Local phase-space Berry curvature and Hall transport in textured twisted bilayer graphene
Abstract
Slow twist-angle and heterostrain textures in twisted bilayer graphene provide a natural route to phase-space Berry geometry. We show that a purely geometric tetrad/shift sector does not generate mixed Berry curvature once the spin connection is treated consistently. By contrast, a projected textured mini-Dirac cone in twisted bilayer graphene acquires genuine mixed phase-space curvature. We analyze a controlled local Hall-bar limit with a one-dimensional texture and mirror Mx. In that limit the pseudogauge gradient renormalizes only the longitudinal conductivity along the textured direction, while a dc nonlinear Hall response appears only when an additional valley-odd tilt generates a Berry-curvature dipole. Both geometric responses peak at the same local filling, μloc=√2 m, providing a gate-tunable fingerprint of their common origin. All local-cone parameters and their texture susceptibilities are extracted from a heterostrained Bistritzer-MacDonald model at θ=1.3∘. The tilt invoked in the transport estimates corresponds to heterostrain of only 0.03%−0.2%, below values routinely imaged in devices. The resulting theory provides a local analytic framework for textured moiré Dirac materials and cleanly separates geometric, texture-induced, and transport-level ingredients relevant to realistic TBG.
Versions
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BibTeX
@misc{farajollahpour2026local,
title = {{Local phase-space Berry curvature and Hall transport in textured twisted bilayer graphene}},
author = {Tohid Farajollahpour},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.30882},
eprint = {2608.30882},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.30882},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Local phase-space Berry curvature and Hall transport in textured twisted bilayer graphene
AU - Tohid Farajollahpour
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.30882
UR - https://arxiv.org/abs/2608.30882
AB - Slow twist-angle and heterostrain textures in twisted bilayer graphene provide a natural route to phase-space Berry geometry. We show that a purely geometric tetrad/shift sector does not generate mixed Berry curvature once the spin connection is treated consistently. By contrast, a projected textured mini-Dirac cone in twisted bilayer graphene acquires genuine mixed phase-space curvature. We analyze a controlled local Hall-bar limit with a one-dimensional texture and mirror M_x. In that limit the pseudogauge gradient renormalizes only the longitudinal conductivity along the textured direction, while a dc nonlinear Hall response appears only when an additional valley-odd tilt generates a Berry-curvature dipole. Both geometric responses peak at the same local filling, μ_loc=√2 m, providing a gate-tunable fingerprint of their common origin. All local-cone parameters and their texture susceptibilities are extracted from a heterostrained Bistritzer-MacDonald model at θ=1.3^∘. The tilt invoked in the transport estimates corresponds to heterostrain of only 0.03%−0.2%, below values routinely imaged in devices. The resulting theory provides a local analytic framework for textured moiré Dirac materials and cleanly separates geometric, texture-induced, and transport-level ingredients relevant to realistic TBG.
ER -