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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.
We study a two-terminal graphene Josephson junction with contacts shaped to form a narrow constriction, less than 100nm in length. The contacts are made from type II superconducting contacts and able to withstand magnetic fields high enough to reach
We report on the transition from magnetic edge to electric edge transport in a split magnetic gate device which applies a notch magnetic field to a two-dimensional electron gas. The gate bias allows tuning the overlap of magnetic and electric edge wa
We study the effect of backward scatterings in the tunneling at a point contact between the edges of a second level hierarchical fractional quantum Hall states. A universal scaling dimension of the tunneling conductance is obtained only when both of
A two-dimensional (2D) topological insulator (TI) exhibits the quantum spin Hall (QSH) effect, in which topologically protected spin-polarized conducting channels exist at the sample edges. Experimental signatures of the QSH effect have recently been
We study proximity coupling between a superconductor and counter-propagating gapless modes arising on the edges of Abelian fractional quantum Hall liquids with filling fraction $ u=1/m$ (with $m$ an odd integer). This setup can be utilized to create