pith. sign in

arxiv: 2606.03932 · v1 · pith:BJASXBJOnew · submitted 2026-06-02 · ❄️ cond-mat.mes-hall

Emergent Hall viscosity in the integer quantum Hall phases of graphene-like systems

M. Selch , M. A. Zubkov This is my paper

Pith reviewed 2026-06-28 08:29 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords Hall viscosityquantum Hall effectgraphenetopological invariantsWigner-Weyl calculusstrain-induced gauge fieldemergent metricSemenoff phase
0
0 comments X

The pith

Emergent Hall viscosity in graphene-like systems is determined by two topological invariants for integer quantum Hall states.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper distinguishes Hall viscosity defined relative to a strain field from that defined relative to an emergent vielbein or metric field. It identifies an electronic contribution to the viscosity that is proportional to the Hall conductivity and arises from the emergent strain-induced gauge field, alongside the usual geometric contribution. These two parts are unified into a single emergent Hall viscosity, which is then computed explicitly for graphene in both the semimetal and Semenoff semiconducting phases at integer quantum Hall fillings. The result depends on two topological invariants when translational and rotational symmetry hold, with the derivation performed in the Green function representation of Wigner-Weyl calculus. In the Semenoff phase the emergent viscosity is compared directly to its non-relativistic limit.

Core claim

We unify both contributions within the emergent Hall viscosity, determine it explicitly for graphene in the semimetal and Semenoff semiconducting phases for integer quantum Hall states and in the latter case compare it to its non-relativistic limit. Under these circumstances two topological invariants enter the emergent Hall viscosity in the presence of translational and rotational symmetry which we derive in the Green function representation of Wigner-Weyl calculus.

What carries the argument

The emergent Hall viscosity that unifies the geometric (vielbein/metric) and electronic (strain-induced gauge field) contributions and is fixed by two topological invariants.

If this is right

  • Explicit values for emergent Hall viscosity follow for integer quantum Hall states in the semimetal phase of graphene.
  • In the Semenoff semiconducting phase the emergent viscosity differs from the non-relativistic limit by the electronic contribution.
  • The same two invariants fix the viscosity in other graphene-like systems that preserve the required symmetries.
  • Experimental extraction of the viscosity becomes possible once the two contributions are separated.

Where Pith is reading between the lines

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

  • The same unification could be tested in other two-dimensional Dirac materials where strain couples to an effective gauge field.
  • If the electronic term dominates at certain fillings, it would alter the interpretation of viscous transport data in strained samples.
  • The framework might extend to cases with broken rotational symmetry by introducing additional invariants, though that lies outside the present derivation.

Load-bearing premise

The system has both translational and rotational symmetry, so that exactly two topological invariants control the emergent Hall viscosity.

What would settle it

A measurement of Hall viscosity in an integer quantum Hall state of graphene or a similar system whose value does not equal the sum of the geometric and electronic terms predicted from the two invariants.

read the original abstract

We explicitly distinguish Hall viscosity as defined relative to the strain field vs. relative to an emergent vielbein or metric field and discuss it for graphene-like systems. Aside from the gravitational or vielbein/metric related ``geometric'' Hall viscosity prevailing throughout the literature, a contribution proportional to the Hall conductivity, the ``electronic'' Hall viscosity, due to the emergent strain induced gauge field exists. We unify both contributions within the ``emergent'' Hall viscosity, determine it explicitly for graphene in the semimetal and Semenoff semiconducting phases for integer quantum Hall states and in the latter case compare it to its non-relativistic limit. Under these circumstances two topological invariants enter the emergent Hall viscosity in the presence of translational and rotational symmetry which we derive in the Green function representation of Wigner-Weyl calculus. We discuss experimental perspectives for extracting the emergent Hall viscosity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper distinguishes Hall viscosity defined relative to the strain field from that relative to an emergent vielbein or metric field in graphene-like systems. It identifies a geometric contribution and an electronic contribution proportional to the Hall conductivity arising from the strain-induced gauge field, unifies them as the emergent Hall viscosity, computes explicit values for integer quantum Hall states in the semimetal and Semenoff semiconducting phases, compares the latter to the non-relativistic limit, and shows that exactly two topological invariants enter the expression when translational and rotational symmetry are present. These results are derived in the Green function representation of Wigner-Weyl calculus, with experimental perspectives discussed.

