Group delay time of fermions in graphene through tilted potential barrier

TL;DR

This paper investigates how the group delay time of Dirac fermions in graphene can be controlled by barrier width, incident energy, and angle, with potential applications in graphene-based electronic devices.

Contribution

It provides a detailed analysis of the group delay time in graphene with a tilted potential barrier, highlighting the influence of various parameters and the possibility of control via gate voltage.

Findings

Group delay time depends on barrier width, energy, and incident angle.

Particles travel through the barrier at the Fermi velocity $v_F$.

Transmission group delay can be modulated, enabling potential device applications.

Abstract

The group delay time of Dirac fermions subjected to a tilting barrier potential along the $ x $-axis is investigated in graphene. We start by finding the eigenspinor solution of the Dirac equation and then relating it to incident, reflected, and transmitted beam waves. This relationship allows us to compute the group delay time in transmission and reflection by obtaining the corresponding phase shifts. We discovered that the barrier width, incident energy, and incident angle can all be used to modify the group delay time, and that the particles travel through the barrier at the Fermi velocity $ v_F $. Our findings also show that the transmission group delay might be controlled, and that gate voltage control could be useful in graphene-based tilting barriers.