“Quantum Materials” describes a broad class of matter that is not simply captured by band theory. This includes strongly interacting electron systems, and often one is tempted to count topological single-particle materials into this class. These materials have predictions of unconventional electronic behavior in common, be it through analogies to relativistic particles in the case of Dirac/Weyl fermions or through the formation of correlated phases, which in turn is expected to impact the electron transport in these materials.
However, quite commonly these materials are also chemically complex and their synthesis by itself is an area of research in solid state chemistry. With micro- and nano-fabrication techniques such as Focused Ion Beam machining, new levels of material shape and quality control allow to probe these ideas in a more controlled manner. I will briefly review the techniques, its advantages and caveats, and then discuss new physics that can uniquely be accessed at this lengthscale – the physics of gradients.
Specifically, I will show how to create strain gradients locally with high precision, and how such strain gradients couple to correlated and topological features. One interesting class of materials are heavy-fermion superconductors, in which the degree of hybridization of the highly localized 4f orbitals with the conduction electrons is strongly tuned by symmetry breaking strain. In topological materials, on the other hand, strain gradients render the position of topological band structure defects spatially dependent, which in turn can be described by an effective gauge field.