Non-Hermitian Zitterbewegung Effect

We investigate the general form of the Zitterbewegung (ZB) effect in non-Hermitian systems for a multi-band Hamiltonian depending on momentum, where the ZB effect is the multifrequency oscillatory motion of the quasiparticle. We propose a real non-Hermitian Luttinger Hamiltonian that describes holes near the top of the valence band in common zinc-blende and diamond-structured semiconductors (GaAs, Si, Ge, etc.) and enables the observation of the ZB effect. By evaluating the dynamical evolution of light and heavy holes, we demonstrate that non-Hermiticity acts as an amplifier for ZB oscillations. This amplification, rooted in the complex energy spectrum, allows us to predict the maximal enhancement of transient ZB oscillations within the short-time physical window. An experimental scheme is proposed to observe the ZB effect by measuring the motion of the holes. Our findings offer a new perspective on the transport properties of open quantum systems and semiconductor carrier transport.