Non-trivial edge profile of the Laughlin wave function*

The wave function proposed by Laughlin in 1983 led to a great advance in understanding the many-body quantum physics of the Fractional Quantum Hall Effect (FQHE). Laughlin’s plasma analogy maps the distribution of electron densities in the FQHE state to the one of the classical 2-dimensional One-Component Plasma (2DOCP), with the temperature of the 2DOCP corresponding to the filling fraction of the FQHE state. We explore this connection further to investigate the non-trivial behavior of the electron density close to the edge of a FQHE droplet. Using a mix of recent Monte Carlo results and analytical methods we show that the observed profile of overshoot plus damped oscillations of the density near the edge can be explained in terms of the partial crystallization of the corresponding 2DOCP close to a boundary. We analyze the dependence of this effect on the proximity to the boundary and on the FQHE filling fraction.