Intrinsic Superflat Bands in General Twisted Bilayer Systems

TL;DR

This paper uncovers a new class of superflat bands in general twisted bilayer systems, revealing intrinsic localized states that are spectrally isolated and spatially centered around AA stacking, with potential applications across various wave systems.

Contribution

It introduces a novel mechanism for superflat bands in twisted bilayer systems beyond magic angles, based on continuous lattice dislocation and intrinsic localized states.

Findings

Localized states are spectrally isolated at energy spectrum edges.

Superflat bands can be realized over a wide parameter space.

The phenomena can be simulated in twisted bilayer nanophotonic systems.

Abstract

Twisted bilayer systems with discrete magic angles, such as twisted bilayer graphene featuring moir\'{e} superlattices, provide a versatile platform for exploring novel physical properties. Here, we discover a class of superflat bands in general twisted bilayer systems beyond the low-energy physics of magic-angle twisted counterparts. By considering continuous lattice dislocation, we obtain intrinsic localized states, which are spectrally isolated at lowest and highest energies and spatially centered around the AA stacked region, governed by the macroscopic effective energy potential well. Such localized states exhibit negligible inter-cell coupling and support the formation of superflat bands in a wide and continuous parameter space, which can be mimicked using a twisted bilayer nanophotonic system. Our finding suggests that general twisted bilayer systems can realize continuously tunable superflat bands and the corresponding localized states for various photonic, phononic and mechanical waves.