantum-geometric velocity corrections in Bloch wavepackets.

Load-bearing premise

The minimal three-component lattice model correctly captures the inversion-odd dipolar component of the crystal potential and the quantum-geometric velocity corrections linking transport to polarization moments.

What would settle it

Experimental data on rectified voltages in tellurium flakes that deviate from the predicted direct proportionality to surface lone-pair polarization, or transport coefficients that do not match the moments derived from the lattice model.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Linear transport coefficients probe the second moment of the net polarization field.
  • Nonlinear transport coefficients probe the first moment of the net polarization field.
  • Rectified voltages in tellurium flakes are directly proportional to surface lone-pair polarization.
  • The results open a route to polarization-driven quantum-geometric electronic devices based on tellurium allotropes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The proportionality could allow engineering of rectification strength by controlling surface polarization in devices.
  • Similar lone-pair effects might be probed in other elemental semiconductors with stereochemically active pairs.
  • Transport-based measurement offers a way to study surface polarity without direct imaging techniques.
  • The model may generalize to predict transport in related crystal structures.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The manuscript claims that quantum-geometric transport provides a sensitive probe of surface lone-pair polarization in trigonal tellurium. A minimal three-component lattice model encodes an inversion-odd dipolar component of the crystal potential that shifts Bloch wavepacket centers of mass and generates quantum-geometric velocity corrections. Linear and nonlinear transport coefficients are shown to probe the second and first moments of the net polarization field, respectively, yielding rectified voltages directly proportional to the surface lone-pair polarization and thereby a microscopic route to polarization-driven devices based on tellurium allotropes.

Significance. If the central derivation holds, the result supplies a concrete link between stereochemically active lone pairs, quantum geometry, and measurable transport in a real material, with potential for device engineering. The approach is falsifiable in principle via voltage measurements on tellurium flakes and could generalize to other polar crystals. No machine-checked proofs or open code are mentioned, but the parameter-free character of the moment-probing relations (if demonstrated) would be a notable strength.

major comments (2)
  1. [Model and transport derivation (abstract)] The abstract states that the three-component lattice model produces transport coefficients that 'probe' the first and second moments of the polarization field, but the explicit construction of the inversion-odd dipolar term and the resulting velocity operator corrections are not visible. Without these equations it cannot be verified whether the claimed proportionality is independent of the model's free parameters or follows tautologically from the definition of the polarization moments inside the minimal model.
  2. [Central claim (abstract)] The central claim that rectified voltages are 'directly proportional' to surface lone-pair polarization rests on the minimal model correctly capturing the microscopic physics of tellurium. No comparison to ab initio calculations, experimental data, or alternative models is referenced in the abstract, leaving open whether the relation survives when the lattice model is replaced by a more complete Hamiltonian.
minor comments (1)
  1. [Abstract] The abstract would benefit from a single sentence indicating the crystal structure (e.g., space group) or the specific tellurium allotrope under study.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review. The manuscript focuses on deriving transport relations within a minimal model; the full text contains the explicit constructions referenced in the comments. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Model and transport derivation (abstract)] The abstract states that the three-component lattice model produces transport coefficients that 'probe' the first and second moments of the polarization field, but the explicit construction of the inversion-odd dipolar term and the resulting velocity operator corrections are not visible. Without these equations it cannot be verified whether the claimed proportionality is independent of the model's free parameters or follows tautologically from the definition of the polarization moments inside the minimal model.

    Authors: The abstract is a concise summary; the explicit construction appears in the main text. Section II defines the three-component lattice model and introduces the inversion-odd dipolar term as an additional on-site potential that encodes the surface lone-pair texture. Section III derives the quantum-geometric velocity corrections from the resulting Bloch wavepacket shifts and computes the linear and nonlinear conductivities. The moment-probing relations follow from symmetry-allowed integration of the polarization field and are independent of specific parameter choices, as they originate in the quantum-geometric formalism rather than being inserted by definition. revision: no

  2. Referee: [Central claim (abstract)] The central claim that rectified voltages are 'directly proportional' to surface lone-pair polarization rests on the minimal model correctly capturing the microscopic physics of tellurium. No comparison to ab initio calculations, experimental data, or alternative models is referenced in the abstract, leaving open whether the relation survives when the lattice model is replaced by a more complete Hamiltonian.

