Klein Tunneling of Dirac Fermions through Electromagnetic Barriers
Abstract
The Lorentz covariance of relativistic Dirac equations serves as a fundamental principle underlying the laws of electromagnetism across different inertial frames. Exploiting the covariance, we obtain the general solutions for Dirac fermions under both the in-plane electric E and perpendicular magnetic B fields, which reduce to either a magnetic or electric field in the inertial frame with drift velocity along the E×B direction. This dichotomy defines the magnetic and electric regimes, separated by the critical field ratio E/B=vF with vF denoting the Fermi velocity of Dirac fermions. Using these solutions, we revisit Klein tunneling through a heterojunction with generalized electromagnetic potentials. In the magnetic regime, the transmission exhibits oscillations governed by the Fabry-Pérot interference. In the electric regime, perfect transmission occurs at normal incidence in the drifted frame. The interference phase is further analyzed in terms of the solid angles on the Bloch sphere, providing a geometric interpretation of Klein tunneling. Finally, we briefly discuss the relation between the tilting of Dirac cones and the in-plane electric field, establishing the correspondence of the undertilted and overtilted cases to the magnetic and electric regimes, respectively. Our findings reveal the manipulation of Klein tunneling by electromagnetic fields, offering a theoretical basis for designing novel electronic devices.
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BibTeX
@misc{zhang2026klein,
title = {{Klein Tunneling of Dirac Fermions through Electromagnetic Barriers}},
author = {Lingang Zhang and Hua Chen},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15287},
eprint = {2609.15287},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15287},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Klein Tunneling of Dirac Fermions through Electromagnetic Barriers
AU - Lingang Zhang
AU - Hua Chen
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.15287
UR - https://arxiv.org/abs/2609.15287
AB - The Lorentz covariance of relativistic Dirac equations serves as a fundamental principle underlying the laws of electromagnetism across different inertial frames. Exploiting the covariance, we obtain the general solutions for Dirac fermions under both the in-plane electric E and perpendicular magnetic B fields, which reduce to either a magnetic or electric field in the inertial frame with drift velocity along the E×B direction. This dichotomy defines the magnetic and electric regimes, separated by the critical field ratio E/B=v_F with v_F denoting the Fermi velocity of Dirac fermions. Using these solutions, we revisit Klein tunneling through a heterojunction with generalized electromagnetic potentials. In the magnetic regime, the transmission exhibits oscillations governed by the Fabry-Pérot interference. In the electric regime, perfect transmission occurs at normal incidence in the drifted frame. The interference phase is further analyzed in terms of the solid angles on the Bloch sphere, providing a geometric interpretation of Klein tunneling. Finally, we briefly discuss the relation between the tilting of Dirac cones and the in-plane electric field, establishing the correspondence of the undertilted and overtilted cases to the magnetic and electric regimes, respectively. Our findings reveal the manipulation of Klein tunneling by electromagnetic fields, offering a theoretical basis for designing novel electronic devices.
ER -