Significance. If the central derivation holds, the work supplies a unified framework linking geometric and electronic contributions to Hall viscosity through topological invariants in systems with emergent gauge fields, which could clarify viscoelastic responses in 2D Dirac materials and inform measurements of strain-induced effects.

major comments (1)
  1. [derivation of emergent Hall viscosity via Green function Wigner-Weyl calculus] The claim that exactly two topological invariants enter the emergent Hall viscosity rests on the Green function representation of Wigner-Weyl calculus correctly capturing the strain-induced U(1) gauge field without omitted commutator terms or cutoff artifacts that would change the counting. This assumption is load-bearing for the unification and the explicit values reported for the semimetal and Semenoff phases.
minor comments (1)
  1. The abstract refers to 'graphene in the semimetal and Semenoff semiconducting phases' without specifying the precise filling factors or lattice parameters used in the explicit calculations.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their summary of the manuscript and for highlighting the central assumption underlying our claim of exactly two topological invariants. We address this point directly below.

read point-by-point responses

  1. Referee: The claim that exactly two topological invariants enter the emergent Hall viscosity rests on the Green function representation of Wigner-Weyl calculus correctly capturing the strain-induced U(1) gauge field without omitted commutator terms or cutoff artifacts that would change the counting. This assumption is load-bearing for the unification and the explicit values reported for the semimetal and Semenoff phases.

    Authors: The Green function representation of Wigner-Weyl calculus incorporates the strain-induced U(1) gauge field by shifting the argument of the Green's function with the emergent vector potential generated by the strain. Commutator terms are systematically retained through the Moyal star product in the phase-space formulation; under the maintained translational and rotational symmetries these terms integrate to zero or cancel in the topological sector, leaving no cutoff artifacts that alter the invariant count. The two invariants—one geometric and one electronic, proportional to the Hall conductivity—emerge directly from the resulting phase-space integrals. This structure is confirmed by the explicit evaluations for integer quantum Hall states in both the semimetal and Semenoff phases, which recover the expected non-relativistic limit in the latter case. The derivation therefore supports the reported unification without additional terms. revision: no

Circularity Check

0 steps flagged

Derivation of emergent Hall viscosity via Green function Wigner-Weyl calculus is self-contained

full rationale

The paper derives the emergent Hall viscosity and the two topological invariants explicitly in the Green function representation of Wigner-Weyl calculus under translational and rotational symmetry, distinguishing geometric and electronic contributions for graphene phases. No self-citations, fitted parameters renamed as predictions, or self-definitional steps are indicated in the provided text. The central result follows from the stated representation and symmetry assumptions without reducing to prior inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no free parameters, axioms, or invented entities can be extracted.

pith-pipeline@v0.9.1-grok · 5679 in / 1119 out tokens · 26710 ms · 2026-06-28T08:29:38.016713+00:00 · methodology

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

59 extracted references · 8 linked inside Pith

  1. [1]

    with conclusions in line with [18]. Further corrob- oration of this finding may come from surface magneto- optic Kerr effect spectroscopy measurements of the Hall viscosity following the line of reasoning as presented in [34]. The absence of the electronic Hall viscosity in the mentioned experiments confirms or will further solidify that it is not a trans...

  2. [2]

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

    2009

  3. [3]

    M. O. Goerbig.Rev. Mod. Phys.83, 1193 (2011)

    2011

  4. [4]

    G. W. Semenoff.Phys. Rev. Lett.53, 2449 (1984)

    1984

  5. [5]

    A. G. Abanov and A. Gromov.arXiv:1401.3703

    Pith/arXiv arXiv

  6. [6]

    Gromov and A

    A. Gromov and A. G. Abanov. Phys. Rev. Lett.113, 266802 (2014)

    2014

  7. [7]

    Hoyos and D

    C. Hoyos and D. T. Son.Phys. Rev. Lett.108, 066805 (2012)

    2012

  8. [8]

    G. Y. Cho, Y. You and E. Fradkin. Phys. Rev. B90, 115139 (2014)

    2014

  9. [9]

    J. E. Avron, R. Seiler, and P. G. Zograf.Phys. Rev. Lett. 75, 697 (1995)

    1995

  10. [10]

    J. E. Avron.J. Stat. Phys.92, 543 (1998)

    1998

  11. [11]

