Energy-gap--controlled current oscillations in graphene under periodic driving

TL;DR

This paper analyzes how an induced energy gap in graphene affects current oscillations under periodic driving, revealing that the gap controls oscillation amplitude, sign, and resonance, with implications for nanoelectronic device design.

Contribution

It provides analytical solutions for current density in gapped graphene under periodic potentials, highlighting the tunable control of Josephson-like oscillations by the energy gap.

Findings

Current oscillations diminish as the energy gap increases.

The sign and amplitude of current depend on the gap magnitude.

Resonance effects weaken with larger energy gaps.

Abstract

We investigate the impact of an induced mass term $\Delta$ on the current density in graphene subjected to a space- and time-dependent periodic potential $U(x,t)$. By solving the Dirac equation and deriving both the quasi-energy spectrum and the corresponding eigenspinors, we obtain explicit analytical expressions for the current density, which exhibits a clear dependence on $\Delta$. We show that $\Delta$ acts as a tunable control parameter that governs the amplitude, sign, and resonance structure of Josephson-like current oscillations. For normal incidence and a purely time-periodic potential, our results reveal that the oscillations within the energy gap gradually diminish as the mass term $\Delta$ increases. This suppression leads to a weakening of the Josephson-like effect typically observed in such systems. When the potential $U(x,t)$ is periodic in both space and time, the behavior becomes more complex. The current density can take either positive or negative values depending on the magnitude of the induced gap, and it generally decreases over time. As a result, the resonance phenomena--prominent at lower gap values--become progressively less significant as $\Delta$ increases. These findings underscore the tunable nature of light-matter interactions and quantum transport in gapped graphene, suggesting potential applications in terahertz (THz) nanoelectronic devices and optically controlled quantum switches.