Effective Hamiltonian of Topologically Protected Qubit in a Helical Crystal

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Abstract

We study a superlattice formed by tunnel-coupled identical antidots periodically situated in a two-dimensional topological insulator placed in a magnetic field. The superlattice spectrum can be controlled by gate electrodes or by changing the magnetic flux through the antidots. We demonstrate that a topologically protected qubit appears at the boundary between two regions with different fluxes. The qubit properties depend on the value of the flux jump on the boundary and can be controlled by the gate voltage. We derive the effective Hamiltonian of such a qubit and analyze the dependence of its properties on the main parameters of the superlattice: the tunnel coupling between antidots, and the probability of jumps with the spin flip.

About the authors

R. A. Niyazov

Petersburg Nuclear Physics Institute, National Research Center Kurchatov Institute;Ioffe Institute

Email: r.niyazov@mail.ioffe.ru
188300, Gatchina, Russia;194021, St. Petersburg, Russia

D. N. Aristov

Petersburg Nuclear Physics Institute, National Research Center Kurchatov Institute;Faculty of Physics, St. Petersburg State University

Email: r.niyazov@mail.ioffe.ru
188300, Gatchina, Russia;199034, St. Petersburg, Russia

V. Yu. Kachorovskiy

Ioffe Institute

Author for correspondence.
Email: r.niyazov@mail.ioffe.ru
194021, St. Petersburg, Russia

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