二维Bloch电子在电场与磁场中的准经典输运行为

QUASI CLASSICAL TRANSPORT OF TWO DIMENSIONAL BLOCH ELECTRONS UNDER ELECTRIC AND MAGNETIC FIELDS *

分别从周期场中电子准经典运动方程和作者之一最近提出的输运平衡方程出发，分析了二维Ｂｌｏｃｈ电子在电场和磁场作用下的准经典输运，给出了不同电场下电子纵向漂移速度ｖｘ和霍耳漂移速度ｖｙ随磁场的变化趋势．结果显示，ｖｘ和ｖｙ均随磁场连续变化，在任何给定电场下都没有发现纵向漂移速度或霍耳漂移速度随磁感应强度发生突变．这一结论与其他作者的预言相左．分析了造成分歧的可能原因，并指出：在电子准经典运动方程中直接引入阻尼力来描述准经典输运的办法有其局限性．

Abstract  We present a theoretical study of quasi classical transport of two dimensional Bloch electrons under the influence of an electric and a magnetic fields, starting respectively from the quasi classical equation of motion of electrons and from the balance equations proposed by one of the authors. The electron longitudinal velocity v x and the Hall drift velocity v y are calculated as functions of the magnetic field under different strengths of the applied electric field. It is shown that both v x and v y always change continuously with variation of magnetic field. No sudden jump in the v x B or the v y B curve has been found at any given electric field, in contradiction with the claim made in a recent paper published in Acta Physica Sinica (vol. 46). The possible cause for this disagreement is discussed. Furthermore, we point out that the validity of the naive way to study electron transport by directly introducing a damping force into the quasi classical equation of motion of electron is quite limited.