[Paper Review] Strain induced quasi-unidimensional channels in twisted moiré lattices

Andreas Sinner, Pierre A. Pantaleón+1 more|PubMed|Oct 13, 2022

Graphene research and applications4 citations

TL;DR

This paper demonstrates that uniaxial strain in twisted bilayer honeycomb lattices—such as twisted bilayer graphene—induces quasi-one-dimensional moiré channels through a strain-twist interplay that collapses the reciprocal space unit cell. The critical strain for this transition is determined by a simple relation involving the twist angle and material-specific Poisson ratio, leading to electronic bands governed by two incommensurate periodicities, akin to Harper-like systems with singular density of states.

ABSTRACT

We study the effects of strain in moiré systems composed of honeycomb lattices. We elucidate the formation of almost perfect one-dimensional moiré patterns in twisted bilayer systems. The formation of such patterns is a consequence of an interplay between twist and strain which gives rise to a collapse of the reciprocal space unit cell. As a criterion for such collapse we find a simple relation between the two quantities and the material specific Poisson ratio. The induced one-dimensional behavior is characterized by two, usually incommensurate, periodicities. Our results offer explanations for the complex patterns of one-dimensional channels observed in low angle twisted bilayer graphene systems and twisted bilayer dicalcogenides. Our findings can be applied to any hexagonal twisted moiré pattern and can be easily extended to other geometries.

Motivation & Objective

• To understand the origin of complex one-dimensional moiré patterns observed in strained low-angle twisted bilayer graphene and dicalcogenides.
• To identify the geometric and electronic conditions under which moiré superlattices transition from two-dimensional to quasi-one-dimensional behavior.
• To derive a general criterion for the onset of one-dimensional character in strained twisted bilayer systems.
• To analyze the resulting electronic band structure and density of states in the one-dimensional limit, particularly the role of incommensurate periodicities.

Proposed method

• Derives strain-dependent real and reciprocal space lattice vectors for twisted bilayer honeycomb lattices using continuum model approximations.
• Models the deformation of the moiré Brillouin zone under uniaxial strain, showing its reduction from a hexagonal to a line-like shape at critical strain.
• Applies a continuum Hamiltonian approach to compute electronic bands and density of states, incorporating interlayer coupling and strain-induced hopping modifications.
• Identifies the critical strain condition via a relation involving twist angle and Poisson ratio, where the reciprocal space unit cell collapses.
• Analyzes the electronic spectrum in the 1D limit, showing resemblance to the Harper equation with incommensurate periodicities.
• Uses numerical simulations to explore band structures and density of states for both commensurate and incommensurate periodicity combinations.

Experimental results

Research questions

• RQ1 What geometric condition leads to the formation of quasi-one-dimensional moiré channels in strained twisted bilayer systems?
• RQ2 How does the interplay between twist angle and uniaxial strain induce a collapse of the reciprocal space unit cell?
• RQ3 What is the critical strain condition that triggers the transition to one-dimensional electronic behavior, and how does it depend on material properties like Poisson ratio?
• RQ4 How do the electronic bands and density of states evolve in the one-dimensional limit, particularly when two periodicities are incommensurate?
• RQ5 To what extent can the electronic structure in the 1D regime be described by models analogous to the Harper equation?

Key findings

• The critical strain for the formation of quasi-one-dimensional moiré patterns is determined by a simple relation involving the twist angle and the material's Poisson ratio.
• At the critical strain, the reciprocal space unit cell collapses into a line, reducing the system's symmetry from C6 to C2 and lifting degeneracies protected by C3 symmetry.
• The electronic bands in the one-dimensional limit are governed by two generally incommensurate periodicities, leading to a singular density of states with gaps of varying size.
• The system exhibits dispersive, extended electronic states for incommensurate periodicity combinations, consistent with the behavior of Harper-like systems.
• Relaxation effects at critical strain in low-angle twisted bilayer graphene favor the formation of parallel one-dimensional channels, where low-energy states are localized.
• The transition to one-dimensionality is robust and generalizable to other hexagonal twisted moiré systems, including transition metal dichalcogenides.