### Rashba Spin-Orbit Coupling in Quantum Wire Networks

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Aron Cummings, Arizona State University
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In recent years, much interest has been given to the field of quantum computing, due to its potential to solve certain problems much more efficiently than classical computational methods. A popular choice for the quantum bit of a quantum computer is the spin of a single electron. It has been shown that the spin of an electron can be manipulated through the mechanism of spin-orbit coupling. In this work we study the effect of Rashba spin-orbit coupling on electron transport through a variety of quantum structures. To do this, we use a scattering matrix formalism that allows us to calculate the evolution of the electron wave function as it propagates through the system under investigation. Three quantum geometries are considered – a straight wire, a ring structure, and a y-branching structure. In the straight wire, we observe the precession of spin-polarized electrons as they propagate through the wire. In the ring structure, interference patterns are observed in the conductance of the device, due to the accumulation of non-Abelian phase by electrons traveling on opposite sides of the ring. In the y-branching structure, we observe a spin-filtering effect, where spin-up electrons are concentrated in one output wire, and spin-down electrons are concentrated in the other output wire.

**Abstract Author(s): **Aron Cummings, David Ferry, and Richard Akis