Fig. Example of topological invariance Continuous deformation of a mug into a donut. Source: Youtube

The Nobel Prize in Physics 2016 was divided, awarded to Prof. David J. Thouless, Prof. F. Duncan M. Haldane and Prof. J. Michael Kosterlitz "for theoretical discoveries of topological phase transitions and topological phases of matter." Topology is usually introduced in the context of mathematics that deals with properties of spaces that are invariant under smooth deformations. For example, one can continuously transform a coffee mug into a donut. In Physics, if two different Hamiltonians can smoothly be deformed into each other, they give rise to many common physical properties and they are topologically invariant.

The research in condensed matter physics is currently undergoing a revolutionary change by the concept of topology. With the introduction of topology, the description of complex systems has changed from local order parameters to global quantities. Therefore, instead of studying properties of each individual systems, it is possible to classify them into phases with certain robust properties and unify the members belong to the same phase.  

This seminar will focus on basic concepts of topology and their application to nanoelectronics and nanomagnetism.

Literature:

Jülich spring school - Topological Matter (2017)

Topological effects in nanomagnetism: from superparamagnetism to chiral quantum soliton