Geometry-Assisted Topological Transitions in Spin Interferometry

We identify a series of topological transitions occurring in electronic spin transport when manipulating spin-guiding fields controlled by the geometric shape of mesoscopic interferometers. They manifest as distinct inversions of the interference pattern in quantum conductance experiments. We establish that Rashba square loops develop weak-(anti)localization transitions (absent in other geometries as Rashba ring loops) as an in-plane Zeeman field is applied. These transitions, boosted by nonadiabatic spin scattering, prove to have a topological interpretation in terms of winding numbers characterizing the structure of spin modes in the Bloch sphere.

Figure 1

Linear conductance of ring (a) and square (b) loops by TR-path interference (red: WL; blue: WAL) and winding number of spin textures $|{\omega }_s|$ in ring (c) and square (b) loops as a function of the Rashba SO and in-plane Zeeman field strengths. Field and spin textures for points (A), (B), (C), and (D) are shown in Fig. 2. For dominating Rashba strengths (field winding $|{\omega }_B|=1$), conductance maxima (blue) take place only when $|{\omega }_s|=1$ (dark). Checkerboardlike patterns in (b) and (d) are indicative of spin-texture topological transitions for weak Zeeman fields in squares, in contrast to rings. Rashba SO field textures (insets) correspond to counterclockwise itinerant spins. Interference fringes in (a) and (b) disappear for dominating Zeeman fields due to a frozen spin dynamics. The rectangles in (a) and (b) show the approximate zones accessible by experiments. Red zones in (c) ($|{\omega }_s|>1$) are due to resonances discussed in Refs. [17] and [26].

Figure 2

Field and spin textures for hybrid Rashba-Zeeman ring and square loops for points (A), (B), (C), and (D) shown in Fig. 1. Field and spin topologies are defined by winding numbers ${\omega }_B$ and ${\omega }_s$ around the origin in the $xy$ plane. For rings (a) and (b) a change in ${\omega }_s$ requires large in-plane Zeeman fields changing ${\omega }_B$ as well. For squares (c) and (d) weak Zeeman fields are sufficient to change ${\omega }_s$ without changing ${\omega }_B$, instead. The Rashba SO components of the field textures correspond to counterclockwise itinerant spins. The color code refers to the position along the loops perimeter.

Figure 3

(a) Laser scanning microscope image of a $40\times 40$ square loop array with square side length $l=700\mathrm{nm}$. (b)–(g) Contour color plots of MR as a function of $V_g$ at different in-plane field strengths $B_Z$. The insets of (b)–(g) contain the MR data at $V_g=-3.6\mathrm{V}$, showing the AAS oscillations.

Figure 4

(a) AAS oscillations for a square loop array at $V_g=-3.6V$ ($\alpha =-2.5\text{\hspace{0.17em}p}\mathrm{eV}\mathrm{m}$) with different in-plane Zeeman fields $B_Z$. The sign reversal of the AAS oscillations corresponds to the transition from a destructive spin interference (WAL) to a constructive one (WL). (b) AAS oscillations for a ring array with radius $r=600\mathrm{nm}$ at $\alpha =-2.9\text{\hspace{0.17em}p}\mathrm{eV}\mathrm{m}$. The transition from WAL to WL is not observed in the ring array.