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.
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