Laughlin pumping assisted by surface acoustic waves

Abstract

The quantum Hall effect is a fascinating electrical transport phenomenon signified by precise quantization of Hall conductivity $\sigma_\mathrm{xy}$ and vanishing longitudinal conductivity $\sigma_\mathrm{xx}$. Laughlin proposed an elegant explanation in which adiabatic insertion of a flux tube pumps charge through the system. This analysis unveils the fundamental role of gauge invariance and provides a compelling argument about the fractional charge of fractional quantum Hall states. While it has been used extensively as a theoretical tool, a quantitative experimental investigation is lacking despite multiple attempts. Here we report successful realizations of Laughlin pumping in several integer and fractional quantum Hall states. One essential technical innovation is using surface acoustic waves to periodically clear the charges accumulated during the pumping process. Magnetic fluxes are inserted at a constant rate so there is no need to perform complicated data fitting. Furthermore, our setting can reliably extract $\sigma_\mathrm{xx}$ that is several orders of magnitude lower than the limit of conventional techniques. Effective energy gaps can be deduced from the temperature dependence of $\sigma_\mathrm{xx}$, which are drastically different from those provided by conventional transport data. This work not only brings a famous gedanken experiment to reality but also serves as a portal for many future investigations.