Nonadiabatic charge pumping by oscillating potentials in one dimension: results for infinite system and finite ring

TL;DR

This paper investigates nonadiabatic charge pumping in one-dimensional systems with static and oscillating potentials, revealing violations of simple rules and conditions for zero current, with analyses for infinite systems and finite rings.

Contribution

It introduces a comprehensive analysis of nonadiabatic charge pumping in 1D systems, including a new method for calculating current in finite rings and insights into conditions for zero current.

Findings

Nonadiabatic pumping violates the sin  rule obeyed by adiabatic pumping.

Average current is zero if the Hamiltonian is real and time-reversal invariant.

Pumped current depends differently on amplitude at resonant and non-resonant frequencies.

Abstract

We study charge pumping when a combination of static potentials and potentials oscillating with a time period T is applied in a one-dimensional system of non-interacting electrons. We consider both an infinite system using the Dirac equation in the continuum approximation, and a periodic ring with a finite number of sites using the tight-binding model. The infinite system is taken to be coupled to reservoirs on the two sides which are at the same chemical potential and temperature. We consider a model in which oscillating potentials help the electrons to access a transmission resonance produced by the static potentials, and show that non-adiabatic pumping violates the simple \sin \phi rule which is obeyed by adiabatic two-site pumping. For the ring, we do not introduce any reservoirs, and we present a method for calculating the current averaged over an infinite time using the time evolution operator U(T) assuming a purely Hamiltonian evolution. We analytically show that the averaged current is zero if the Hamiltonian is real and time reversal invariant. Numerical studies indicate another interesting result, namely, that the integrated current is zero for any time-dependence of the potential if it is applied to only one site. Finally we study the effects of pumping at two sites on a ring at resonant and non-resonant frequencies, and show that the pumped current has different dependences on the pumping amplitude in the two cases.