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Quantum Flatland and Monolayer Graphene from a Viewpoint of Geometric Algebra

100%
Dargys A.
Acta Physica Polonica A
|
2013
|
vol. 124
|
issue 4
732-739
EN
Quantum mechanical properties of the graphene are, as a rule, treated within the Hilbert space formalism. However a different approach is possible using the geometric algebra, where quantum mechanics is done in a real space rather than in the abstract Hilbert space. In this article the geometric algebra is applied to a simple quantum system, a single valley of monolayer graphene, to show the advantages and drawbacks of geometric algebra over the Hilbert space approach. In particular, 3D and 2D Euclidean space algebras Cl_{3, 0} and Cl_{2, 0} are applied to analyze relativistic properties of the graphene. It is shown that only three-dimensional Cl_{3, 0} rather than two-dimensional Cl_{2, 0} algebra is compatible with a relativistic flatland.
2
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Valence Band of Cubic Semiconductors from Viewpoint of Clifford Algebra

100%
Dargys A.
Acta Physica Polonica A
|
2009
|
vol. 116
|
issue 2
226-231
EN
In this paper the properties of semiconductors having cubic symmetry are considered in a real multidimensional Euclidean space within the formalism of multivector Clifford algebra rather than, usually used for this purpose, complex Hilbert space. In particular, it is demonstrated how the valence band energy spectrum and spin properties may be calculated within Cl_5 Clifford algebra and SO(5) symmetry group related with it.
3
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Double Reflection of Electron Spin in Semiconductors

100%
Dargys A.
Acta Physica Polonica A
|
2011
|
vol. 119
|
issue 2
161-163
EN
Reflection of spin-polarized electron from a potential barrier in bulk semiconductor in the presence of spin-orbit interaction is considered. The spin-orbit interaction brings about double electron reflection at oblique incidence of electronic beam onto the barrier. The competition between the Rashba and Dresselhaus spin-orbit mechanisms during double reflection is discussed. The problem was solved within the Clifford algebra framework, which allows one to describe the spin in a real Euclidean ℰ_3 space rather than in an abstract Hilbert space.
4
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Control of Valence-Band Hole Spin by Electric Field

100%
Dargys A.
Acta Physica Polonica A
|
2004
|
vol. 105
|
issue 3
295-306
EN
Coherent properties of the hole spin in an electric field are investigated. The tunneling between valence bands is used to control the transitions between the spin states. Extensive numerical studies using the time-dependent Schrödinger equation for valence band are presented to demonstrate the characteristic properties of the hole spin dynamics in dc, harmonic, as well as optimized electric fields for real valence bands of silicon. The paper also shows how one can connect the average hole spin with the initial hole wave function in the time-dependent Schrödinger equation.
5
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Spin Conductance of the Quantum Wire

100%
Dargys A.
Acta Physica Polonica A
|
2008
|
vol. 113
|
issue 3
937-942
EN
Spin transport in a semiconducting quantum wire connected to two spin-unpolarized electron reservoirs is investigated. The spin-orbit interaction is included via the Rashba Hamiltonian which together with the Zeeman Hamiltonian determines spin-filtering properties of the wire. The spin current as a function of the voltage was found to have an oscillatory or growing character.
6
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Semiconductor Spintronics: Role of the Valence-Band Holes

100%
Dargys A.
|
EN
Two aspects related to valence-band hole spin are considered: spin surfaces in p-type semiconductors and flipping of the hole spin by an ultrashort electric field pulse. It is shown that heavy, light, and split-off holes have different spin surfaces. In general, the shape of the surface in real semiconductors may depend on the hole wave vector direction and magnitude. The concept of spin surface is used to explain very strong anisotropy of hole spin injection efficiency observed recently in ferromagnetic-semiconductor structures and in optimizing ultrafast spin switching. It was shown that, of all spin flipping mechanisms, the most effective one is associated with hole transfer between different spin surfaces in high electric fields. The less effective mechanisms are related to valence band warping and nonparabolicity. Examples of the hole spin flipping dynamics and the discussion on ultrafast control of spin in semiconductors by π-type electrical pulses are presented.
7
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Acoustic Phonon Activated and Assisted Tunnelling in Ge:Sb,P

64%
Žurauskienė N., Dargys A.
Acta Physica Polonica A
|
1996
|
vol. 90
|
issue 5
993-996
EN
The influence of lattice vibrations on the field ionization rate of shallow donors in germanium at low lattice temperatures is investigated experimentally and theoretically. The role played by acoustic phonons in the tunnelling of electrons from the ground donor level (phonon assisted tunnelling) and through the excited donor levels (phonon activated tunnelling) is considered. Both processes are shown to enhance the tunnelling rate.
8
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Field Ionization of Shallow Acceptors

51%
Dargys A., Žurauskas S., Žurauskienė N.
Acta Physica Polonica A
|
1993
|
vol. 84
|
issue 4
629-632
EN
Experimental studies on hole tunneling from the substitutional boron impurity into degenerate valence band of silicon single crystals are presented. The results are interpreted within the framework of acceptor ground state quartet splitting into the Kramers doublet due to presence of random strains and electric field in the lattice.
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