Semiclassical Analysis of Tunneling in Graphene under Nonuniform Electrostatic and Magnetic Fields

Mathematical Physics [Submitted on 16 Jun 2026] Title:Semiclassical Analysis of Tunneling in Graphene under Nonuniform Electrostatic and Magnetic Fields View PDF HTML (experimental)Abstract:We develop a semiclassical theory of tunnelling of Dirac fermions through an n-p-n junction in monolayer graphene subjected to a perpendicular magnetic field. Electrostatic and magnetic fields are assumed to be smooth functions of a single spatial coordinate, supported on a finite interval, vanishing outside it, and thus ensuring asymptotically free states. In contrast to earlier studies restricted to constant magnetic fields and exactly solvable electrostatic potential profiles, we consider a general electrostatic potential forming an n-p-n junction and an arbitrary magnetic field, and formulate the corresponding scattering problem. Within the semiclassical approximation, and under an additional assumption on the incidence angle, the problem reduces to a connection problem for a pair of degeneracy points, treated using results from our earlier work. We obtain explicit expressions for the reflection and transmission coefficients, including their phases, as functions of energy and incidence angle. Furthermore, we derive semiclassical conditions for Fabry-Pérot resonances and "magic" angles, and analyse the resulting interference pattern. Numerical results demonstrate the angular dependence of transmission induced by the magnetic field. Current browse context: math-ph Change to browse by: References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.