Decorated lattices with flat bands: Trapping electrons with destructive interference

Quantum interference plays an essential role in almost all the quantum phenomena. In particular, the interference of a single electron wavefunction with itself is behind many interesting quantum phenomena, such as resonant tunneling at the nanoscale or double slit interference patterns. In this talk, we show how destructive self-interference of an electron wavefunction in a crystal structure may lead to the caging of the electron, that is, the electron wavefunction becomes zero everywhere except in a small crystal region.
Such behavior is obtained allowing longer range electron jumps between atoms of the crystal or by "decorating" simple lattices with additional atoms.
These decorated lattices have dispersionless (flat) bands, reflecting the existence of the (highly degenerate) compact localized electron states. In this talk, I discuss methods of construction of these flat band systems, their behavior under magnetic field and the effects of electronic interactions. Two particular decorated lattices will be discussed in detail, the diamond chain and the Lieb lattice.