    Authors: The abstract summarizes the result obtained inside the minimal model, whose construction is motivated in the introduction by the known stereochemistry and surface polarity of trigonal tellurium. The full manuscript justifies the model as capturing the essential inversion-odd dipolar physics without claiming it exhausts all microscopic details. Direct ab initio benchmarks or experimental comparisons lie outside the present scope, which is limited to analytic relations within the minimal Hamiltonian; whether the proportionality persists in a more complete description remains an open question for future work. revision: no

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained

full rationale

The abstract presents a minimal three-component lattice model constructed to encode an inversion-odd dipolar potential, from which quantum-geometric velocity corrections are derived and shown to link transport coefficients to polarization moments. No quoted equations, self-citations, or steps in the provided text reduce any claimed prediction or proportionality to a fitted input or definitional tautology by construction. The relation between rectified voltage and surface polarization follows from the model's explicit construction and transport derivations rather than renaming or self-referential fitting. The central claim therefore rests on the model's physical fidelity, which is an independent modeling choice rather than a circular reduction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Review is abstract-only; the ledger therefore records only the explicit modeling assumptions stated in the abstract. The three-component lattice model is expected to contain free parameters whose values are not specified here.

free parameters (1)
  • parameters of the three-component lattice model
    A minimal lattice model is introduced to describe the polar texture; such models typically contain adjustable parameters for hopping or potential terms.
axioms (1)
  • domain assumption Surface lone-pair polarization appears microscopically as an inversion-odd dipolar component of the crystal potential that shifts the center of mass of Bloch wavepackets.
    This premise is stated directly in the abstract as the origin of the quantum-geometric corrections.

reviewed 2026-06-28 · how reviews work

0 comments
Cite this review

Pith. "Pith review of Surface lone-pair polarization probed by quantum-geometric transport in tellurium." pith.science (2026). https://pith.science/paper/BYCXDSQS

@misc{pith2026260531197,
  author       = {Pith},
  title        = {Pith review of: Surface lone-pair polarization probed by quantum-geometric transport in tellurium},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BYCXDSQS}},
  note         = {Machine review of arXiv:2605.31197}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Stereochemically active lone pairs are ubiquitous microscopic sources of polarity in molecules and solids, but their collective behavior in crystals is often hidden by symmetry or confined to surfaces. Here we show that quantum-geometry transport provides a sensitive probe of surface lone-pair polarization in trigonal tellurium. This surface polarization appears microscopically as an inversion-odd dipolar component of the crystal potential, which shifts the center of mass of Bloch wavepackets and produces quantum-geometric corrections to their velocity. We describe this lone-pair polar texture through a minimal three-component lattice model, and we show that the resulting linear and nonlinear transport coefficients probe, respectively, the second and first moments of the net polarization field. Because rectified voltages in tellurium flakes are directly proportional to the surface lone-pair polarization, our results provide a microscopic route to understanding and engineering polarization-driven, quantum-geometric electronic devices based on tellurium allotropes.

Figures

Figures reproduced from arXiv: 2605.31197 by Caio Lewenkopf, Chang Niu, F\`elix Casanova, Luis E. Hueso, Manuel Su\'arez-Rodr\'iguez, Marcello B. Silva Neto, Marco Gobbi, Marcus V. O. Moutinho, Nathanael N. Batista, Peide D. Ye, Pierpaolo Fontana, Victor Velasco, Wendel S. Paz.

