An Unusual Dresselhaus Spin-Orbit Contribution of Even Order in Momentum

Abstract

The spin-orbit (SO) coupling is conventionally known to manifest as \emph{odd} functions of momentum. Here, through both model calculations and symmetry analysis along with the method of invariants, we reveal that, in ordinary semiconductor heterostructures, a \emph{quadratic} Dresselhaus SO term -- inheriting from its bulk crystal form -- emerges via the interband effect, while complying with time-reversal and spatial symmetries. Furthermore, we observe that this unusual SO term gives rise to a range of striking quantum phenomena, including hybridized swirling texture, anisotropic energy dispersion, avoided band crossing, longitudinal \emph{Zitterbewegung}, and opposite spin evolution between different bands in quantum dynamics. These stand in stark contrast to those associated with the usual \emph{linear} SO terms. Our findings uncover a previously overlooked route for exploiting interband effects and open new avenues for spintronic functionalities that leverage unusual SO terms of \emph{even} orders in momentum.