  The edge of a two-dimensional electron system (2DES) in a magnetic field
consists of one-dimensional (1D) edge-channels that arise from the confining
electric field at the edge of the specimen$^{1-3}$. The crossed electric and
magnetic fields, E x B, cause electrons to drift parallel to the sample
boundary creating a chiral current that travels along the edge in only one
direction. Remarkably, in an ideal 2DES in the quantum Hall regime all current
flows along the edge$^{4-6}$. Quantization of the Hall resistance, $R_{xy}=
h/Ne^{2}$, arises from occupation of N 1D edge channels, each contributing a
conductance of $e^{2}/h^{7-11}$. To explore this unusual one-dimensional
property of an otherwise two-dimensional system, we have studied tunneling
between the edges of 2DESs in the regime of integer quantum Hall effect (QHE).
In the presence of an atomically precise, high-quality tunnel barrier, the
resultant interaction between the edge states leads to the formation of new
energy gaps and an intriguing dispersion relation for electrons traveling along
the barrier. The absence of tunneling features due to the electron spin and the
persistence of a conductance peak at zero bias are not consistent with a model
of weakly interacting edge states.
