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.