Transverse force generated by an electric field and transverse charge imbalance in spin-orbit coupled systems by an electric field and transverse charge imbalance in spin-orbit coupled systems

Abstract

We use linear-response theory to study the transverse force generated by an external electric field and hence possible charge Hall effect in spin-orbit coupled systems. In addition to the Lorentz force that is parallel to the electric field, we find that the transverse force perpendicular to the applied electric field may not vanish in a system with an anisotropic energy dispersion. Surprisingly, in contrast to the previous results, the transverse force generated by the electric field does not depend on the spin current, but in general, it is related to the second derivative of energy dispersion only. The transverse force always vanishes in the system with an isotropic energy dispersion. However, the transverse force may also vanish in some systems with an anisotropic energy dispersion such as the two-dimensional k-cubic Dresselhaus system. Furthermore, we find that the transverse force does not vanish in the Rashba-Dresselhaus system. Therefore, the nonvanishing transverse force acts as a driving force and results in charge imbalance at the edges of the sample. This implies that a nonzero Hall voltage can be detected in the absence of an external magnetic field in anisotropic systems such as the Rashba-Dresselhaus system. The estimated ratio of the Hall voltage to the longitudinal voltage is ∼10−3. The disorder effect is also considered in the study of the Rashba-Dresselhaus system. We find that the transverse force vanishes in the presence of impurities in this system because the vertex correction and the anomalous velocity of the electron accidently cancel each other. Nonetheless, we believe that the transverse charge imbalance can be detected in the ballistic region by measuring the Hall voltage. Our interesting prediction would stimulate measurements of the Hall voltage in such spin-orbit coupled systems with an anisotropic dispersion as the Rashba-Dresselhaus system in the near future.