Rashba precession in quantum wires with interaction

Abstract

Rashba precession of spins moving along a one-dimensional quantum channel is calculated, accounting for Coulomb interactions. The Tomonaga-Luttinger model is formulated in the presence of spin-orbit scattering and solved by Bosonization. Increasing interaction strength at decreasing carrier density is found to enhance spin precession and the nominal Rashba parameter due to the decreasing spin velocity compared with the Fermi velocity. This result can elucidate the observed pronounced changes of the spin splitting on applied gate voltages which are estimated to influence the interface electric field in heterostructures only little. : 71.10.Pm, 71.70.Ej, 73.20.Dx According to recent speculations spin could replace the electric charge to carry information in future electronic devices [1]. The 'spin transistor' proposed by Datta and Das [2] might switch faster than traditional transistors since during operation it avoids redistributing charges. The idea is based on the Rashba effect [3] which causes spins to precess as they move along a heterostructure [4] so that the conductance depends on the final spin orientation relative to the magnetization of the ferromagnetic drain contact [5,6]. The strength of the Rashba effect is proportional to the electric field acting perpendicular to the electron plane which, when varied by a gate, changes the final spin orientation and thus the transport properties of the device. Advantage is taken of long spin coherence times and lengths [7], found in semiconductors. In the attempt of experimental realization considerable progress has been achieved meanwhile to inject finite spin densities [8]. Polarizations of 90% have been reported in GaAs [9]. PACSBeating patterns varying with gate voltages have indeed been observed in Shubnikov-de Haas (SdH) measurements [10][11][12]. Estimates show, however, that the the gate voltage adds an electric field contribution to a much stronger intrinsic field at the interface which does not suffice to explain the observed variations in spin splittings by a factor of two. One should notice that the gate voltage not only changes the strength of the electric field but at the same time it also alters the carrier density in the heterostructure as is directly monitored by the SdH oscillations. Without interactions this would not change the Rashba precession within the effective mass approximation [13] but, since particularly in semiconductors the strength of Coulomb interactions change with density through the r s -parameter, the question arises whether interactions influence the Rashba precession. This is demonstrated in the present Communications. In principle, the two effects of the gate, changing field strength and density, can be separated experimentally by varying the voltage at a front gate and a back gate independently [11].Usually, Rashba spin precession is described as a band structure effect, resulting from spin splitting [2,4], as calculated in the original work by Rashba [3] for the homogeneous two-dimensional case. Such a single particle a...

Low-energy theory and RKKY interaction for interacting quantum wires with Rashba spin-orbit coupling

“…The small-α dependence δ ∝ α 4 follows for the model below and has also been reported in Ref. 20. Therefore, the velocity splitting (1) is typically weak.…”

Electronic and spin properties of Rashba billiards

“…It is straightforward to obtain corresponding spinor eigenstates and calculate their expectation value for the z component of spin. Similar to the case of Rashba-split eigenstates in rings [36], but in contrast to that of quantum wires [8,10], it turns out to be finite. We find…”

“…Its tunability by external gate voltages [5,6] has motivated the theoretical design of a spin-controlled field-effect transistor [7]. Novel spin properties arise from the interplay between Rashba spin splitting and further confinement of two-dimensional electrons in quantum wires [8,9,10,11] or dots [12,13,14,15,16,17]. Spinorbit coupling has also been shown to affect the statistics of energy levels and eigenfunctions as well as current distributions [18,19].…”

Rashba spin–orbit coupling and spin precession in carbon nanotubes

“…Here we confine ourselves to the noninteracting problem in order to not overly complicate the analysis, but study the many-band case and details of the band structure. Interactions can be taken into account within the Luttinger liquid approach at a later stage, and may enhance the effect of SO couplings [22,25]. We shall also neglect disorder effects.…”

“…Recent theoretical studies of spin-dependent transport in CNTs have mainly focused on the single-channel limit, taking into account electron-electron interactions within the framework of the Luttinger liquid theory [17,18,19,20,21] (see also [22,23,24] for related discussions on interacting quantum wires with Rashba SO coupling). Here we confine ourselves to the noninteracting problem in order to not overly complicate the analysis, but study the many-band case and details of the band structure.…”