Wave packet dynamics in hole Luttinger systems

Journal Article · Mon Mar 15 00:00:00 EDT 2010 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PHYSREVB.81.115206· OSTI ID:21366705

Demikhovskii, V Ya; Maksimova, G M; Frolova, E V ^[1]

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1. Nizhny Novgorod State University, Gagarin Avenue, 23, Nizhny Novgorod 603950 (Russian Federation)

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 4x4 Luttinger Hamiltonian. We work in the space of arbitrary superposition of light- and heavy-hole states of the ''one-particle system.'' For strong anisotropic packets in three-dimensional semiconductors 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{sub 0}d (k{sub 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 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.

• OSTI ID: 21366705
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Vol. 81, Issue 11; Other Information: DOI: 10.1103/PhysRevB.81.115206; (c) 2010 The American Physical Society; ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ANALYTICAL SOLUTION
ANISOTROPY
DENSITY
DISTRIBUTION
HAMILTONIANS
INTERFERENCE
MAGNETIC FIELDS
OSCILLATIONS
PARTICLES
POLARIZATION
PRECESSION
PROBABILITY
SEMICONDUCTOR MATERIALS
SIMULATION
SPACE-TIME
SPIN
SYMMETRY
THREE-DIMENSIONAL CALCULATIONS
TRANSIENTS
WAVE FUNCTIONS
WAVE PACKETS
ZITTERBEWEGUNG
ANGULAR MOMENTUM
FUNCTIONS
MATERIALS
MATHEMATICAL OPERATORS
MATHEMATICAL SOLUTIONS
PARTICLE PROPERTIES
PHYSICAL PROPERTIES
QUANTUM OPERATORS