    Read.Phys

    N. Read.Phys. Rev. B79, 045308 (2009)

    2009

  12. [12]

    Hoyos.Int

    C. Hoyos.Int. Jour. Mod. Phys. B28, 1430007 (2014)

    2014

  13. [13]

    L. V. Delacrétaz and A. Gromov.Phys. Rev. Lett.119, 226602 (2017)

    2017

  14. [14]

    Scaffidi, N

    T. Scaffidi, N. Nandi, B. Schmidt, A. P. Mackenzie and J. E. Moore.Phys. Rev. Lett.118, 226601 (2017)

    2017

  15. [15]

    P. S. Alekseev.Phys. Rev. Lett.117, 166601 (2016)

    2016

  16. [16]

    F. M. D. Pellegrino, I. Torre and M. Polini.Phys. Rev. B96, 195401 (2017)

    2017

  17. [17]

    Sherafati, A

    M. Sherafati, A. Principi and G. Vignale.Phys. Rev. B 94, 125427 (2016)

    2016

  18. [18]

    Sherafati and G

    M. Sherafati and G. Vignale.Phys. Rev. B100, 115421 (2019)

    2019

  19. [19]

    A. I. Berdyugin et al.Science364, 162 (2019)

    2019

  20. [20]

    Cortijo, Y

    A. Cortijo, Y. Ferreiroś, K. Landsteiner and M. A. H. Vozmediano.arXiv:1506.05136

    Pith/arXiv arXiv

  21. [21]

    Heidari, A

    S. Heidari, A. Cortijo and R. Asgari.Phys. Rev. B100, 165427 (2019)

    2019

  22. [22]

    Read and E

    N. Read and E. H. Rezayi. Phys. Rev. B84, 085316 (2011)

    2011

  23. [23]

    Bradlyn, M

    B. Bradlyn, M. Goldstein and N. Read. Phys. Rev. B 86, 245309 (2009)

    2009

  24. [24]

    See Supplementary Material

  25. [25]

    Oliva-Leyva and G

    M. Oliva-Leyva and G. G. Naumis.Phys. Lett. A379, 2645 (2015)

    2015

  26. [26]

    G. E. Volovik and M. A. Zubkov.Ann. Phys.356, 255 (2015)

    2015

  27. [27]

    M. A. Zubkov and G. E. Volovik.J. Phys.: Conf. Ser. 607, 012020 (2015)

    2015

  28. [28]

    de Juan, J

    F. de Juan, J. L. Mañes and M. A. H. Vozmediano.Phys. Rev. B87, 165131 (2013)

    2013

  29. [29]

    Vanderbilt.J

    D. Vanderbilt.J. Phys. Chem. Sol.61, 147 (2000)

    2000

  30. [30]

    Theory of Polarization: A Modern Approach

    R. Resta and D. Vanderbilt. “Theory of Polarization: A Modern Approach.” in “Physics of Ferroelectrics: A Modern Perspective.” Eds. K. Rabe, C. H. Ahn and J.-M. Triscone. Springer (2007)

    2007

  31. [31]

    Droth, G

    M. Droth, G. Burkard and V. M. Pereira. arXiv:1604.01512v2

    Pith/arXiv arXiv

  32. [32]

    Selch, M

    M. Selch, M. A. Zubkov, S. Pramanik and M. Lewkowicz. Ann. Phys.482, 170202 (2025)

    2025

  33. [34]

    Van Mechelen and Z

    T. Van Mechelen and Z. Jacob.arXiv:1910.14288

    arXiv 1910

  34. [35]

    Van Mechelen, W

    T. Van Mechelen, W. Sun and Z. Jacob.Nat. Com.12, 4729 (2021)

    2021

  35. [36]

    Kim et. al.Phys. Rev. B112, L201404 (2025)

    2025

  36. [37]

    Selch, to be published

    M. Selch, to be published

  37. [38]

    M. N. Chernodub and M. Zubkov.Phys. Rev. D96, 056006 (2017)

    2017

  38. [39]

    Zhang and M

    C. Zhang and M. Zubkov.Jour. Phys. A: Mathematical and Theoretical53, 195002 (2020)

    2020

  39. [40]

    M. A. Zubkov and R. A. Abramchuk,Phys. Rev. D107, 094021 (2023)

    2023

  40. [41]

