电磁场调制下石墨烯中Hartman效应的研究

Hartman Effect in Single-layer Graphene with Combined Electric and Magnetic Field Modulation

从理论上研究了电磁场调制下非本征石墨烯中的Hartman效应。利用相位移动及传递矩阵的方法计算粒子隧穿的群延迟时间τg,系统地分析群延迟时间与不同参数(如粒子能量E、入射角度θ、电磁场强度U和A珤等)之间的关系。石墨烯中的载流子是狄拉克费米子,故用狄拉克方程表征。研究发现在势垒宽度足够大时,石墨烯中的狄拉克费米子隧穿通过势垒的群延迟时间τg与势垒宽度无关,证明Hartman效应不仅存在于静电场下零带隙的石墨烯中,还存在于电磁场调制下非本征(非零带隙)的石墨烯中。

The Hartman effect in single-layer graphene, where a bandgap can be generated at the Dirac point under the modulation of combined electric and magnetic fields, was investigated theoretically. The group delay time re was calculated with phase shift and transfer-matrix, wherein the particles were described by the massless Dirac equation rather than the Schr6dinger equation, re was also analyzed as a function of several parameters （energy E, incident angle 0, electric and magnetic field U and .4）. It is shown that the tunneling time becomes independent of barrier length for thick enough barriers, which indicates that the Hartman effect exists, where a bandgap can be generated at the Dirac point under the modulation of combined electric and magnetic fields.