Optical Probing of a Fractionally Charged Quasihole in an Incompressible Liquid

In photoluminescence spectroscopy of a low-mobility two-dimensional electron gas subjected to a quantizing magnetic field, we observe an anomaly around $\nu =\frac{1}{3}$ at a very low temperature (0.1 K) and an intermediate electron density ($0.9\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-2}$). The anomaly is explained as due to perturbation of the incompressible liquid at the Laughlin state due to close proximity of a localized charged exciton which creates a fractionally charged quasihole in the liquid. The anomaly of $\sim 2\mathrm{m}\mathrm{e}\mathrm{V}$ can be destroyed by applying a small thermal energy of $\sim 0.2\mathrm{m}\mathrm{e}\mathrm{V}$ that is enough to close the quasihole energy gap.

Figure 1

Left-circularly polarized photoluminescence spectra for a carrier density of $9\times {10}^{10}{\mathrm{c}\mathrm{m}}^{-2}$ and a magnetic field of $B=10.6\mathrm{T}$, corresponding to $\nu =\frac{1}{3}$, at temperatures 0.1 and 1.3 K.

Figure 2

Positions of left-circularly polarized PL lines versus magnetic field for a density of $0.9\times {10}^{11}{\mathrm{c}\mathrm{m}}^{-2}$ and temperatures 0.1 K (solid symbols) and 1.8 K (open symbols).

Figure 3

Energy (in units of Coulomb energy) versus the azimuthal rotational quantum number $M$ for an isolated quantum dot ($*$), a two-dimensional electron liquid (◇), and a QD liquid (○). The QD of the QD liquid either contains $(1e,h)$ [in (a) and (c)], or $(2e,h)$ [in (b) and (d)]. In (c) and (d) the QD liquid also contains a free quasihole.

Figure 4

Charge-density profile of the ground state and low-lying excitations of electrons in the dot (QD) and the liquid (L) of a QD liquid at $\nu =\frac{1}{3}$ (for $M=0–3$, as indicated in the figure) corresponding to Fig. 3b. The density distribution in the case where the QD liquid contains a free quasihole [Fig. 3d] is shown in (b).