Dynamic polarizability and collective modes in narrow-band electron systems

Abstract

The family of moiré materials, in particular the magic angle twisted bilayer graphene, has emerged recently as a platform to study strongly interacting physics. This thesis analyzes the impact of the ultranarrow Bloch bands and strong electron-electron interactions on the dynamical polarization response of these systems. Strong interactions alter the collective charge dynamics in a number of interesting ways, in particular by stiffening the frequency-momentum dispersion of surface plasmons and making it much stronger than that of the underlying narrow-band carriers. Strongly dispersing plasmons pierce through the particle-hole continuum and extend in the forbidden energy band above it. This behavior enables decoupling of plasmons from particle-hole excitations. Such over-the-band plasmons are unable to decay into particle-hole pairs and thus are not subject to Landau damping. As a result, plasmons acquire longer lifetimes as well as an enhanced spatial optical coherence. The optical coherence manifests itself in spatial interference patterns that provide telltale signatures of over-the-band plasmons that are readily accessible in near-field imaging experiments. We further show that the over-the-band plasmon dispersion remains robust in the presence of ordering of the narrow-band carriers. The specific examples of a Wigner crystal and a Mott-Hubbard order, worked out in detail, show that interaction-driven gap opening has no impact on the over-the-band plasmon dispersion. Lastly, we consider the implications of the mechanisms behind the over-the-band behavior for achieving of unidirectional collective modes. We present a new mechanism for plasmon nonreciprocity the magnitude of which is controllable through the strength of electron-electron interactions, which makes it particularly pronounced in the moiré materials.