Transmissions in Graphene through Double Barriers and Periodic Potential

TL;DR

This paper investigates how Dirac fermions in graphene transmit through double barriers under magnetic and oscillating potentials, revealing complex quantum interference effects and energy quantization.

Contribution

It introduces a model combining magnetic fields and time-varying potentials in graphene, analyzing resulting quantum states with high degeneracy and addressing computational challenges.

Findings

Quantum interference significantly affects tunneling.

Energy states are doubly quantized with high degeneracy.

Numerical analysis focused on central and adjacent energy bands.

Abstract

Transmission of Dirac fermions through a chip of graphene under the effect of magnetic field and a time vibrating double barrier with frequency $w$ is investigated. Quantum interference within the oscillating barrier has an important effect on quasi-particles tunneling. A combination of both a time dependent potential and a magnetic field generate physical states whose energy is double quantified by the pair of integers $(n, l)$ with high degeneracy. The large number of modes that exist in the energy spectrum presents a colossal difficulty in numerical computations. Thus we were obliged to make a truncation and limit ourselves to the central $(n = 0)$ and two adjacent side band ($n=\pm 1$).