Eight-band<b>k</b>⋅<b>p</b>model of strained zinc-blende crystals

Bahder, Thomas B.

doi:10.1103/physrevb.41.11992

Cited by 483 publications

(293 citation statements)

References 26 publications

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“…Surprisingly, the spin splitting is more of a BIA-type rather than an SIA-type, contradicting the conventional knowledge that an SIA-type term described by H 2 is responsible for spin splitting in strained semiconductors [23,25,26,27,28,29]. Theoretically, the Dresselhaus term H 1 is a bulkinversion asymmetry term that appears even in the absence of strain.…”

Section: Fig 1: Direction Of the Internal Magnetic Fieldcontrasting

confidence: 41%

“…Upon straining, the matrix elements between the conduction and valence band have the form s|ǫ xy |z (plus cyclic permutations) where |s is the s-orbital and |z is one of the p orbitals. Through perturbation theory, one can compute the effect of this valence-conduction band interaction when projected to the conduction band and obtain the conduction band effective Hamiltonian H 2 [23,26,27,28]. Taking into account that the electric field is in-plane (< k z >= 0) and that ǫ xy = 0 (see Table[ 1]), in H 2 the components of the internal magnetic field (which due to the rescaling by gµ B has units of energy) are: [1].…”

Section: Fig 1: Direction Of the Internal Magnetic Fieldmentioning

confidence: 99%

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Spin splitting and spin current in strained bulk semiconductors

Bernevig

Zhang

2005

Phys. Rev. B

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We present a theory for two recent experiments in bulk strained semiconductors [1,2] and show that a new, previously overlooked, strain spin-orbit coupling term may play a fundamental role. We propose simple experiments that could clarify the origin of strain-induced spin-orbit coupling terms in inversion asymmetric semiconductors. We predict that a uniform magnetization parallel to the electric field will be induced in the samples studied in [1,2] for specific directions of the applied electric field. We also propose special geometries to detect spin currents in strained semiconductors. 72.15. Gd Spin manipulation in semiconductors has seen remarkable theoretical and experimental interest in recent years with the advent of spin-electronics and with the realization that strong spin-orbit coupling in certain materials can influence the transport of carriers in so-called spintronics devices [3]. In particular, the issue of creating spin polarization of carriers in nonmagnetic semiconductors with spin-orbit coupling using only electric fields has caused a flurry of theoretical and experimental activity [4,5,6,7,8,9,10,11,12,13,14,15,16]. Two kinds of theories of spin-polarization under the action of an electric field have been put forward. The first kind, dating back since the mid 1980's [9], predicts the existence of a spatially homogeneous net spin polarization perpendicular to the applied electric current in two dimensional samples with spin-orbit interaction. This effect is dissipative and has been recently observed experimentally [17]. There also exist two very recent [4,5] theories predicting non-dissipative, intrinsic spin currents with the spin polarization and flow direction perpendicular to each other and to the electric field. This effect does not create a bulk magnetization but, if observed, can be used for spin injection, and its validity is being experimentally tested at the present time. One of the theories [5] predicts a spin current polarized out of plane and flowing perpendicular to the in-plane electric field applied on a 2-dimensional semiconductor sample exhibiting Rashba spin-orbit coupling. As long as the Rashba spin splitting is large enough, the spin conductivity is 'universal' (e/8π ) in the sense that it does not depend on the value of the coupling. The other effect [4] appears in the valence band of the bulk samples and is proportional to the spin-orbit splitting of the valence bands (to the difference between the Fermi momenta of the heavy and light-hole bands).In the first part of this letter we analyze the theory behind two recent experiments in bulk strained semiconductors [1,2] where an electric-field-induced uniform homogeneous spin polarization upon an applied electric field is observed. We make the case that the observed spinsplitting (whose origin is puzzling) and spin polarization is due to a previously overlooked strain-spin-splitting term, and propose easy experimental checks of our theory.In the second part of this letter we predict the appearance of an intrinsic spin po...

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Section: Fig 1: Direction Of the Internal Magnetic Fieldcontrasting

confidence: 41%

Section: Fig 1: Direction Of the Internal Magnetic Fieldmentioning

confidence: 99%

Spin splitting and spin current in strained bulk semiconductors

Bernevig

Zhang

2005

Phys. Rev. B

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“…31 and the matrix elements of the 8-band k · p Hamiltonian in the case of a magnetic field of arbitrary direction are given in Ref. 32.…”

Section: The Plane Wave Methodsmentioning

confidence: 99%

Symmetry ofk∙pHamiltonian in pyramidalInAs∕GaAsquantum dots: Application to the

et al. 2005

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A method for the calculation of the electronic structure of pyramidal self-assembled InAs/GaAs quantum dots is presented. The method is based on exploiting the C 4 symmetry of the 8-band k · p Hamiltonian with the strain taken into account via the continuum mechanical model. The operators representing symmetry group elements were represented in the plane wave basis and the group projectors were used to find the symmetry adapted basis in which the corresponding Hamiltonian matrix is block diagonal with four blocks of approximately equal size. The quantum number of total quasi-angular momentum is introduced and the states are classified according to its value. Selection rules for interaction with electromagnetic field in the dipole approximation are derived. The method was applied to calculate electron and hole quasibound states in a periodic array of vertically stacked pyramidal self-assembled InAs/GaAs quantum dots for different values of the distance between the dots and external axial magnetic field. As the distance between the dots in an array is varied, an interesting effect of simultaneous change of ground hole state symmetry, type and the sign of miniband effective mass is predicted. This effect is explained in terms of the change of biaxial strain. It is also found that the magnetic field splitting of Kramer's double degenerate states is most prominent for the first and second excited state in the conduction band and that the magnetic field can both separate otherwise overlapping minibands and concatenate otherwise nonoverlapping minibands.

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“…2(a) and 2(c), strain is changing the g c factor only quantitatively and not qualitatively. The strain Hamiltonian has the same functional form as the kinetic part of the Hamiltonian, 32 meaning that its effect will only be able to modify the size of the couplings and energy gaps between the different bands. From this point of view strain can be regarded as a perturbation onto the system, not affecting the mechanisms determining the g c factor.…”

Section: A Electron Statementioning

confidence: 99%

gfactors and diamagnetic coefficients of electrons, holes, and excitons in InAs/InP quantum dots

et al. 2012

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The electron, hole, and exciton g factors and diamagnetic coefficients have been calculated using envelopefunction theory for cylindrical InAs/InP quantum dots in the presence of a magnetic field parallel to the dot symmetry axis. A clear connection is established between the electron g factor and the amplitude of those valence-state envelope functions that possess nonzero orbital momentum associated with the envelope function. The dependence of the exciton diamagnetic coefficients on the quantum dot height is found to correlate with the energy dependence of the effective mass. Calculated exciton g factor and diamagnetic coefficients, constructed from the values associated with the electron and hole constituents of the exciton, match experimental data well, however including the Coulomb interaction between the electron and hole states improves the agreement. Remote-band contributions to the valence-band electronic structure, included perturbatively, reduce the agreement between theory and experiment.

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Eight-bandk⋅pmodel of strained zinc-blende crystals

Cited by 483 publications

References 26 publications

Spin splitting and spin current in strained bulk semiconductors

Spin splitting and spin current in strained bulk semiconductors

Symmetry ofk∙pHamiltonian in pyramidalInAs∕GaAsquantum dots: Application to the

gfactors and diamagnetic coefficients of electrons, holes, and excitons in InAs/InP quantum dots

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