Random spin-orbit gates in the system of a Topological insulator and a Quantum dot

TL;DR

This paper investigates how random spin-orbit interactions in a topological insulator and quantum dot system can generate robust long-range entanglement, even amid strong disorder, using a formalism of random unitary gates.

Contribution

It introduces a formalism of random unitary gates to analyze spin-dependent scattering and entanglement in topological insulator-quantum dot systems under disorder.

Findings

External magnetic field induces long-range entanglement.

Topological features support robust entanglement despite disorder.

Long-distance entanglement persists under strong impurity effects.

Abstract

The spin-dependent scattering process in a system of topological insulator and quantum dot is studied. The unitary scattering process is viewed as a gate transformation applied to an initial state of two electrons. Due to the randomness imposed through the impurities and alloying-induced effects of band parameters, the formalism of the random unitary gates is implemented. For quantifying entanglement in the system, we explored concurrence and ensemble-averaged R\'enyi entropy. We found that applied external magnetic field leads to long-range entanglement on the distances much larger than the confinement length. We showed that topological features of itinerant electrons sustain the formation of robust long-distance entanglement, which survives even in the presence of a strong disorder.