Hall Effects in Doubly Connected Specimens

We examine the impact on the Hall effect, when a hole is inserted inside the canonical Hall geometry, in 2-D electron gas specimens that exhibit an ultrahigh mobility (
$\mu \sim \hbox{10}^{7}\ \hbox{cm}^{2}\hbox{/V}{\cdot}\hbox{s}$
) at liquid helium temperatures. We demonstrate that an “anti-Hall bar” configuration generates an ordinary Hall effect within the interior boundary and that the interior Hall voltage divided by the interior injected current equals the Hall resistance. Further, we show that it is possible to simultaneously realize two independent Hall effects in the high-quality specimen by injecting two currents into a single doubly connected device.