Figure 1
Illustration: Alan Stonebraker

Figure 1: Particle-hole duality transforms: holes as doppelgängers for particles. (Top left) Sand particles in the top of an hourglass empty downwards from a filled region, ν=1, and leave behind an empty region, ν=0. (Top right) Its dual ν'=1-ν can describe the same process, except now the regions “filled” with air in the bottom half “empty” upwards. (Bottom left) Top view of a real sheet of electrons with different electrostatically gated filling factors νe, bounded by chiral electron currents flowing as shown. (Bottom right) Its dual system is measured in terms of hole filling νh=1-νe, bounded by opposite flowing chiral hole currents. The dotted line indicates the weak-coupling point where holes tunnel from νh=1 to probe the νh=1/3 density of states. The desired quantum point contact on the right is extremely challenging to fabricate directly, yet its dual on the left was readily realized by Roddaro and co-workers and reveals the same physics.