Incommensurability enabled quasi-fractal order in 1D narrow-band moir\'e systems

TL;DR

This paper shows that quasiperiodicity in 1D moiré systems can induce a quasi-fractional order with contributions from infinitely many wave vectors, even at infinitesimal interactions, unlike periodic systems.

Contribution

It reveals that quasiperiodicity enables a novel quasi-fractional order in 1D moiré systems, extending ordered phases to very weak interactions, a phenomenon absent in periodic counterparts.

Findings

Quasiperiodicity extends ordered phases to infinitesimal interactions.

The quasi-fractional order involves contributions from infinitely many wave vectors.

Quasiperiodic systems exhibit multifractal non-interacting phases.

Abstract

We demonstrate that quasiperiodicity can radically change the ground state properties of 1D moir\'e systems with respect to their periodic counterparts. By studying an illustrative example we show that while narrow bands play a significant role in enhancing interactions both for commensurate and incommensurate structures, only quasiperiodicity is able to extend the ordered phase down to an infinitesimal interaction strength. In this regime, the quasiperiodic-enabled state has contributions from infinitely many wave vectors. This quasi-factal regime cannot be stabilized in the commensurate case even in the presence of a narrow band. These findings suggest that quasiperiodicity may be a critical factor in stabilizing non-trivial ordered phases in interacting moir\'e structures and signal out multifractal non-interacting phases, recently found in 2D incommensurate moir\'e systems, as particularly promising parent states.