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arXiv:cond-mat/0409678 · Physical Review Letters

Competing Effects of Interactions and Spin-Orbit Coupling in a Quantum Wire

Vladimir Gritsev, G. I. Japaridze, Mikhail Pletyukhov, D. Baeriswyl

Published Apr 7, 2005• 59 citations
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Abstract

We study the interplay of electron-electron interactions and Rashba spin-orbit coupling in one-dimensional ballistic wires. Using the renormalization group approach we construct the phase diagram in terms of Rashba coupling, Tomonaga-Luttinger stiffness and backward scattering strength. We identify the parameter regimes with a dynamically generated spin gap and show where the Luttinger liquid prevails. We also discuss the consequences for the operation of the Datta-Das transistor.

DOI
10.1103/physrevlett.94.137207

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A key concept in the emerging field of spintronics is the electric field control of spin precession via the effective magnetic field generated by the Rashba spin orbit interaction (RSOI). Here we model a quantum wire as a system of electrons on a discrete one-dimensional chain with nearest neighbor hopping. By extensive density matrix renormalization group computations we demonstrate the presence of alternating spin current order in the gapped phases of this quantum wire with spatially modulated RSOI and repulsive electron-electron interactions. Our results are analytically supported by bosonization and by a mapping to a locally rotated spin basis.
We study the effects of electron-electron interactions on the transport properties of a junction of three quantum wires enclosing a magnetic flux. The wires are modeled as single channel spin-12\frac{1}{2}21​ Tomonaga--Luttinger liquids. The system exhibits a rich phase diagram as a function of the electronic interaction strength, which includes a chiral fixed point with an asymmetric current flow highly sensitive to the sign of the flux and another fixed point where pair tunneling dominates, which is similar to the case of spinless electrons. While in the case of spinless electrons the perturbations that correspond to unequal couplings between the three wires are always irrelevant, we find that, when the electron spin is included, there are small regions in the phase diagram where a current flows only between two of the wires and the third wire is decoupled.
We consider theoretically spin correlations in a one-dimensional quantum wire with Rashba-Dresselhaus spin-orbit interaction (RDI). The correlations of noninteracting electrons display electron spin resonance at a frequency proportional to the RDI coupling. Interacting electrons, upon varying the direction of the external magnetic field, transit from the state of Luttinger liquid (LL) to the spin-density wave (SDW) state. We show that the two-time total-spin correlations of these states are significantly different. In the LL, the projection of total spin to the direction of the RDI-induced field is conserved and the corresponding correlator is equal to zero. The correlators of two components perpendicular to the RDI field display a sharp electron-spin resonance driven by the RDI-induced intrinsic field. In contrast, in the SDW state, the longitudinal projection of spin dominates, whereas the transverse components are suppressed. This prediction indicates a simple way for an experimental diagnostic of the SDW in a quantum wire. We point out that the Luttinger model does not respect the spin conservation since it assumes the infinite Fermi sea. We propose a proper cutoff to correct this failure.
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