Spin Interference Effect in a Square Loop Array including the Rashba and Dresselhaus Terms*

The effect of electron wave interference to the electric conductivity ($\sigma$), including the effect of spin degree of freedom, is investigated through nanolithographically defined square (and other) loop array structures fabricated on In$_ {0.52} $Al$_{0.48}$As/In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48} $As quantum wells (QW). In this experiment, we measure $\sigma$'s of QWs as a function of magnetic field $B$ (${\bf B}$$\perp$QW plane). These samples had a gate electrode covering the entire loop array structures, where a gate voltage $V_g$ was applied between the metal gate electrode and the QW. We note that $V_g$ controls both the carrier density and the Rashba and Dresselhaus spin-orbit terms within the QWs. It turned out that the magnetoconductance $\sigma(B)$ oscillates as a function of $B$ with a period corresponding to $h/2e$, which is denoted as the AAS oscillation. We found that the amplitude of the AAS oscillation in this system also oscillated as a function of $V_g$, which is called as a ``spin interference'' effect. We investigated this effect, which is also in close relation to the ``Aharonov-Casher'' effect (electric control of the phase of the electronic wave function), in detail including both the Rashba and Dresselhaus spin-orbit terms quantitatively.