Abstract The spin-dependent group delay time and the Hartman effect in the ferromagnetic monolayer graphene electrostatic barrier are theoretically studied with a time-dependent oscillating potential. It was found that the spin-dependent group delay time could be controlled by adjusting the amplitude of the oscillating potential. The results showed that for an electron beam at an oblique angle of incidence, unlike the normal angle, the spin-dependent group delay time depends on the sign of n for the nth sideband. Interestingly, for the central band, the Hartman effect can be observed for all angles of incidence. Whereas, for the sidebands, this phenomenon can only occur when the angle of incidence is larger than the critical angle ( φ ≥ π / 6 ).

中文翻译：

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具有时间周期电位的石墨烯中的自旋相关群延迟时间

摘要 利用瞬态振荡电位从理论上研究了铁磁单层石墨烯静电势垒中的自旋相关群延迟时间和哈特曼效应。发现可以通过调节振荡电位的幅度来控制与自旋相关的群延迟时间。结果表明，对于倾斜入射角的电子束，与法向角不同，自旋相关群延迟时间取决于第 n 个边带的 n 符号。有趣的是，对于中心带，可以观察到所有入射角的哈特曼效应。而对于边带，这种现象只有在入射角大于临界角 (φ ≥ π / 6 ) 时才会发生。