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

Abstract

Geometric phases of scattering states in a ring geometry are studied on the basis of avariant of the adiabatic theorem. Three timescales, i.e., the adiabatic period, the systemtime and the dwell time, associated with adiabatic scattering in a ring geometry play acrucial role in determining geometric phases, in contrast to only two timescales, i.e., theadiabatic period and the dwell time, in an open system. We derive a formulaconnecting the gauge invariant geometric phases acquired by time-reversed scatteringstates and the circulating (pumping) current. A numerical calculation shows thatthe effect of the geometric phases is observable in a nanoscale electronic device.