Renormalization of spin-orbit coupling in quantum dots due to the Zeeman interaction

Valín-Rodríguez, Manuel

doi:10.1103/physrevb.70.033306

Cited by 15 publications

(21 citation statements)

References 27 publications

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“…͑For a harmonic potential describing single dots, operators H lin op have been derived 56 for the case of finite magnetic field, so that the Zeeman term can be included into H 0 .͒ Up to the second order in the perturbation couplings ͑being now ␣ SO and ␣ Z ͒, there is no coupled Zeeman-spin-orbit term. This means that in the effective Hamiltonians H eff that we already derived for the case of zero magnetic field, the Zeeman term appears as a shift of the energies on the diagonal without bringing any new couplings ͑nondiagonal terms͒.…”

Section: Effective Spin-orbit Hamiltonianmentioning

confidence: 99%

Spin-orbit effects in single-electron states in coupled quantum dots

2005

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Spin-orbit effects in single-electron states in laterally coupled quantum dots in the presence of a perpendicular magnetic field are studied by exact numerical diagonalization. Dresselhaus ͑linear and cubic͒ and Bychkov-Rashba spin-orbit couplings are included in a realistic model of confined dots based on GaAs. Group theoretical classification of quantum states with and without spin-orbit coupling is provided. Spin-orbit effects on the g factor are rather weak. It is shown that the frequency of coherent oscillations ͑tunneling amplitude͒ in coupled dots is largely unaffected by spin-orbit effects due to symmetry requirements. The leading contributions to the frequency involves the cubic term of the Dresselhaus coupling. Spin-orbit coupling in the presence of a magnetic field leads to a spin-dependent tunneling amplitude, and thus to the possibility of spin to charge conversion, namely, spatial separation of spin by coherent oscillations in a uniform magnetic field. It is also shown that spin hot spots exist in coupled GaAs dots already at moderate magnetic fields, and that spin hot spots at zero magnetic field are due to the cubic Dresselhaus term only.

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Section: Effective Spin-orbit Hamiltonianmentioning

confidence: 99%

Spin-orbit effects in single-electron states in coupled quantum dots

2005

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“…1B). Such result emphasizes the intricate competition between external magnetic field and intrinsic SO coupling in QDs [6]. In GaAs QDs, the anisotropic nature of the g-factor is much more pronounced, despite the small values of the SO constants.…”

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confidence: 85%

“…In general, SO effects have been considered via perturbation theory [3], although exact treatments have also been presented [4,5]. The perturbative approach, which includes only a few states, has been called into question by the demonstration that a larger basis is needed in order to achieve convergence even for the lowest QD states when the QD vertical width is narrow [4], as a complex interplay between different energy scales can be present [6]. Insights on the purity of the spin degree of freedom of electrons in QDs can also be extracted from measurements of their effective g-factor, e.g., by means of capacitance [7] and energy [8] spectroscopies.…”

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confidence: 99%

Spin relaxation and g-factor manipulation in quantum dots

Destefani¹,

Ulloa²

2006

Braz. J. Phys.

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Phonon-induced spin relaxation rates and electron g-factor tuning of quantum dots are studied as function of in-plane and perpendicular magnetic fields for different dot sizes. We consider Rashba and Dresselhaus spinorbit mixing in wide and narrow-gap semiconductors, and show how Zeeman sublevels can relax via piezoelectric (GaAs) and deformation (InSb) potential coupling to acoustic phonons. We find that strong confinement may induce minima in the rates at particular values of the magnetic field (due to a magnetic field-induced cancellation of the spin-orbit effects), where spin relaxation times can reach seconds. We also report on g-factor anisotropy. We obtain good agreement with available experimental values.Keywords: g-factor; Phonon-induced spin relaxation; Quantum dotsSince the proposal of a qubit based on the electron spin of quantum dots (QDs) [1], much work has been done to understand the processes that may cause their relaxation, since long coherence times are required. One of those processes is related to the phonon-induced spin-flip rates of Zeeman sublevels in QDs in magnetic fields, where the spin purity of the levels is broken by the spin-orbit (SO) interaction. A recent experiment [2] has shown a spin relaxation time ≈ 0.55 ms at an in-plane field of 10 T in a GaAs QD defined in a 2DEG. In general, SO effects have been considered via perturbation theory [3], although exact treatments have also been presented [4,5]. The perturbative approach, which includes only a few states, has been called into question by the demonstration that a larger basis is needed in order to achieve convergence even for the lowest QD states when the QD vertical width is narrow [4], as a complex interplay between different energy scales can be present [6]. Insights on the purity of the spin degree of freedom of electrons in QDs can also be extracted from measurements of their effective g-factor, e.g., by means of capacitance [7] and energy [8] spectroscopies.In this work we study spin-flip rates and g-factor tuning in QDs under SO influence. Our goal is to compare wide and narrow-gap materials under in-plane and perpendicular magnetic fields, at different QD sizes.The QD is defined by an in-plane parabolic confinement, V (r) = mω 2 0 r 2 /2, where m (ω 0 = E 0 / ) is the electronic effective mass (confinement frequency); the QD lateral length is l 0 = /(mω 0 ). The vertical confinement V (z) is strong enough so that only the state in the first quantum well subband is relevant, and its function is ϕ z (z) = 2/z 0 sin (πz/z 0 ) if a hard wall is assumed, z 0 being the QD vertical well thickness. In a magnetic field B, the unperturbed Hamiltonian, H 0 = 2 k 2 /2m+V (r)+H Z , has the well-known FockDarwin (FD) solution, where H Z = g 0 µ B B · σ/2 is the Zeeman term, g 0 is the bulk g-factor, and k is the kinetic momentum that includes the magnetic vector potential. We include all SO terms in 2D zincblende QDs, namely Rashba * present address: Physics Department, University of Ottawa, Ottawa, Ontario K1N6N5, Canada.and Dresse...