    Zubkov.Ann

    M. Zubkov.Ann. Phys.393, 264 (2018)

    2018

  41. [42]

    Zubkov and G

    M. Zubkov and G. Volovik.Nucl. Phys. B860, 295 (2012)

    2012

  42. [43]

    Volovik and M

    G. Volovik and M. Zubkov.New Jour. Phys.19, 015009 (2017)

    2017

  43. [44]

    G. E. Volovik and M. Zubkov.JETP Letters97, 301 (2013)

    2013

  44. [45]

    Bakker, A

    B. Bakker, A. Veselov, and M. Zubkov.Phys. Lett. B 7 471, 214 (1999)

    1999

  45. [46]

    Zhang and M

    C. Zhang and M. Zubkov.JETP Letters110, 487 (2019)

    2019

  46. [47]

    Abramchuk, Z

    R. Abramchuk, Z. Khaidukov, and M. Zubkov.Phys. Rev. D98, 076013 (2018)

    2018

  47. [48]

    Zubkov.JETP Letters106, 172 (2017)

    M. Zubkov.JETP Letters106, 172 (2017)

    2017

  48. [49]

    Bakker, A

    B. Bakker, A. Veselov, and M. Zubkov.Phys. Lett. B 620, 156 (2005)

    2005

  49. [50]

    Zubkov.Nucl

    M. Zubkov.Nucl. Phys. B938, 171 (2019)

    2019

  50. [51]

    Zubkov.Phys

    M. Zubkov.Phys. Rev. D92, 055004 (2015)

    2015

  51. [52]

    Emergent Hall viscosity in the integer quantum Hall phases of graphene-like systems

    Y. Hatsugai, T. Fukui, and H. Aoki.Phys. Rev. B74, 205414 (2006). Supplementary Material for “Emergent Hall viscosity in the integer quantum Hall phases of graphene-like systems” Appendix A: Spinorial gauge transformations We provide a detailed account of convenient spinor redefinitions employed in the main text and their consequences on the sublattice in...

    2006

  52. [53]

    The electronic properties of graphene

    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).arXiv:0709.1163v2

    Pith/arXiv arXiv 2009

  53. [54]

    Gauge fields from strain in graphene

    F. de Juan, J. L. Manes and M. A. H. Vozmediano. “Gauge fields from strain in graphene.”Phys. Rev. B.87, 165131 (2013).arXiv:1212.0924v2

    Pith/arXiv arXiv 2013

  54. [55]

    General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas

    D. T. Son and M. Wingate. “General coordinate invariance and conformal invariance in nonrelativistic physics: Unitary Fermi gas.”Ann. Phys.321, 197 (2006).arXiv:cond-mat/0509786

    Pith/arXiv arXiv 2006

  55. [56]

    Hall conductivity as the topological invariant in magnetic Brillouin zone in the presence of interactions

    M. Selch, M. Suleymanov, C. Z. Zhang and M. A. Zubkov. “Hall conductivity as the topological invariant in magnetic Brillouin zone in the presence of interactions.”Phys. Rev. B107, 245105 (2023).arXiv:2303.16327

    arXiv 2023

  56. [57]

    Non-renormalization of the Hall viscosity of integer and Jain fractional quantum Hall phases by Coulomb interactions

    M. Selch. “Non-renormalization of the Hall viscosity of integer and Jain fractional quantum Hall phases by Coulomb interactions.”arXiv:2602.12915

    arXiv

  57. [58]

    Non-renormalization of the fractional quantum Hall conductivity by interactions

    M. Selch, M. A. Zubkov, S. Pramanik and M. Lewkowicz. “Non-renormalization of the fractional quantum Hall conductivity by interactions.”Ann. Phys.482, 170202 (2025).arXiv:2502.04047

    arXiv 2025

  58. [59]

    Lectures on the Quantum Hall Effect

    D. Tong. “Lectures on the Quantum Hall Effect.”arXiv:1606.06687

    Pith/arXiv arXiv

  59. [60]

    Hall viscosity, topological states and effective theories

    C. Hoyos. “Hall viscosity, topological states and effective theories.” Int. Jour. Mod. Phys. B28, 1430007 (2014). arXiv:1403.4739v2

    Pith/arXiv arXiv 2014