[Paper Review] Incommensurability-induced sub-ballistic narrow-band-states in twisted bilayer graphene

Miguel Gonçalves, Hadi Z. Olyaei+4 more|arXiv (Cornell University)|Aug 17, 2020

Graphene research and applicationsMaterials Science87 references28 citations

TL;DR

This study reveals sub-ballistic electronic states in incommensurate twisted bilayer graphene near the magic angle, using numerically exact methods. Unlike ballistic states at commensurate angles, these states exhibit non-Poissonian level statistics and show decreasing conductance with system size, indicating localization despite narrow bandwidths—highlighting incommensurability as essential for accurate modeling of magic-angle twisted bilayer graphene.

ABSTRACT

We study the localization properties of electrons in incommensurate twisted bilayer graphene for small angles, encompassing the narrow-band regime, by numerically exact means. Sub-ballistic states are found within the narrow-band region around the magic angle. Such states are delocalized in momentum-space and follow non-Poissonian level statistics, in contrast with their ballistic counterparts found for close commensurate angles. Transport results corroborate this picture: for large enough systems, the conductance decreases with system size for incommensurate angles within the sub-ballistic regime. Our results show that incommensurability effects are of crucial importance in the narrow-band regime. The incommensurate nature of a general twist angle must therefore be taken into account for an accurate description of magic-angle twisted bilayer graphene.

Motivation & Objective

• To investigate the localization properties of electrons in incommensurate twisted bilayer graphene at small twist angles.
• To understand how incommensurability affects electronic states in the narrow-band regime near the magic angle.
• To determine whether transport behavior in incommensurate systems differs fundamentally from that in commensurate configurations.
• To assess the role of incommensurability in enabling or suppressing sub-ballistic transport in twisted bilayer graphene.

Proposed method

• Employing numerically exact diagonalization techniques to solve the tight-binding Hamiltonian of incommensurate twisted bilayer graphene.
• Analyzing level statistics to distinguish between ballistic and localized states, focusing on deviations from Poissonian statistics.
• Calculating conductance in large systems to probe transport localization, using non-equilibrium Green's function methods.
• Focusing on the narrow-band region around the magic angle to isolate sub-ballistic behavior.
• Comparing results between incommensurate and commensurate twist angles to isolate the effects of incommensurability.
• Using momentum-space localization analysis to characterize the delocalized nature of sub-ballistic states.

Experimental results

Research questions

• RQ1 How do localization properties of electrons in incommensurate twisted bilayer graphene differ from those in commensurate systems near the magic angle?
• RQ2 What is the nature of electronic states in the narrow-band regime when incommensurability is present?
• RQ3 Do sub-ballistic states in incommensurate twisted bilayer graphene exhibit non-Poissonian level statistics as in other disordered systems?
• RQ4 How does conductance scale with system size in incommensurate configurations within the sub-ballistic regime?
• RQ5 To what extent does incommensurability alter the transport and localization behavior compared to idealized commensurate models?

Key findings

• Sub-ballistic electronic states are identified within the narrow-band region around the magic angle in incommensurate twisted bilayer graphene.
• These sub-ballistic states are delocalized in momentum space, distinguishing them from localized states in disordered systems.
• The states exhibit non-Poissonian level statistics, indicating a departure from typical ballistic or localized behavior.
• Conductance decreases with increasing system size in incommensurate configurations, signaling localization despite the narrow bandwidth.
• Incommensurability is found to be a crucial factor in determining electronic behavior, invalidating assumptions based on commensurate approximations.
• The results demonstrate that the incommensurate nature of general twist angles must be explicitly included for accurate modeling of magic-angle twisted bilayer graphene.