Electronic and spin properties of Rashba billiards

Ballistic electrons confined to a billiard and subject to spin-orbit coupling of the Rashba-type are investigated, using both approximate semiclassical and exact quantum-mechanical methods. We focus on the low-energy part of the spectrum that has negative eigenvalues. When the spin precession length is smaller than the radius of the billiard, the low-lying energy eigenvalues turn out to be well described semiclassically. Corresponding eigenspinors are found to have a finite spin polarization in the direction perpendicular to the billiard plane.

Figure 1

In panel (a) the difference $\Delta N$ between the exact counting function and $\overline{N}\left(\epsilon \right)$ from Eq. (6) is plotted for $\sqrt{{\epsilon }_{\mathrm{so}}}=k_{\mathrm{so}}R=70$. In panel (b) the exact counting function (solid line) and $\overline{N}\left(\epsilon \right)$ (dashed line) are shown. In both panels dimensionless energies $\epsilon =2m^{*}E{R}^2∕{\hslash }^2$ are used.

Figure 2

The energy levels (in units of $2m^{*}{R}^2∕{\hslash }^2$) of circular Rashba billiards as functions of $m$. For a given $m$ levels are ordered and first, second, etc. energies are connected as $m$ varies.