# Adiabatic almost-topological pumping of fractional charges in non-interacting quantum dots

## TL;DR

This paper demonstrates theoretically that adiabatic modulation of a quantum dot's coupling can pump fractional charges, with quantization determined by the reservoir's band-structure, revealing a form of topological charge pumping without exotic particles.

## Contribution

The study introduces the concept of adiabatic almost-topological pumping of fractional charges in non-interacting quantum dots, highlighting the role of Berry curvature and reservoir band-structure.

## Key findings

- Pumped charge is quantized at a fraction of an electron per cycle.
- The fractional quantization depends on the ratio of Lamb shift to level-broadening.
- Topological protection is limited to adiabatic conditions, with non-adiabatic corrections growing linearly.

## Abstract

We use exact techniques to demonstrate theoretically the pumping of fractional charges in a single-level non-interacting quantum dot, when the dot-reservoir coupling is adiabatically driven from weak to strong coupling. The pumped charge averaged over many cycles is quantized at a fraction of an electron per cycle, determined by the ratio of Lamb shift to level-broadening; this ratio is imposed by the reservoir band-structure. For uniform density of states, half an electron is pumped per cycle. We call this "adiabatic almost-topological pumping", because the pumping's Berry curvature is sharply peaked in the parameter space. Hence, so long as the pumping contour does not touch the peak, the pumped charge depends only on how many times the contour winds around the peak (up to exponentially small corrections). However, the topology does not protect against non-adiabatic corrections, which grow linearly with pump speed. In one limit the peak becomes a delta-function, so the adiabatic pumping of fractional charges becomes entirely topological. Our results show that quantization of the adiabatic pumped charge at a fraction of an electron does not require fractional particles or other exotic physics.