Spin eigen-states of Dirac equation for quasi-two-dimensional electrons

Journal Article · Thu Oct 15 04:00:00 EDT 2015 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2015.07.007· OSTI ID:22451240

Eremko, Alexander ^[1]; Brizhik, Larissa ^[1]; Loktev, Vadim ^[1]

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1. Bogolyubov Institute for Theoretical Physics, Metrologichna Sttr., 14-b, Kyiv, 03680 (Ukraine)

Dirac equation for electrons in a potential created by quantum well is solved and the three sets of the eigen-functions are obtained. In each set the wavefunction is at the same time the eigen-function of one of the three spin operators, which do not commute with each other, but do commute with the Dirac Hamiltonian. This means that the eigen-functions of Dirac equation describe three independent spin eigen-states. The energy spectrum of electrons confined by the rectangular quantum well is calculated for each of these spin states at the values of energies relevant for solid state physics. It is shown that the standard Rashba spin splitting takes place in one of such states only. In another one, 2D electron subbands remain spin degenerate, and for the third one the spin splitting is anisotropic for different directions of 2D wave vector.

• OSTI ID: 22451240
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 361; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIRAC EQUATION
EIGENSTATES
ELECTRONS
ENERGY SPECTRA
HAMILTONIANS
QUANTUM WELLS
SPIN
TWO-DIMENSIONAL CALCULATIONS
VECTORS
WAVE FUNCTIONS