Wave packet dynamics in hole Luttinger systems

Abstract

For hole systems with an effective spin 3/2 we analyzed analytically and numerically the evolution of wave packets with the different initial polarizations. The dynamics of such systems is determined by the $4\times 4$ Luttinger Hamiltonian. We work in the space of arbitrary superposition of light- and heavy-hole states of the "one-particle system". For 2D packets we obtained the analytical solution for the components of wave function and analyzed the space-time dependence of probability densities as well as angular momentum densities. Depending on the value of the parameter $a=k_{0}d$ ($k_0$ is the average momentum vector and $d$ is the packet width) two scenarios of evolution are realized. For $a>>1$ the initial wave packet splits into two parts and the coordinates of packet center experience the transient oscillations or {\it Zitterbewegung} (ZB) as for other two-band systems. In the case when $a<<1$ the distribution of probability density at $t>0$ remains almost cylindrically symmetric and the ripples arise at the circumference of wave packet. The ZB in this case is absent. We evaluated and visualized for different values of parameter $a$ the space-time dependence of angular momentum densities, which have the multipole structure. It was shown that the average momentum components can precess in the absence of external or effective magnetic fields due to the interference of the light- and heavy hole states. For localized initial states this precession has a transient character.

9 pages, 8 gigure

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• Space-time evolution of Dirac wave packets
• Wave packet dynamics and zitterbewegung of heavy holes in a quantizing magnetic field
• The long-term cyclotron dynamics of relativistic wave packets: spontaneous collapse and revival
• Zitterbewegung of electrons in carbon nanotubes created by laser pulses
• Wave packet dynamics in monolayer MoS${}_2$ with and without a magnetic field
• RKKY interaction in Mn-doped 4 $\times$ 4 Luttinger systems
• Electrical and optical conductivities of hole gas in $p$-doped bulk III-V semiconductors