Current-induced spin polarization in a two-dimensional hole gas

Liu, Chao Xing; Zhou, Bin; Shen, Shun-Qing; Zhu, Bang Fen

doi:10.1103/physrevb.77.125345

Cited by 24 publications

(46 citation statements)

References 58 publications

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“…The expansion for τ in powers of w can also be obtained by replacing the wavevectors in Eq. (25). Comparing the leading order terms in w of these two expressions for τ , we find the coefficient δ.…”

Section: Analytic Solution In Semiclassical Approximationmentioning

confidence: 99%

“…The problem is, what are the parameters that should be used in those models, and how are they related to parameters obtained from spectroscopic measurements in 2D structures. We will see that simplified models of 2D hole systems [17][18][19][20][21][22][23][24][25][26] have to be adjusted in order to capture the true nature of holes. Third, our understanding of particle interactions, and the possibilities to control these interactions is often based on an understanding of single-particle properties.…”

Section: Introductionmentioning

confidence: 99%

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Magnetic field spectral crossings of Luttinger holes in quantum wells

Simion

Lyanda-Geller

2014

Phys. Rev. B

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We develop an analytic approach to two-dimensional (2D) holes in a magnetic field that allows us to gain insight into physics of measuring the parameters of holes, such as cyclotron resonance, Shubnikov-De Haas effect and spin resonance. We derive hole energies, cyclotron masses and the g-factors in the semiclassical regime analytically, as well as analyze numerical results outside the semiclassical range of parameters, qualitatively explaining experimentally observed magnetic field dependence of the cyclotron mass. In the semiclassical regime with large Landau level indices, and for size quantization energy much bigger than the cyclotron energy, the cyclotron mass coinsides with the in-plane effective mass, calculated in the absence of a magnetic field.The hole g-factor in a magnetic field perpendicular to the 2D plane is defined not only by the constant of direct coupling of the angular momentum of the holes to the magnetic field, but also by the Luttinger constants defining the effective masses of holes. We find that the g-factor for quasi 2D holes with heavy mass in the [001] growth direction in GaAs quantum well is g = 4.05 in the semiclasssical regime. Outside the semiclassical range of parameters, holes behave as a species completely different from electrons. Spectra for size-and magnetic-field-quantized holes are non-equidistant, not fan-like, and exhibit multiple crossings, including crossing in the ground level. We calculate the effect of Dresselhaus terms, which transform some of the crossings into anticrossings, and the effects of the anisotropy of the Luttinger Hamiltonian on the 2D hole spectra. Dresselhaus terms of different symmetries are taken into account, and a regularization procedure is developed for the k 3 z Dresselhaus terms. Control of the non-equidistant levels and crossing structure by the magnetic field can be used to control Landau level mixing in hole systems, and thereby control hole-hole interactions in the magnetic field.

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Section: Analytic Solution In Semiclassical Approximationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Magnetic field spectral crossings of Luttinger holes in quantum wells

Simion

Lyanda-Geller

2014

Phys. Rev. B

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“…We will therefore focus only on the heavy holes, and will make explicit their spinorbit interaction H SO , which is simply the off-diagonal element of the two-band effective Hamiltonian which governs the heavy holes. Various previous works have developed two-band models of the heavy holes [25][26][27][28][29]; ours distinguishes itself by including strain.…”

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confidence: 99%

“…Following common practice, we choose the bulk Hamiltonian appropriate for crystal growth along the highsymmetry z (001) axis, and we take the hole carrier concentration to be small enough that only the first 2-D subband in the quantum well contributes to transport. [18,19,22,27,[29][30][31][32][33][34] We include a strain field ij using the Bir-Pikus strain Hamiltonian H [35], and we model the quantum well with a confinement potential V c and a small charge asymmetry V E = −eEz;…”

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confidence: 99%

Hole spin helix: Anomalous spin diffusion in anisotropic strained hole quantum wells

