Geometric phases of scattering states in a ring geometry: adiabatic pumping in mesoscopic devices

TL;DR

This paper investigates how geometric phases in scattering states within a ring geometry influence adiabatic pumping, revealing their dependence on three key time scales and demonstrating observable effects in nanoscale electronic devices.

Contribution

It introduces a new formula linking geometric phases of time-reversed states to circulating current, considering three time scales in a ring geometry.

Findings

Geometric phases depend on adiabatic period, system time, and dwell time.

Derived a gauge-invariant formula connecting phases and current.

Numerical results show observable effects in nanoscale devices.

Abstract

Geometric phases of scattering states in a ring geometry are studied based on a variant of the adiabatic theorem. Three time scales, i.e., the adiabatic period, the system time and the dwell time, associated with adiabatic scattering in a ring geometry plays a crucial role in determining geometric phases, in contrast to only two time scales, i.e., the adiabatic period and the dwell time, in an open system. We derive a formula connecting the gauge invariant geometric phases acquired by time-reversed scattering states and the circulating (pumping) current. A numerical calculation shows that the effect of the geometric phases is observable in a nanoscale electronic device.