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“…(8), depends quadratically on the intensities of the different spin-orbit terms, in contrast with the situation at zero magnetic field, where the effect in the spectrum depends linearly on these intensities. For a quantum dot, when only Zeeman and Rashba terms are considered [19], the interplay between the above terms modifies the spin-orbit intensity, while the kinetic term manifests a weak dependence on the spit-orbit coupling. For g * = 0 (Zeeman term is absent) in a quantum dot, the kinetic term and the spin-orbit coupling remain without modifications.…”

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confidence: 99%

Model for spin-orbit effects in two-dimensional semiconductors in magnetic fields

Valín-Rodríguez

Nazmitdinov

2006

Phys. Rev. B

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We analyse the interplay between Dresselhaus, Bychkov-Rashba, and Zeeman interactions in a two-dimensional semiconductor quantum system under the action of a magnetic field. When a vertical magnetic field is considered, we predict that the interplay results in an effective cyclotron frequency that depends on a spin-dependent contribution. For in-plane magnetic fields, we found that the interplay induces an anisotropic effective gyromagnetic factor that depends on the orientation of the applied field as well as on the orientation of the electron momentum.PACS numbers: PACS 71.70. Ej, 73.21.Fg The effects produced by different spin-dependent interactions in semiconductor structures are currently in the forefront of experimental and theoretical efforts in mesoscopic physics. The explosive activity is motivated by the desire for a deep understanding of quantum coherence phenomena. The other driving force is the hope that the spintronics research would provide novel, lowdissipative microelectronic devices [1,2].Most measurements of spin effects in semiconductor microstructures are performed applying a magnetic field. In this case, two intrinsic spin-dependent interactions naturally appear: the well-known Zeeman interaction, which couples the electron spin with the applied field, and the spin-orbit coupling. The latter has been extensively studied starting from two-dimensional electron gas to quantum dots [3,4,5,6,7,8], and constitutes the basis of several proposals for spin-based applications [9,10,11].In a semiconductor, the spin-orbit coupling originates as a relativistic effect caused by electric fields present in the material (cf [12]). Such a system can be described by the HamiltonianHere* is the kinetic energy with the effective mass m * of electrons in the conduction band of the sample and p x , p y are components of the momentum. The electric field caused by the bulk inversion asymmetry of the crystalline structure contributes to the Hamiltonian, Eq.(1), with the Dresselhaus term, H D [13]. This term has, in general, a cubic dependence on the momentum of the carriers. For a narrow [0, 0, 1] quantum well, it reduces to the 2D, linear momentum dependent term H D = β (p x σ x − p y σ y ) / . Here, the σ's are the Pauli matrices, and β is the intensity of this interaction (cf Ref.12). The electric field caused by the structure inversion asymmetry (SIA) of the heterostructure generates the Bychkov-Rashba term, H R [14]. Since in the asymmetric quantum wells the SIA comes from the vertical direction, the Bychkov-Rashba interaction H R has the form: H R = α (p y σ x − p x σ y ) / , where α is the corresponding strength [12].The correlation between different spin-dependent interactions is a key point in the understanding of spin phenomena in semiconductors. In this work, we shall study a two-dimensional (2D) semiconductor system in a magnetic field, described by the Hamiltonian (1), paying special attention to the interplay between the Zeeman and spin-orbit interactions. We will show that depending on the orienta...

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Renormalization of spin-orbit coupling in quantum dots due to the Zeeman interaction

Cited by 15 publications

References 27 publications

Spin-orbit effects in single-electron states in coupled quantum dots

Spin-orbit effects in single-electron states in coupled quantum dots

Spin relaxation and g-factor manipulation in quantum dots

Model for spin-orbit effects in two-dimensional semiconductors in magnetic fields

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