Double Point Contact in Quantum Hall Line Junctions

We show that multiple point contacts on a barrier separating two laterally coupled quantum Hall fluids induce Aharonov-Bohm (AB) oscillations in the tunneling conductance. These quantum coherence effects provide new evidence for the Luttinger liquid behavior of the edge states of quantum Hall fluids. For a two point contact, we identify coherent and incoherent regimes determined by the relative magnitude of their separation and the temperature. We analyze both regimes in the strong and weak tunneling amplitude limits as well as their temperature dependence. We find that the tunneling conductance should exhibit AB oscillations in the coherent regime, both at strong and weak tunneling amplitudes with the same period but with different functional form.

Figure 1

A line junction with two tunneling centers. The two shaded regions represent two identical 2DEG, separated by an insulating barrier mimicking the junctions used in Ref. 8.

Figure 2

(a) AB oscillations in the weak tunneling limit of the coherent regime; (b) AB effect in the strong tunneling limit of the coherent regime for $K<1/4$.

Figure 3

RG flow for (a) $1/4<K<1/2$ and (b) $K<1/4$.