Electronic Effects of a Twisted Graphene Catenoid Bridge
Abstract
The interplay between non-trivial background geometries and quantum dynamics has emerged as a powerful tool to tailor the electronic properties of 2D materials. In this work, we investigate the effective quantum dynamics of massless Dirac fermions confined to a twisted graphene structure called a catenoid bridge, which connects two single-layer sheets. By adopting a continuum approach, where the electron dynamics is governed by a purely covariant curved Dirac equation, we obtain the effective Hamiltonian containing both curvature and twist interactions. We found that the torsion modifies the electronic states by producing a geometric phase on the wave function. In addition, the twist also deforms the surface geometry, which leads to a new geometric term in the effective Hamiltonian. This twist potential enhances the barrier around the catenoid throat, which increases the suppression of the inter-layer transmission coefficient. Like the spin-curvature interaction, the spin-twist term has a chiral dependence which is invariant under a combined parity and spin flip transformation. As a result, the electronic states can be restricted to the upper or lower layer. These findings provide valuable insights into how mechanical deformations can be harnessed to control quantum transport in graphene-based wormhole architectures.
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BibTeX
@misc{delgado2026electronic,
title = {{Electronic Effects of a Twisted Graphene Catenoid Bridge}},
author = {G. M. Delgado and J. E. G. Silva},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26988},
eprint = {2609.26988},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26988},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Electronic Effects of a Twisted Graphene Catenoid Bridge
AU - G. M. Delgado
AU - J. E. G. Silva
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.26988
UR - https://arxiv.org/abs/2609.26988
AB - The interplay between non-trivial background geometries and quantum dynamics has emerged as a powerful tool to tailor the electronic properties of 2D materials. In this work, we investigate the effective quantum dynamics of massless Dirac fermions confined to a twisted graphene structure called a catenoid bridge, which connects two single-layer sheets. By adopting a continuum approach, where the electron dynamics is governed by a purely covariant curved Dirac equation, we obtain the effective Hamiltonian containing both curvature and twist interactions. We found that the torsion modifies the electronic states by producing a geometric phase on the wave function. In addition, the twist also deforms the surface geometry, which leads to a new geometric term in the effective Hamiltonian. This twist potential enhances the barrier around the catenoid throat, which increases the suppression of the inter-layer transmission coefficient. Like the spin-curvature interaction, the spin-twist term has a chiral dependence which is invariant under a combined parity and spin flip transformation. As a result, the electronic states can be restricted to the upper or lower layer. These findings provide valuable insights into how mechanical deformations can be harnessed to control quantum transport in graphene-based wormhole architectures.
ER -