Collective excitation of quantum wires and effect of spin-orbit coupling in the presence of a magnetic field along the wire

Abstract

The band structure of a quantum wire with the Rashba spin-orbit coupling develops a pseudogap in the presence of a magnetic field along the wire. In such a system spin mixing at the Fermi wavevectors −kF and kF can be different. We have investigated theoretically the collective mode of this system, and found that the velocity of this collective excitation depends sensitively on the strength of the Rashba spin-orbit interaction and magnetic field. Our result suggests that the strength of the spin-orbit interaction can be determined from the measurement of the velocity.

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

“…We mention in passing that in the presence of a magnetic field (which we do not consider), a spin gap can be present because of spin-nonconserving e-e "Cooper" scattering processes; 39,40 the effects of e-e forward scattering in Rashba wires with magnetic field were studied as well. 41,42,43,44 Below, we also provide estimates for the renormalized couplings entering the modified LL theory, see Eq. (26) below.…”

Influences of an impurity on the transport properties of a one-dimensional antisymmetric spin filter

“…This section is based on Refs. [4,7], and the basic setup, the band structure, and the Hamiltonian of 1D ASF are reviewed. 1D ASF (along x-axis) can be realized by applying the confinement potentials in y and z direction, so that the electrons are forced to move along the x-axis.…”

“…3 Středa and Šeba 4 proposed an antisymmetric filter (ASF) which employs the Zeeman interaction with in-plane magnetic field (or parallel to quantum wire) as well as Rashba SOI. 5,6 The interplay of Rashba SOI and the Zeeman interaction with the magnetic field parallel to wire gives rise to an interesting one-dimensional (1D) band structure of quantum wire 4,7 , where the orientation of electron spin depends on wave number (see Fig. 1).…”

“…This dependence on wave number causes the charge and the spin degrees of freedom to mix, which is a feature distinct from the well-known spin-charge separation of 1D Luttinger liquid (LL). 8 The diverse properties of quantum wires in the presence of SOI and/or magnetic field have been studied: the collective excitations 7,9 , the interplay of Rashba SOI and electron-electron interaction 10,11 , the optical property 12 , and the transmission/reflection coefficients in the presence of a potential step. 13 However, as far as we know there is no report on the systematic study of charge/spin transport of 1D ASF in the presence of impurity scattering and electron-electron interaction.…”

“…II, we introduce 1D ASF and review the previous results, in particular the band structure and the bosonized Hamitonian. 4,7 In Sec. III, the impurity Hamiltonian and the coupling to external fields which produce the charge/spin transport are discussed.…”