Sacksteder

Bernevig

2014

Phys. Rev. B

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We obtain the spin-orbit interaction and spin-charge coupled transport equations of a twodimensional heavy hole gas under the influence of strain and anisotropy. We show that a simple two-band Hamiltonian can be used to describe the holes. In addition to the well-known cubic hole spin-orbit interaction, anisotropy causes a Dresselhaus-like term, and strain causes a Rashba term. We discover that strain can cause a shifting symmetry of the Fermi surfaces for spin up and down holes. We predict an enhanced spin lifetime associated with a spin helix standing wave similar to the Persistent Spin Helix which exists in the two-dimensional electron gas with equal Rashba and Dresselhaus spin-orbit interactions. These results may be useful both for spin-based experimental determination of the Luttinger parameters of the valence band Hamiltonian and for creating long-lived spin excitations.PACS numbers: 72.25. Dc, 73.63.Hs Systems with spin-orbit interactions have generated great academic and practical interest [1-5] because they allow for purely electric manipulation of the electron spin [6][7][8], which could be of use in areas ranging from spintronics to quantum computing. However spin-orbit interactions have also the undesired effect of causing spin decoherence [9]. Recently a new mechanism by which a system can sustain both strong spin-orbit interactions and long spin relaxation times has been proposed [10]. In properly tuned systems a non-decaying spin density standing wave can be excited. This Persistent Spin Helix (PSH) has been observed through spin transient experiments in electron doped GaAs quantum wells. [11,12] In electron doped samples the PSH occurs when the Rashba and Dresselhaus spin-orbit interaction strengths are tuned to match each other. At equal strength the spin dynamics conserve an SU (2) triplet of spin operators, two of which describe spin standing waves, while the third describes a uniform spin density that is selected and preserved by the tuned spin-orbit interaction. The triplet's infinite lifetime is obtained by tuning the spinorbit interaction to have a constant phase independent of electron momentum, in which case the electron spin structure is independent of momentum and conserved under scattering. In particular, the Rashba and linear Dresselhaus terms are proportional to k − = k x − ık y and to k + = k x + ık y respectively, so when they are at equal strength the total spin-orbit interaction has constant phase, producing long-lived spin excitations.The experimental discovery of the PSH in the 2-D electron gas raises the question of whether it exists in other systems. Recently one of us predicted that tuned topological insulators can host PSHs with very long lifetimes [13]. Here we examine 2-D hole gases under strain, calculate the spin orbit interaction of the heavy holes, and find Rashba and Dresselhaus-like terms caused respectively by applied strain and anisotropy. When fine-tuned properly the spin orbit term has constant phase, producing long-lived spin helices aligned with the strai...

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“…Contributions of order ͑␣ / v F ͒ 2 are neglected throughout. We focus on intrinsic effects in the Rashba model; extrinsic ones, 23 Dresselhaus terms, 24 and hole gases 25 are not taken into account. Finally, weak localization corrections, which could in principle play an important role, 11 are beyond the scope of our present work.…”

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confidence: 99%

Spin polarizations and spin Hall currents in a two-dimensional electron gas with magnetic impurities

et al. 2008

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We consider a two-dimensional electron gas in the presence of Rashba spin-orbit coupling, and study the effects of magnetic s-wave and long-range nonmagnetic impurities on the spin-charge dynamics of the system. We focus on voltage induced spin polarizations and their relation to spin Hall currents. Our results are obtained using the quasiclassical Green function technique, and hold in the full range of the disorder parameter ␣p F . DOI: 10.1103/PhysRevB.78.125327 PACS number͑s͒: 72.25.Ϫb In the field of spintronics, much attention has recently been paid to spin-orbit related phenomena in semiconductors. One such phenomenon is the spin Hall effect, i.e., a spin current flowing perpendicular to an applied electric field. [1][2][3][4] It is now well known that, for linear-in-momentum spin-orbit couplings such as the Rashba or Dresselhaus ones, the spin Hall current vanishes exactly in the bulk of a disordered two-dimensional electron gas ͑2DEG͒.5-8 This can be understood by looking at the peculiar form of the continuity equations for the spin, as derived from its equations of motion in operator form.9-11 For a magnetically disordered 2DEG things are, however, different, and a nonvanishing spin Hall conductivity is found.12-14 Once more, a look at the continuity equations provides a clear and simple explanation of the effect:13 a term, whose appearance is due to magnetic impurities, directly relates in-plane spin polarizations, induced by the electric field, to spin currents. As the former, which have been the object of both theoretical and experimental studies, [15][16][17][18][19][20] are influenced by the type of nonmagnetic scatterers considered, we forgo the simplified assumption that these are s wave and take into account the full angle dependence of the scattering potential. Besides going beyond what is currently found in the literature, where, in the presence of magnetic impurities, the nonmagnetic disorder is either neglected or purely s wave, our approach also shows the interplay between polarizations and spin currents in a 2DEG. 21 We note that in the correct limits our results agree with what is found in Ref. 14. On the other hand a discrepancy with Ref. 12 arises.For the calculations we rely on the Eilenberger equation for the quasiclassical Green function in the presence of spinorbit coupling. 22 The spin-orbit energy is taken to be small compared to the Fermi energy, i.e., ␣p F Ӷ ⑀ F -or equivalently ␣ Ӷ v F , and the standard metallic regime condition 1 / Ӷ ⑀ F is also assumed. Here ␣ is the spin-orbit coupling constant, p F ͑v F ͒ the Fermi momentum ͑velocity͒ in the absence of such coupling, and the elastic quasiparticle lifetime due to nonmagnetic scatterers. Our results hold for a wide range of values of the dimensionless parameter ␣p F since this is not restricted by the above assumptions. Contributions of order ͑␣ / v F ͒ 2 are neglected throughout. We focus on intrinsic effects in the Rashba model; extrinsic ones, 23 Dresselhaus terms, 24 and hole gases 25 are not taken into account. Fina...

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Current-induced spin polarization in a two-dimensional hole gas

Cited by 24 publications

References 58 publications

Magnetic field spectral crossings of Luttinger holes in quantum wells

Magnetic field spectral crossings of Luttinger holes in quantum wells

Hole spin helix: Anomalous spin diffusion in anisotropic strained hole quantum wells

Spin polarizations and spin Hall currents in a two-dimensional electron gas with magnetic impurities

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