Crystallization of fractional charges in a strongly interacting quasi-helical quantum dot

The ground-state electron density of a one-dimensional spin-orbit coupled quantum dot with a Zeeman term and strong electron interaction is studied at the fractional helical liquid points. We show that at fractional filling factors $\nu =(2n+1{)}^{-1}$ (with $n$ a non-negative integer) the density oscillates with $N_0\mathrm{/}\nu$ peak. For $n\ge 1$ a number of peaks larger than the number of electrons $N_0$ suggests that a crystal of fractional quasi-particles with charge $\nu e$ (with $e$ the electron charge) occurs. The reported effect is amenable of verification via transport measurements in charged AFM-coupled dot.