Topological Transverse Transport without a Gap in Critical Topological Flat Bands
Abstract
Quantized Hall transport is traditionally anchored to a bulk spectral gap, which isolates the occupied subspace and exponentially suppresses thermal deviations. Recently discovered critical topological flat bands (CTFBs) challenge this paradigm: an exactly flat band touches a dispersive continuum while retaining a well-defined integer Chern number. However, their finite-temperature transverse transport properties remain entirely unexplored. Here, we develop a low-temperature theory of the intrinsic electrical, thermoelectric, and thermal Hall responses in CTFBs. At fixed particle number, the macroscopic flat-band degeneracy forces a singular Lambert-W drift of the chemical potential, generating an algebraic-logarithmic hierarchy of low-temperature corrections: Tln(1/T) for electrical Hall, T[ln(1/T)]2 for thermoelectric Hall, and T[ln(1/T)]3 for thermal Hall conductivity, replacing the activated thermal protection of a gapped Chern insulator. By contrast, externally pinning the chemical potential to the flat-band energy locks the flat band to half occupation at any nonzero temperature, obstructing the recovery of the fully filled topological ground state as T→0+. Our results establish that a bulk spectral gap is unnecessary for zero-temperature Hall quantization, but indispensable for its exponential thermal protection.
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BibTeX
@misc{oh2026topological,
title = {{Topological Transverse Transport without a Gap in Critical Topological Flat Bands}},
author = {Chang-geun Oh and Tomoki Ozawa and Jun-Won Rhim},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.40065},
eprint = {2609.40065},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.40065},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Topological Transverse Transport without a Gap in Critical Topological Flat Bands
AU - Chang-geun Oh
AU - Tomoki Ozawa
AU - Jun-Won Rhim
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.40065
UR - https://arxiv.org/abs/2609.40065
AB - Quantized Hall transport is traditionally anchored to a bulk spectral gap, which isolates the occupied subspace and exponentially suppresses thermal deviations. Recently discovered critical topological flat bands (CTFBs) challenge this paradigm: an exactly flat band touches a dispersive continuum while retaining a well-defined integer Chern number. However, their finite-temperature transverse transport properties remain entirely unexplored. Here, we develop a low-temperature theory of the intrinsic electrical, thermoelectric, and thermal Hall responses in CTFBs. At fixed particle number, the macroscopic flat-band degeneracy forces a singular Lambert-W drift of the chemical potential, generating an algebraic-logarithmic hierarchy of low-temperature corrections: Tln(1/T) for electrical Hall, T[ln(1/T)]^2 for thermoelectric Hall, and T[ln(1/T)]^3 for thermal Hall conductivity, replacing the activated thermal protection of a gapped Chern insulator. By contrast, externally pinning the chemical potential to the flat-band energy locks the flat band to half occupation at any nonzero temperature, obstructing the recovery of the fully filled topological ground state as T→0^+. Our results establish that a bulk spectral gap is unnecessary for zero-temperature Hall quantization, but indispensable for its exponential thermal protection.
ER -