Conductance Quantization in Graphene Nanoconstrictions

We present measurements of conductance quantization in a narrow Graphene constriction, of approximate width 200nm. Graphene is exfoliated on top of a Silicon Dioxide, and is not suspended. In high mobility samples ($>$10000cm$^{2}$V$^{-1}$s$^{-1})$ , we observe pinch-off at the Diract point, with a resistance at 4.2K of $\sim $ 40k$\Omega $. As a function of gate voltage at zero magnetic field, the conductance displays a few plateaus with the quantized value close to G$_{0}$=2e$^{2}$/h, indicating valley degeneracy splitting. At high carrier density ($>$5x10$^{12}$/cm$^{2})$ in a weak magnetic field, conductance exhibits ~strong beating in the Shubnikov-de Haas oscillations, which is also attributed to the valley splitting, analogous the Rashba interaction beats observed in the Shubnikov-de Haas oscillations in semiconducting quantum wells. In the Quantum Hall regime, the conductance of the constriction has quantized values nG$_{0}$, ..,. In comparison, measurements in the leads of the constriction display normal graphene behavior without the valley splitting.