Single electron control in n-type semiconductor quantum dots using non-Abelian holonomies generated by spin orbit coupling

Yang, S.-R. Eric; Hwang, N. Y.

doi:10.1103/physrevb.73.125330

Cited by 26 publications

(21 citation statements)

References 22 publications

(20 reference statements)

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“…In principle one can obtain straightforwardly the spatial dependence for all condense components by solving the boundary problem Eqs. (56)(57)(58)(59)(60). Here we present the solution for the long-range component f z t in the region x > 0.…”

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confidence: 99%

Spin-orbit coupling as a source of long-range triplet proximity effect in superconductor-ferromagnet hybrid structures

2014

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We investigate the proximity effect in diffusive superconducting hybrid structures with a spin-orbit (SO) coupling. Our study is focused on the singlet-triplet conversion and the generation of long-range superconducting correlations in ferromagnetic elements. We derive the quasiclassical equations for the Green's functions including the SO coupling terms in form of a background SU(2) field. With the help of these equations, we first present an interesting complete analogy between the spin diffusion process in normal metals and the generation of the triplet components of the condensate in a diffusive superconducting structure in the presence of SO coupling. From this analogy it turns out naturally that the SO coupling is an additional source of the long-range triplet component (LRTC) besides the magnetic inhomogeneities studied in the past. This analogy opens a range of possibilities for the generation and manipulation of the triplet condensate in hybrid structures. In particular we demonstrate that a normal metal with a SO coupling can be used as source of LRTC if attached to a S/F bilayer. We also demonstrate an explicit connection between an inhomogeneous exchange field and SO coupling mechanisms for the generation of the LRTC and establish the conditions for the appearance of the LRTC in different geometries. Our work gives a global description of the singlet-triplet conversion in hybrids structures in terms of generic spin-fields and our results are particularly important for the understanding of the physics underlying spintronic devices with superconductors.

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confidence: 99%

Spin-orbit coupling as a source of long-range triplet proximity effect in superconductor-ferromagnet hybrid structures

2014

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“…Fortunately, these dynamics become uncoupled not only for vanishing SOC, but also when it corresponds to an effective non-Abelian vector potential [11][12][13][14][15][16][17][18][19][20][21][22][23] of a pure gauge form, which happens in a broad class of systems. Remarkably, the three-dimensional (3D) fermionic gases with SOC realized in recent experiments [7,9,24] belong to this interesting class.…”

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confidence: 99%

Spin dynamics of cold fermions with synthetic spin-orbit coupling

Tokatly

Sherman

2013

Phys. Rev. A

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We consider spin relaxation dynamics in cold Fermi gases with a pure-gauge spin-orbit coupling corresponding to recent experiments. We show that such experiments can give a direct access to the collisional spin drag rate, and establish conditions for the observation of spin drag effects. In the recent experiments the dynamics is found to be mainly ballistic leading to new regimes of reversible spin relaxation-like processes.PACS numbers: 03.75. Ss, 05.30.Fk, The development of spintronics, the branch of physics studying spin-determined dynamical and transport phenomena was mainly related to solid-state structures. In these systems, spin-orbit coupling (SOC), one of the key elements of spintronics, is well-understood [1-4] and many interesting spin-related effects have been studied experimentally and theoretically. Very recently a detailed study of spin dynamics in ultracold atomic gases has become experimentally feasible [6][7][8][9]. In particular, two systems where SOC is produced by a special design of optical fields, attracted a great deal of attention. One of them is the spin-orbit coupled Bose-Einstein condensates [5,6], with the pseudospin 1/2 degree of freedom. The other class is represented by the cold fermion isotopes 40 K in Ref. [7] and much lighter 6 Li studied in Ref. [9]. In both cases, in addition to the SOC, an effective Zeeman magnetic field can be produced optically.Typically in solids, e.g. in doped semiconductors, a disorder, randomizing motion of electrons, plays the dominant role in the spin dynamics. The electron-electron collisions become crucial only at high temperatures, or in intrinsic semiconductors with optically pumped electrons and holes [10]. From this point of view, cold atomic gases offer a unique possibility of seeing basic effects of interactions in the pure form since the disorder is absent there. The interatomic collisions lead to the spin drag determining the spin diffusion and, as we will see below, can be important for the spin dynamics in cold Fermi gases with SOC.It is well-appreciated that in the presence of strong SOC the effects of interatomic interactions in the spin dynamics are difficult to analyze as this requires tracing essentially coupled orbital and spin subsystems. Fortunately, these dynamics become uncoupled not only for vanishing SOC, but also when it corresponds to an effective non-Abelian vector potential [11-23] of a pure gauge form, which happens in a broad class of systems. Remarkably, the three-dimensional (3D) fermionic gases with SOC realized in recent experiments [7,9,24] belong to this interesting class. For a pure gauge SOC the behavior of the physical system maps to that of a system without SOC, which allows to consider effects of SOC of an arbitrary strength. In this case all qualitative features of the spin dynamics are the same as for a generic SO field, but the analysis is much easier. Here we study spin dynamics for systems with a pure gauge SO coupling, where the entire pattern even if it is complicated by the interatomic interactions, c...

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“…The curvatureinduced effective geometrical field is determined by simple expressions, containing surface curvatures and the coupling constants α and β from Eqs. (22), (23), and (24). We believe that a geometric effective field would help to elucidate the profound physics of spin transport in spintronic devices with curved spaces, such as nanotubes and nanopillars.…”

Section: Discussionmentioning

confidence: 98%

“…10,14,15 Complicated spin dynamics due to the spin-orbit coupling can then be easily understood in terms of a theory where the coupling is treated as a non-Abelian gauge field, and the corresponding formalism can be used to study the singleelectron spin transport in 2DEGs and spin manipulation in quantum dot systems. [15][16][17][18][19][20][21][22][23][24] When applied to the 2DEG, the approach based on a formal SU (2) gauge invariance of the spin-orbit Hamiltonian proved that the equilibrium spin current can be gauged away if the spin-orbital field is a pure gauge. 25 Until now, most studies of the spin electrons have been concentrated on planar 2D systems.…”

Section: Introductionmentioning

confidence: 99%

Geometrical effect on the non-Abelian spin-orbital gauge field of a curved surface

Cheng¹,

Chen²,

Chang³

2011

Phys. Rev. B

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The geometrical effect of a two-dimensional electron gas system with the Rashba and Dresselhaus spin-orbital interactions on a curved surface is studied; it corresponds to a non-Abelian gauge field and a scalar field. The behavior of electrons with spin on a curved space can be transformed into that of a simple system of an electron with spin on a flat surface with a geometrical metric tensor. In addition to the dynamic phase of traveling electrons on a flat surface, a geometrical phase induced by curved space is also observed, and this phase can be demonstrated by use of the path integral. Therefore, the spin-rotation operator and quantum loop of electrons with spin on a curved space are obtained. The induced phases on three curved spaces with flat, cylindrical, and spherical geometry are calculated, and the roles of space curvature in spin precession are also analyzed

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Single electron control in n-type semiconductor quantum dots using non-Abelian holonomies generated by spin orbit coupling

Cited by 26 publications

References 22 publications

Spin-orbit coupling as a source of long-range triplet proximity effect in superconductor-ferromagnet hybrid structures

Spin-orbit coupling as a source of long-range triplet proximity effect in superconductor-ferromagnet hybrid structures

Spin dynamics of cold fermions with synthetic spin-orbit coupling

Geometrical effect on the non-Abelian spin-orbital gauge field of a curved surface

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