Topology in condensed matter physics

by Raffaele Resta (Dipartimento di Fisica, Università di Trieste)

Tuesday 24 Jan 2017, 16:00 → 18:00 Europe/Rome

Aula Conversi (Dip. di Fisica - Edificio G. Marconi)

The celebrated 1983 paper by Thouless and coworkers (TKNN) marks the first ap- pearance of topology in nonrelativistic quantum mechanics and in condensed matter physics. In 1988 Haldane proposed a model material (named by us “Haldanium”) which has two phases, one trivial and one very exotic: what discriminates between the two is the topology of the electronic ground state. Haldane’s work opened a new avenue, and several topological materials were later synthetised; the current literature is flooded with “topological” papers: experimental, theoretical, and com- putational. Topology describes the properties that remain intact when an object is stretched, twisted, or deformed, but not “cut”. Such properties are labelled by integer numbers, named topological invariants. If a measurable physical property of a macroscopic system is an integer (in appropriate units), then it can be measured in principle with infinite precision; it is also extremely robust under variations of the experimental conditions. In this talk I will convey the main message of the two papers quoted above by keeping the technical level as low as possible; in the final part I will also give a flavour of some recent developments.