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

Abstract

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.

Wave packet dynamics in various two-dimensional systems: A unified description

“…Note that the expectation values of the position and velocity operators for systems with k-cubic Rashba SOI have recently been reported in Ref. [15], and are presented here for completeness, and to emphasize that they can be derived from our unified description. The oscillation, classical, and revival timescales are now given by,…”

“…Zitterbewegung and wave-packet dynamics in several 2D condensed matter systems with Landau-levels have been explored earlier [10][11][12][13][14][15][16], but the phenomena of spontaneous collapse and revival has largely gone unaddressed [17][18][19]. Motivated by the unified description of zitterbewegung in solid state systems in Refs.…”

Effect of zitterbewegung on the propagation of wave packets in ABC-stacked multilayer graphene: an analytical and computational approach

“…In the last decades, Schrödinger's idea stimulated numerous theoretical studies e.g. in ultracold atoms [3,4], semiconductors [5][6][7][8][9][10], carbon nanotubes [11], topological insulators [12], crystalline solids [13,14] and other systems [15][16][17][18]. Although ZBW was theoretically found using a quantum simulation of the Dirac equation for trapped ions [19], Bose-Einstein condensates [20][21][22] and, most recently, an optical simulation [23], up to now, no direct experimental observations have been carried out.…”

Generating a topological anomalous Hall effect in a non-magnetic conductor

“…Since the equilibrium system is not magnetized the effect is tunable in situ by altering the magnetic field orientation. It is observable in state-of-theart hole samples, which are developing at a brisk pace, motivated in part by quantum computing applications [40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57], where holes are actively investigated [58][59][60], by their large spin-orbit coupling [61][62][63], interesting transport properties [64][65][66][67][68], and by unconventional properties stemming from their spin-3/2 nature [69][70][71][72][73][74][75][76][77][78][79][80][81][82]. We consider a two-dimensional hole gas grown along (113).…”