Historically, the majority of studies in condensed matter physics have focused on Hermitian systems – closed systems that conserve energy. However, in reality, dissipative processes or non-equilibrium dynamics are commonly present and so real-world systems are anything but Hermitian.

Recently however people have begun to study non-Hermitian systems in detail and have found a range of interesting topological properties. The term topology was originally used to refer to a branch of mathematics describing geometric objects. Here, however, it means the study of the electron band structure in solids, as well as periodic motion more generally.

Topological arguments are often used to determine universal material properties such as conductivity or magnetic susceptibility. For example, topological insulators are insulating in the bulk but have conducting surface or edge states and can be used in a range of applications, such as quantum computing.

Previous work on non-Hermitian band topology has been restricted to one system at a time, or one property at a time. There’s been no way to link between materials or scenarios and no generalisation.

A research team formed of scientists from the Freie Universität Berlin, the Perimeter Institute, and Stockholm University have now brought everything together by using symmetry arguments to build a general, comprehensive theoretical framework for these exciting new systems.

Predictions made by the authors’ analysis will lead to a better understanding of condensed matter physics and hopefully to new developments in a range of fields including optics, acoustics, and electronics.