Magnetoplasmon excitations in quasi-one-dimensional Rashba spintronic systems: Maxons, rotons, and negative-energy dispersion.

We report on the theoretical investigation of plasmon excitations in a quasi-two-dimensional electron

gas in the presence of a harmonic potential (oriented along the x direction), an applied perpendicular

(to the x-y plane) magnetic field, and the spin-orbit interaction (SOI) induced by the Rashba effect.

The resultant system is a quasi-one-dimensional (Q1D) quantum wire with free propagation along the y

direction and magnetoelectric quantization along the x. The motion along the z direction is neglected

since the charge carriers are assumed to be strongly confined to the lowest subband at low temperatures

desirably attainable in the experiments on the low-dimensional systems. The problem involves three

length scales: ${\it l}_0=\sqrt{\hbar/m^*\omega_0}$, ${\it l}_c=\sqrt{\hbar/m^*\omega_c}$, and

${\it l}_{\alpha}=\hbar^2/(2m^*\alpha)$, which characterize the relative strengths in the interplay of

confinement, the magnetic field, and the Rashba SOI. The resulting Schr\"odinger-like equations satisfied

by the wave function (accounting for the spin-up and spin-down states) are two coupled equations, which

cannot be solved in an explicit analytical form. However, invoking the limits of a strong magnetic field,

${\it l}_c \ll {\it l}_0$, and $k_y{\it l}_0\ll 1$ allow us to solve this set of coupled equations exactly.

We then derive and discuss the dispersion relations for charge-density excitations within the framework of

Bohm-Pines' random-phase approximation. The Q1D electron gas (Q1DEG) in the presence of a perpendicular

magnetic field is well-known for the magnetic depopulation of 1D subbands and oscillations in the Fermi

energy akin to the Shubnikov-de Haas oscillations. The intrasubband and intersubband magnetoplasmons in

a Q1DEG are characterized, respectively, by the negative energy dispersion with increasing magnetic

field and the magnetoroton excitation which changes its group velocity twice before merging with the

respective single-particle continuum. Here we scrutinize the effect of the Rashba SOI on these

characteristics in depth. We observe that the SOI modifies drastically the behavior of both the

intrasubband and intersubband magnetoplasmons in the long wavelength limit and may render them relatively

more susceptible to the Landau damping in the short wavelength limit. We discuss the dependence of the

magnetoplasmon energy on the propagation vector, the magnetic field, the 1D charge-density, and the

Rashba parameter characterizing the SOI.