Appearance of Topological Phases in Superconducting Nanocircuits

TL;DR

This paper demonstrates how to create non-Abelian geometric phases in superconducting nanocircuits, enabling topological charge pumping with localized effective magnetic fields and relaxed adiabaticity conditions.

Contribution

It introduces a novel scheme for topological charge pumping using non-Abelian geometric transformations in superconducting nanocircuits.

Findings

Non-Abelian geometric phases can be realized in superconducting circuits.

Localized effective magnetic fields enable robust topological effects.

The scheme relaxes the adiabaticity condition for phase manipulation.

Abstract

We construct non-Abelian geometric transformations in superconducting nanocircuits, which resemble in properties the Aharonov-Bohm phase for an electron transported around a magnetic flux line. The effective magnetic fields can be strongly localized, and the path is traversed in the region where the energy separation between the states involved is at maximum, so that the adiabaticity condition is weakened. In particular, we present a scheme of topological charge pumping.