Magnetic-field dependence of the level spacing of a small electron droplet

The temperature dependence of conductance resonances is used to measure the evolution with the magnetic field of the average level spacing $\Delta \epsilon$ of a droplet containing ∼30 electrons created by lateral confinement of a two-dimensional electron gas in GaAs. $\Delta \epsilon$ becomes very small (<30 μeV) near two critical magnetic fields at which the symmetry of the droplet changes, and these decreases of $\Delta \epsilon$ are predicted by Hartree-Fock (HF) for charge excitations. Between the two critical fields, however, the largest measured $\Delta \epsilon =100\mathrm{}$ μeV is an order of magnitude smaller than predicted by HF but comparable to the Zeeman splitting at this field, which suggests that excitations of the spin degrees of freedom are important.