Rashba interaction in quantum wires with in-plane magnetic fields

We analyze the spectral and transport properties of ballistic quasi-one-dimensional systems in the presence of spin-orbit coupling and in-plane magnetic fields. Our results demonstrate that Rashba precession and intersubband coupling must be treated on equal footing for wave vectors near the magnetic-field-induced gaps. We find that intersubband coupling limits the occurrence of negative effective masses at the gap edges and modifies the linear conductance curves in the strong-coupling limit. The effect of the magnetic field on the spin-textured orientation of the wire magnetization is discussed.

Figure 1

(Color online) Schematic representation of the wire potential ${\mathcal{H}}_{\mathrm{conf}}\equiv V\left(y\right)=m{\omega }_0^2{y}^2∕2$ and magnetic-field orientation considered in this work.

Figure 2

(Color online) (a) Dispersion relation for $\theta =0$, $l_Z=2l_0$, and $l_1=l_0$. The solid line corresponds to the case where the Rashba intersubband coupling is fully included $(l_2=l_1)$ while the dashed line shows the case without it $(l_2=\infty )$. (b) Same as (a) for $\theta =\pi ∕2$.

Figure 3

(Color online) Lower plot: dependence with $k$ of the spin expectation values in the lowest subband. Solid lines are obtained including both Rashba terms while dashed lines are the results when RIC is neglected. We set $l_Z=2.2l_0$, $l_1=l_2=l_0$, and $\theta =0$. Upper panels display the spin texture for three selected propagation momenta and taking into account both Rashba terms. The $k{l}_0$ values (indicated by the thick arrows pointing on the $k{l}_0$ axis) are $-0.75$, 0, and 0.75 for left, center and right upper plots, respectively. The vector plot shows the in-plane spin and the solid line corresponds to the $z$ component.

Figure 4

(Color online) Same as Fig. 3 for the second subband.

Figure 5

Variation of the conductance with Rashba intensity and the Fermi energy $\mu$ in the full Rashba model ($l_2=l_1$, upper panel) and neglecting RIC ($l_2=\infty$, lower panel). We set $l_Z=1.8l_0$ and parallel magnetic field $\theta =0$. A rigid shift with Rashba intensity has been taken into account defining $\tilde{\mu }∕\hslash {\omega }_0=\mu ∕\hslash {\omega }_0+l_0^2∕8l_1^2$. The numbers in the plateaus give the conductance in units of the conductance quantum. Right small plots show vertical cuts of the corresponding left figures for the given values of $l_0∕2l_1$.

Figure 6

Same as Fig. 5 for a perpendicular field $(\theta =\pi ∕2)$.