Spin interference effect in a triangular loop array fabricated in (001)In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As quantum wells*

We report, for the first time, the spin interference (SI) effect in a triangular loop array fabricated in (001) In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As quantum wells (QW). Previously [1], we studied the SI effect in a square loop array, where the sides of the squares are either parallel or perpendicular to the $<$110$>$ crystallographic axis. For an electron with a wave vector\textbf{ k} that is parallel or perpendicular to the $<$110$>$ direction, the magnitude of the effective magnetic field due to the all spin-orbit effects,$ B_{TOT}$, is given either by the sum ($B_{R}+B_{D})$ or by the difference ($B_{R}-B_{D})$ between the Rashba and Dresselhaus fields, which makes the analysis relatively simple. Though the situation is more complicated in a triangular loop array, theory including both the Rashba and Dresselhaus terms predicts clear difference in the SI patterns between the following two situations: the bases of the triangles in the array are placed parallel/perpendicular to the $<$110$>$ crystallographic axis. This finding is being confirmed experimentally. [1] T. Koga\textit{ et al.}, Phys. Rev. B \textbf{70}, 161302(R) (2004); \textit{ibid}. \textbf{74}, 041302(R) (2006).