Quantum confinement in circular graphene p – n junctions: A reproducible Kwant framework with density of states, LDOS, and magnetic field effects

We present a reproducible computational framework to investigate quantum confinement and transport in circular graphene p–n junctions using the Kwant package. The system consists of a finite circular graphene flake under a smooth electrostatic potential described by a hyperbolic tangent profile, forming a continuous p–n interface. Two non collinear semi-infinite graphene leads enable current injection and extraction. We compute the eigenvalue spectra, density of states, local density of states, and two-terminal conductance. The framework incorporates a perpendicular magnetic field through the Peierls phase, allowing analysis of magneto-confinement and Landau-like resonances. We further derive semiclassical confinement conditions from the Dirac equation, linking analytic estimates to numerical eigenstates. All simulations and figures are generated in a headless Python environment, ensuring full reproducibility. This work highlights the interplay between smooth electrostatic potentials, magnetic quantization, and finite size confinement in graphene nanostructures.