CORRELATIONS IN QUASI-PERIODIC STRUCTURES

The present research plan aims at understanding the interplay between incommensurability and electronic interactions in systems with different dimensionalities, including 1D quasiperiodic systems (QPS) and 2D moiré structures, such as twisted bilayer graphene (tBLG).

Currently, there is not much overlap between the low-dimensional systems community and that dealing with incommensurability effects. In 1D QPS, the effects of incommensurability on localization and transport properties are well established, whereas they are almost completely neglected in most theoretical studies related to 2D moiré systems. Conversely, the study of moiré physics, such as the formation of narrow-bands and the associated exotic correlation phenomena, is overlooked in 1D QPS.

By studying the interplay between incommensurability and interactions, we intend to bridge this gap and provide insights into the superconducting and correlated phases in tBLG. Our results will be of interest to other systems where incommensurate structures can naturally appear or be induced, such as other twisted layered compounds and optical lattices.