General solution of the Dirac equation for quasi-two-dimensional electrons

Journal Article · Wed Jun 15 04:00:00 EDT 2016 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2016.03.008· OSTI ID:22560325

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

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

The general solution of the Dirac equation for quasi-two-dimensional electrons confined in an asymmetric quantum well, is found. The energy spectrum of such a system is exactly calculated using special unitary operator and is shown to depend on the electron spin polarization. This solution contains free parameters, whose variation continuously transforms one known particular solution into another. As an example, two different cases are considered in detail: electron in a deep and in a strongly asymmetric shallow quantum well. The effective mass renormalized by relativistic corrections and Bychkov–Rashba coefficients are analytically obtained for both cases. It is demonstrated that the general solution transforms to the particular solutions, found previously (Eremko et al., 2015) with the use of spin invariants. The general solution allows to establish conditions at which a specific (accompanied or non-accompanied by Rashba splitting) spin state can be realized. These results can prompt the ways to control the spin degree of freedom via the synthesis of spintronic heterostructures with the required properties.

• OSTI ID: 22560325
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Journal Issue: Complete Vol. 369; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ASYMMETRY
DEGREES OF FREEDOM
DIRAC EQUATION
EFFECTIVE MASS
ELECTRON GAS
ELECTRONS
ENERGY SPECTRA
L-S COUPLING
MATHEMATICAL SOLUTIONS
QUANTUM WELLS
RELATIVISTIC RANGE
RENORMALIZATION
SPIN
SPIN ORIENTATION
TWO-DIMENSIONAL CALCULATIONS
VARIATIONS