Figure 1
Figure 1. Figure 1: Quantum-geometric transport. Experimental data [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Excess electronic density (red) and charge de [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Lone-pair polarization. (a) Schematic showing how [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Thermodynamics of lone-pair polarization. (a) [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

45 extracted references · 2 canonical work pages

  1. [1]

    ERDF A way of making Europe

    ×10−2 Figure 3. Excess electronic density (red) and charge de- pletion (blue) relative to the atomic densities of constituent atoms. The three panels correspond to slices at (a)z= 0, (b) z=L z/3, and (c)z= 2L z/3, for the three non-equivalent atoms in the unit cell. The black arrows indicate the local inversion-odd dipolar slopes computed from the gradien...

    work page doi:10.13039/501100011033 2023

  2. [2]

    R. J. Gillespie and R. S. Nyholm, Inorganic stereochem- istry, Q. Rev. Chem. Soc.11, 339 (1957)

    1957

  3. [3]

    D. J. Payne, R. G. Egdell, A. Walsh, G. W. Wat- son, J. Guo, P.-A. Glans, T. Learmonth, and K. E. Smith, Electronic origins of structural distortions in post- transition metal oxides: Experimental and theoretical ev- idence for a revision of the lone pair model, Phys. Rev. Lett.96, 157403 (2006)

    2006

  4. [4]

    D. J. Payne, R. G. Egdell, D. S. L. Law, P.-A. Glans, T. Learmonth, K. E. Smith, J. Guo, A. Walsh, and G. W. Watson, Experimental and theoretical study of the elec- tronic structures ofα-PbO andβ-PbO 2, J. Mater. Chem. 17, 267 (2007)

    2007

  5. [5]

    R. E. Cohen, Origin of ferroelectricity in perovskite ox- ides, Nature358, 136 (1992)

    1992

  6. [6]

    Laurita and R

    G. Laurita and R. Seshadri, Chemistry, structure, and function of lone pairs in extended solids, Accounts of Chemical Research55, 1004 (2022)

    2022

  7. [7]

    D. H. Fabini, R. Seshadri, and M. G. Kanatzidis, The un- derappreciated lone pair in halide perovskites underpins their unusual properties, MRS Bulletin45, 467 (2020)

    2020

  8. [8]

    Gattinoni, N

    C. Gattinoni, N. Strkalj, R. H¨ ardi, M. Fiebig, M. Trassin, and N. A. Spaldin, Interface and surface stabilization of the polarization in ferroelectric thin films, Proceedings of the National Academy of Sciences117, 28589 (2020)

    2020

  9. [9]

    Y. Wang, M. K. Niranjan, K. Janicka, J. P. Velev, M. Y. Zhuravlev, S. S. Jaswal, and E. Y. Tsymbal, Ferroelectric dead layer driven by a polar interface, Phys. Rev. B82, 094114 (2010)

    2010

  10. [10]

    G. Qiu, A. Charnas, C. Niu, Y. Wang, W. Wu, and P. D. Ye, The resurrection of tellurium as an elemental two- dimensional semiconductor, npj 2D Mater. Appl.6, 17 (2022)

    2022

  11. [11]

    S. Yi, Z. Zhu, X. Cai, Y. Jia, and J.-H. Cho, The nature of bonding in bulk tellurium composed of one-dimensional helical chains, Inorg. Chem.57, 5083 (2018)

    2018

  12. [12]

    M. S. Dresselhaus, G. Dresselhaus, and A. Jorio,Group Theory: Applications to the Physics of Condensed Matter (Springer-Verlag Berlin Heidelberg, 2008)

    2008

  13. [13]

    Cheng, Y

    B. Cheng, Y. Gao, Z. Zheng, S. Chen, Z. Liu, L. Zhang, Q. Zhu, H. Li, L. Li, and C. Zeng, Giant nonlinear Hall and wireless rectification effects at room temperature in the elemental semiconductor tellurium, Nat. Commun. 15, 5513 (2024)

    2024

  14. [14]

    Sodemann and L

    I. Sodemann and L. Fu, Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal in- variant materials, Phys. Rev. Lett.115, 216806 (2015)

    2015

  15. [15]

    Z. Z. Du, C. M. Wang, H.-P. Sun, H.-Z. Lu, and X. C. Xie, Quantum theory of the nonlinear Hall effect, Nat. Commun.12, 5038 (2021)

    2021

  16. [16]

    Su´ arez-Rodr´ ıguez, B

    M. Su´ arez-Rodr´ ıguez, B. Mart´ ın-Garc´ ıa, W. Skowro´ nski, F. Calavalle, S. S. Tsirkin, I. Souza, F. De Juan, A. Chuvilin, A. Fert, M. Gobbi, F. Casanova, and L. E. Hueso, Odd nonlinear conductivity under spatial inver- sion in chiral tellurium, Phys. Rev. Lett.132, 046303 (2024)

