Topological Quantum Matter
Topological quantum matter encompasses large classes of materials where the electronic structure hosts a global non-trivial topology. We are interested in understanding and describing the unique properties of topological quantum matter, including topologically protected edge states, distinctive bulk transport, and effects of a nontrivial quantum metric.
The defining property of topological quantum matter is the global non-trivial topology of their electronic structure. This global perspective of topology is fundamentally different from the traditional way of classifying matter, where local order parameters instead are the key concept. In topological superconductors these two disparate views of matter even naturally merge, as they have both a global non-trivial topology and a locally defined (superconducting) order.
Non-trivial topology is quantified using topological invariants, such as Chern or winding numbers. Non-zero topological invariants give rise to various distinctive transport phenomena, for example the quantum Hall effect resulting from a finite Chern number. More generally, the geometric properties of quantum states are encapsulated by the quantum geometric tensor, which real part is the ‘amplitude distance’ or the quantum metric and imaginary part the ‘phase change’ or Berry curvature giving the Chern number.
Due to the bulk-boundary correspondence, topological matter also hosts protected surface states. These often have exotic properties, including dissipation-free surface transport in topological insulators or Majorana fermions in topological superconductors The non-Abelian statistics of Majorana fermions makes them promising for future quantum computation.
We study a range of different novel topological phases of matter, including insulators, semimetals, and superconductors, as well as engineered systems such as adatoms structures or hybrid structures. We focus on both bulk properties and especially utilizing the unique topological surface states for new and novel functionalities. We are also interested in effects of finite quantum metric, including generating finite superfluid stiffness in flat bands systems and describing localization phenomena in non-crystalline systems. Other areas of interest are Dirac and Weyl semimetals and consequences of non-trivial quantum geometry in non-Hermitian systems.