The Nobel Prize in Physics 2016 goes to David Thouless, Michael Kosterlitz and Duncan Haldane for theoretical discoveries in the field of topological materials. These only conduct electricity on their surface and hold a big promise for future applications in electronics, superconductors or even quantum computers. Haldane spent part of 2008 in Leiden; he is the 14th Lorentz Professor to win a Nobel Prize.
We are used to assign properties to materials as we experience them in our everyday life; three-dimensional objects. But if you look at extremely thin, ‘two-dimensional’ layers, you will see completely new physical phenomena at ultra-low temperatures in strong magnetic fields. A famous example is the quantum Hall effect: changing the magnetic field affects the electric conductance, but only in discrete steps.
Thouless and Haldane explained this effect using the mathematical field of topology. In topology, objects are classified by the number of holes. A coffee cup is therefore similar to a donut because they both contain one hole, and a sphere occupies the same category as a bowl for having zero holes. The number of holes can only be an integer, so this parameter goes up step-by-step. Thouless and Haldane linked two-dimensional layers and one-dimensional chains in a clever way to this principle, and deduced that their properties also change in steps (see figure 1).
Alongside the discovery of topological phases of matter, this year’s Nobel Prize is also awarded for the discovery of topological phase transitions, made by Thouless (again) and Kosterlitz. Topological phases are not like the well-known phases solid, liquid or gas. They occur at very low temperatures in two-dimensional layers and manifest themselves as vortices of atomic magnets (see figure 2). If the temperature increases slightly, a tight pair of vortices gets separated and single vortices are created. This phase transition is a universal phenomenon for any type of material, making it an important breakthrough.
Duncan Haldane spent part of 2008 in Leiden as Lorentz Professor. ‘It was great to have him here, we became good friends,’ says Leiden theoretical physicist Jan Zaanen. ‘He even made a big discovery during his time in Leiden: entanglement entropy for topologically ordered systems. I am delighted for him, he very much deserves this prize. He and Thouless were way ahead of their time. For the Kosterlitz-Thouless transition I have actually been expecting a Nobel prize for a long time. I’m surprised it didn’t happen earlier.’