---
OA_place: repository
OA_type: green
_id: '22404'
abstract:
- lang: eng
  text: We consider a class of two-dimensional tight binding models displaying conical
    intersections of the Bloch bands at the Fermi level. The setting includes the
    case of generic transitions between quantum Hall phases. We consider the longitudinal
    conductivity, as given by Kubo formula, describing the variation of the current
    after introducing a space-homogeneous electric field, in an adiabatic way. We
    obtain an explicit expression for the longitudinal conductivity, completely determined
    by the number of conical intersections and by the shape of the cones. In particular,
    the formula reproduces the known quantized values found for graphene and for the
    critical Haldane model. Furthermore, we discuss the validity of Kubo formula in
    presence of conical intersections in the spectrum, starting from the time-dependent
    Schrödinger equation. For electric fields which are weak and slowly varying in
    space and in time, we prove the validity of linear response from quantum dynamics.
acknowledgement: G. M. and M. P. acknowledge support by the European Research Council
  through the ERC-StG MaMBoQ, n. 802901. G. M. acknowledges financial support from
  the Independent Research Fund Denmark–Natural Sciences, grant DFF–10.46540/2032-00005B
  and from the European Research Council through the ERC CoG UniCoSM, grant agreement
  n.724939. M. P. acknowledges support from the MUR, PRIN 2022 project MaIQuFi cod.
  20223J85K3. This work has been carried out under the auspices of the GNFM of INdAM.
  We thank the anonymous referees for comments on a previous version of this manuscript.
article_number: '82'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giovanna
  full_name: Marcelli, Giovanna
  last_name: Marcelli
- first_name: Lorenzo
  full_name: Pigozzi, Lorenzo
  id: efb8f850-3208-11ee-ac71-8c4f5803b9c6
  last_name: Pigozzi
- first_name: Marcello
  full_name: Porta, Marcello
  last_name: Porta
citation:
  ama: Marcelli G, Pigozzi L, Porta M. Longitudinal conductivity at integer quantum
    Hall transitions. <i>Letters in Mathematical Physics</i>. 2026;116(4). doi:<a
    href="https://doi.org/10.1007/s11005-026-02087-3">10.1007/s11005-026-02087-3</a>
  apa: Marcelli, G., Pigozzi, L., &#38; Porta, M. (2026). Longitudinal conductivity
    at integer quantum Hall transitions. <i>Letters in Mathematical Physics</i>. Springer
    Nature. <a href="https://doi.org/10.1007/s11005-026-02087-3">https://doi.org/10.1007/s11005-026-02087-3</a>
  chicago: Marcelli, Giovanna, Lorenzo Pigozzi, and Marcello Porta. “Longitudinal
    Conductivity at Integer Quantum Hall Transitions.” <i>Letters in Mathematical
    Physics</i>. Springer Nature, 2026. <a href="https://doi.org/10.1007/s11005-026-02087-3">https://doi.org/10.1007/s11005-026-02087-3</a>.
  ieee: G. Marcelli, L. Pigozzi, and M. Porta, “Longitudinal conductivity at integer
    quantum Hall transitions,” <i>Letters in Mathematical Physics</i>, vol. 116, no.
    4. Springer Nature, 2026.
  ista: Marcelli G, Pigozzi L, Porta M. 2026. Longitudinal conductivity at integer
    quantum Hall transitions. Letters in Mathematical Physics. 116(4), 82.
  mla: Marcelli, Giovanna, et al. “Longitudinal Conductivity at Integer Quantum Hall
    Transitions.” <i>Letters in Mathematical Physics</i>, vol. 116, no. 4, 82, Springer
    Nature, 2026, doi:<a href="https://doi.org/10.1007/s11005-026-02087-3">10.1007/s11005-026-02087-3</a>.
  short: G. Marcelli, L. Pigozzi, M. Porta, Letters in Mathematical Physics 116 (2026).
das_tickbox: '1'
dataavailabilitystatement: Data sharing is not applicable to this article as no datasets
  were generated or analyzed during the current study.
date_created: 2026-07-26T22:01:40Z
date_published: 2026-08-01T00:00:00Z
date_updated: 2026-07-29T10:51:55Z
day: '01'
department:
- _id: RoSe
- _id: GradSch
doi: 10.1007/s11005-026-02087-3
external_id:
  arxiv:
  - '2503.01381'
intvolume: '       116'
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.2503.01381
mathsc:
- 81V70
month: '08'
oa: 1
oa_version: Preprint
publication: Letters in Mathematical Physics
publication_identifier:
  eissn:
  - 1573-0530
  issn:
  - 0377-9017
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: not applicable
scopus_import: '1'
status: public
supplementarymaterial: no
title: Longitudinal conductivity at integer quantum Hall transitions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 116
year: '2026'
...