Por Ricardo Dias (Departamento de Física, Universidade de Aveiro, Portugal).
Geometric frustration and destructive interference give rise to characteristic phenomena in seemingly unrelated systems, such as itinerant fermions in decorated lattices, magnetic systems, and Josephson junction (JJ) arrays. Examples of these phenomena include the presence of flat bands in the energy dispersion of decorated tight-binding lattices, magnetization plateaus in frustrated magnetic systems, and current blocking in JJ arrays.
The topic of this seminar is flat-band systems. Flat bands are usually associated with subspaces of one-body compact localized states. These states are a consequence of destructive interference between different classical trajectories of particles and are associated with specific lattice geometries and particular choices of the hopping parameters in the corresponding tight-binding Hamiltonian.
Flat-band systems have been the subject of intense study over the past two decades. One reason for the significant attention these systems have received is the intriguing phenomena they exhibit due to their enhanced sensitivity to interactions, such as the fractional quantum Hall effect and superconductivity in twisted bilayer graphene, among others. In fact, flat-band systems always belong to the category of strongly correlated electronic systems, even when interactions are relatively weak.
In this seminar, I will describe the contributions we made to this topic over the past 10 years.
