Observation of Size Effect in the Quantum Hall Regime

Striking changes are observed in the characteristic features of the quantum Hall effect when the width of the conducting channel, fabricated on high-mobility ($\mu \gtrsim 1\times {10}^5$ ${\mathrm{cm}}^2$/V·sec) $\mathrm{GaAs}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ heterostructures, is reduced to several microns. The quantum oscillations in ${\rho }_{\mathrm{xx}}$ vs $B$ appear saw-toothed and the quantized Hall plateaus become highly asymmetric about complete Landau-level fillings. The ${\rho }_{\mathrm{xx}}$ peaks are shifted to lower $B$ and drastically reduced from their wide-channel values. These results suggest possible dimensional crossover and enhancement of the electron-electron interaction in the quantum Hall regime.