# Transmission in Graphene through Time-oscillating Linear Barrier

## TL;DR

This paper investigates how Dirac fermions in graphene transmit through a time-oscillating linear barrier, deriving transmission probabilities for multiple modes by solving the Dirac equation and constructing a transfer matrix.

## Contribution

It introduces a method to analyze transmission in graphene with a time-dependent barrier by solving the Dirac equation and calculating transmission for multiple oscillation modes.

## Key findings

- Transmission probabilities depend on oscillation modes
- Numerical approach limited to low quantum channels
- Provides a framework for analyzing time-dependent barriers in graphene

## Abstract

Transmission probabilities of Dirac fermions in graphene under linear barrier potential oscillating in time are investigated. Solving Dirac equation we end up with the solutions of the energy spectrum depending on several modes coming from the oscillations. These will be used to obtain a transfer matrix that allows to determine transmission amplitudes of all modes. Due to numerical difficulties in truncating the resulting coupled channel equations, we limit ourselves to low quantum channels, i.e. $l = 0, \pm1$, and study the three corresponding transmission probabilities.