Influence of Interactions on Flux and Back-Gate Period of Quantum Hall Interferometers

In quantum Hall systems with two narrow constrictions, tunneling between opposite edges can give rise to quantum interference and Aharonov-Bohm–like oscillations of the conductance. When there is an integer quantized Hall state within the constrictions, a region between them, with higher electron density, may form a compressible island. Electron tunneling through this island can lead to residual transport, modulated by Coulomb-blockade–type effects. We find that the coupling between the fully occupied lower Landau levels and the higher-partially occupied level gives rise to flux subperiods smaller than one flux quantum. We generalize this scenario to other geometries and to fractional quantum Hall systems, and compare our predictions to experiments.

Figure 1

A sketch of a QH interferometer with (a) compressible island and bulk, where light and dark shading indicate regions of lower and higher conductivity ${\sigma }_{xx}$. In panel (b), an additional incompressible region (white) surrounds the (shaded) compressible regions. Three possible tunneling paths indicated by dashed lines: (i) forward tunneling through the constrictions and center island (horizontal lines), (ii) backwards tunneling between opposite edge states through the island (slanting lines), and (iii) backwards tunneling across the constrictions (vertical lines).

Figure 2

Flux dependence of the conductance due to backscattering at the constrictions [process (iii)] for $\beta e^2/2C_i=5$ and $f_c=4$. (a) Weak coupling ${\Delta }_X/\Delta =0.1$ between compressible island and edge. The period is one flux quantum. (b) Stronger coupling ${\Delta }_X/\Delta =0.35$, with zero gate voltage ($N_{\mathrm{gate}}=0$). An additional modulation with small amplitude can be seen. (c) Gate voltage with $N_{\mathrm{gate}}=0.4$ and ${\Delta }_X/\Delta =0.35$ leads to a splitting of the main peak. (d) Strong coupling ${\Delta }_X/\Delta =0.7$. With one large and two smaller peaks, one sees an apparent subperiod of $1/(f_c-1)$ flux quanta.