  We create laterally large and low disorder quantum well based quantum dots to
study single electron additions to two dimensional electron systems (2DES).
Electrons tunnel into these dots across an AlGaAs tunnel barrier from a single
$n+$ electrode. Using single-electron capacitance spectroscopy in a dilution
refrigerator, we identify capacitance peaks for the addition of the first
electron to a dot and record subsequent peaks in the addition spectrum up to
occupancies of thousands of electrons. Here, we report two remarkable phenomena
that occur in the filling factor range $\nu=2$ to $\nu=5$ while selectively
probing electron additions to the edge states of the dot: (1) Coulomb blockade
peaks arise from the entrance of two electrons rather than one; (2) at and near
filling factor 5/2 and at fixed gate voltage, these double-height peaks appear
uniformly with a periodicity of $h/2e$. At other filling factors in the range
$\nu=2$ to $\nu=5$, the mean periodicity for the twice-height electron peaks
remains $h/2e$, but the twice-height peaks are instead further bunched into
pairs of double-height peaks, with pairs spaced $h/e$ apart. The unusual
two-electron Coulomb blockade peaks suggest a novel pair tunneling effect that
involves electron correlations that arise in the quantum dot, with spectra at
$\nu=5/2$ identical to those previously only seen in superconducting dots.