    2024

  17. [17]

    Ortix, Nonlinear Hall effect with time-reversal sym- metry: Theory and material realizations, Adv

    C. Ortix, Nonlinear Hall effect with time-reversal sym- metry: Theory and material realizations, Adv. Quantum Technol.4, 2100056 (2021)

    2021

  18. [18]

    Su´ arez-Rodr´ ıguez, F

    M. Su´ arez-Rodr´ ıguez, F. De Juan, I. Souza, M. Gobbi, F. Casanova, and L. E. Hueso, Nonlinear transport in non-centrosymmetric systems, Nat. Mater.24, 1005 (2025)

    2025

  19. [19]

    T. B. Smith, L. Pullasseri, and A. Srivastava, Momentum-space gravity from the quantum geometry and entropy of Bloch electrons, Phys. Rev. Res.4, 013217 (2022)

    2022

  20. [20]

    Kaplan, T

    D. Kaplan, T. Holder, and B. Yan, Unification of nonlin- ear anomalous Hall effect and nonreciprocal magnetore- sistance in metals by the quantum geometry, Phys. Rev. Lett.132, 026301 (2024)

    2024

  21. [21]

    Sundaram and Q

    G. Sundaram and Q. Niu, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects, Phys. Rev. B59, 14915 (1999)

    1999

  22. [22]

    Y. Gao, S. A. Yang, and Q. Niu, Field induced positional shift of Bloch electrons and its dynamical implications, Phys. Rev. Lett.112, 166601 (2014)

    2014

  23. [23]

    Su´ arez-Rodr´ ıguez, B

    M. Su´ arez-Rodr´ ıguez, B. Mart´ ın-Garc´ ıa, W. Skowro´ nski, K. Staszek, F. Calavalle, A. Fert, M. Gobbi, F. Casanova, and L. E. Hueso, Microscale chiral rectennas for energy harvesting, Advanced Materials36, 2400729 (2024)

    2024

  24. [24]

    T. Doi, K. Nakao, and H. Kamimura, The valence band structure of tellurium. I. The k·p perturbation method, J. Phys. Soc. Jpn.28, 36 (1970)

    1970

  25. [25]

    Iacovelli, P

    C. Iacovelli, P. Fontana, V. Velasco, C. Niu, P. D. Ye, M. V. O. Moutinho, C. Lewenkopf, and M. B. Silva Neto, Polar unidirectional magnetotransport inp-type tel- lurene from quantum geometry (2026), arXiv:2602.13721 [cond-mat.mes-hall]

    work page arXiv 2026

  26. [26]

    See Supplemental Material at [URL-will-be-inserted-by- publisher] for further details regarding harmonics gener- ated byj(E), parity-odd semiclassical dynamics, L¨ owdin downfolding and Christoffel symbols in the valence sec- tor, derivation of the first and second thermal moments from the coarse-grained polar lattice model, and compu- tational methods

  27. [27]

    Cardy,Scaling and Renormalization in Statistical Physics(Cambridge University Press, 1996)

    J. Cardy,Scaling and Renormalization in Statistical Physics(Cambridge University Press, 1996)

    1996

  28. [28]

    Ozaki, Variationally optimized atomic orbitals for large-scale electronic structures, Phys

    T. Ozaki, Variationally optimized atomic orbitals for large-scale electronic structures, Phys. Rev. B67, 155108 (2003)

    2003

  29. [29]

    Ozaki and H

    T. Ozaki and H. Kino, Numerical atomic basis orbitals from h to kr, Phys. Rev. B69, 195113 (2004)

    2004

  30. [30]

    Ozaki and H

    T. Ozaki and H. Kino, Efficient projector expansion for theab initioLCAO method, Phys. Rev. B72, 045121 (2005)

    2005

  31. [31]

    Ozaki,Total Energy and Forces: Ver

    T. Ozaki,Total Energy and Forces: Ver. 1.3, OpenMX Technical Note (Institute for Solid State Physics, The 7 University of Tokyo) accessed: 2026-05-14

