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.

Graphical abstract

FIG. 1. (color online) The group delay time in transmission tt/t0 as a function of the barrier width d for V0 = V1 = 80 meV, f = \(30^\circ \) , E = 20 meV (blue line), E = 25 meV (red line), and E = 30 meV (green line).

中文翻译：

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石墨烯中费米子通过倾斜势垒的群延迟时间

摘要

在石墨烯中研究了沿x轴受到倾斜势垒电位的狄拉克费米子的群延迟时间。我们首先找到狄拉克方程的本征旋量解，然后将其与入射、反射和透射的光束波相关联。这种关系允许我们通过获得相应的相移来计算传输和反射中的群延迟时间。我们发现势垒宽度、入射能量和入射角都可以用来修改群延迟时间，并且粒子以费米速度\( v_F \)穿过势垒。我们的研究结果还表明，传输群延迟可以被控制，并且栅极电压控制在基于石墨烯的倾斜势垒中可能有用。

图形概要

如图。1.（在线颜色）传输中的群延迟时间 tt/t0 作为势垒宽度 d 的函数 V0 = V1 = 80 meV, f = \(30^\circ \) , E = 20 meV（蓝线） ，E = 25 meV（红线）和 E = 30 meV（绿线）。