Wave packet dynamics and zitterbewegung of heavy holes in a quantizing magnetic field

In this work we study wave packet dynamics and $zitterbewegung$, an oscillatory quantum motion, of heavy holes in III-V semiconductor quantum wells in presence of a quantizing magnetic field. It is revealed that a Gaussian wave-packet describing a heavy hole diffuses asymmetrically along the circular orbit while performing cyclotron motion. The wave packet splits into two peaks with unequal amplitudes after a certain time depending on spin-orbit coupling constant. This unequal splitting of the wave packet is attributed to the cubic Rashba interaction for heavy holes. The difference in the peak amplitudes disappears with time. At a certain time the two peaks diffuse almost along the entire cyclotron orbit. Then tail and head of the diffused wave packet interfere and as a result a completely randomized pattern of the wave packet is observed. The diffusion rate of the wave packet increases with increase of the spin-orbit interaction strength. Also strong spin-orbit coupling expedite the splitting and the randomization of the wave packet. We also study the $zitterbewegung$ in various physical observables such as position, charge current and spin angular momentum of the heavy hole. The $zitterbewegung$ oscillations are very much sensitive to the initial wave vector of the Gaussian wave packet and the strength of the Rashba spin-orbit coupling.