    2026

  32. [32]

    Ozaki,Electric Polarization by Berry Phase: Ver

    T. Ozaki,Electric Polarization by Berry Phase: Ver. 1.1, OpenMX Technical Note (Institute for Solid State Physics, The University of Tokyo) accessed: 2026-05-14

    2026

  33. [33]

    J. P. Perdew, M. Ernzerhof, and K. Burke, Rationale for mixing exact exchange with density functional approxi- mations, J. Chem. Phys.105, 9982 (1996)

    1996

  34. [34]

    H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B13, 5188 (1976)

    1976

  35. [35]

    R. D. King-Smith and D. Vanderbilt, Theory of polariza- tion of crystalline solids, Phys. Rev. B47, 1651 (1993)

    1993

  36. [36]

    Resta, Macroscopic polarization in crystalline di- electrics: the geometric phase approach, Rev

    R. Resta, Macroscopic polarization in crystalline di- electrics: the geometric phase approach, Rev. Mod. Phys. 66, 899 (1994)

    1994

  37. [37]

    Xiao, M.-C

    D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys.82, 1959 (2010)

    1959

  38. [38]

    J. M. Ziman,Principles of the theory of solids(Cam- bridge University Press, Cambridge, 1972)

    1972

  39. [39]

    C. Niu, G. Qiu, Y. Wang, P. Tan, M. Wang, J. Jian, H. Wang, W. Wu, and P. D. Ye, Tunable chirality- dependent nonlinear electrical responses in 2D tellurium, Nano Lett.23, 8445 (2023)

    2023

  40. [40]

    Fontana, V

    P. Fontana, V. Velasco, C. Niu, P. D. Ye, P. V. Lopes, K. E. M. de Souza, M. V. O. Moutinho, C. Lewenkopf, and M. B. S. Neto, Quantum geometry and the electric magnetochiral anisotropy in noncentrosymmetric polar media, Phys. Rev. Lett.135, 106602 (2025)

    2025

  41. [41]

    Su´ arez-Rodr´ ıguez,Non-linear transport in chiral Tel- lurium: From fundamentals to applications, Ph.D

    M. Su´ arez-Rodr´ ıguez,Non-linear transport in chiral Tel- lurium: From fundamentals to applications, Ph.D. thesis, Universidad del Pa´ ıs Vasco / Euskal Herriko Unibertsi- tatea (2025)

    2025

  42. [42]

    Su´ arez-Rodr´ ıguez, B

    M. Su´ arez-Rodr´ ıguez, B. Mart´ ın-Garc´ ıa, F. Calavalle, S. S. Tsirkin, I. Souza, F. de Juan, A. Fert, M. Gobbi, L. E. Hueso, and F. Casanova, Symmetry origin and microscopic mechanism of electrical magnetochi- ral anisotropy in tellurium, Phys. Rev. B111, 024405 (2025)

    2025

  43. [43]

    X n Z k Γ(n) xxx(k)vx,n(k) −∂εf(0) n # sin3 θ,(S38) V 2ω ⊥ (I ω)2 =− L⊥ A2 e4τ E0 ℏ ρ3 xx

    T. Doi, K. Nakao, and H. Kamimura, The valence band structure of tellurium. II. The infrared absorption, J. Phys. Soc. Jpn.28, 822 (1970). 8 Supplementary Information Surface lone-pair polarization probed by quantum-geometric transport in tellurium Nathanael N. Batista, Wendel S. Paz, Manuel Su´ arez-Rodr´ ıguez, Pierpaolo Fontana, Victor Velasco, Marcus ...

    1970

  44. [44]

    they penalize local deviations from bulk equiva- lence (∝κ),

  45. [45]

    they renormalize the response to the boundary field through inter-triangle correlations (∝J). At the level of a single-site mean-field treatment, these effects can be absorbed into an effective local fieldheff(T), so that the effective local energy reads Eloc(s) =−h eff(T)s, s∈ {+1,0,−1}.(S129) We define the corresponding dimensionless field x(T)≡βh eff(T...

    2019

This paper was first reviewed by grok-4.3 on June 28, 2026.