Tunable angle-dependent electrochemistry at twisted bilayer graphene with moiré flat bands

Yu, Yun; Zhang, Kaidi; Parks, Holden; Babar, Mohammad; Carr, Stephen; Craig, Isaac M.; Winkle, Madeline Van; Lyssenko, Artur; Taniguchi, Takashi; Watanabe, Kenji; Viswanathan, Venkatasubramanian; Bediako, D. Kwabena

doi:10.1038/s41557-021-00865-1

Cited by 88 publications

(154 citation statements)

References 59 publications

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“…The nodes of the network where dislocation lines meet in the relaxed moiré system (sometimes known as AA points in graphene or TMD moiré) have been referred to as topological defects by Alden et al [20], and again by Turkel et al [21], who also emphasize their role in transport as tunable, local concentrations of twist angle. They have also been shown to play the role of defects in electrochemistry [22]. However, we find that the or-der parameter describing the topology of these defects is rather different from that of the conventional vortex descriptions in the planar magnet or superfluid, where the order parameter can be described by a complex number of unit length.…”

Section: Introductionmentioning

confidence: 57%

Non-Abelian topological defects and strain mapping in 2D moiré materials

Engelke¹,

Carr²,

Xu³

et al. 2022

Preprint

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We present a general method to analyze the topological nature of the domain boundary connectivity that appeared in relaxed moiré superlattice patterns at the interface of 2-dimensional (2D) van der Waals (vdW) materials. At large enough moiré lengths, all moiré systems relax into commensurated 2D domains separated by networks of dislocation lines. The nodes of the 2D dislocation line network can be considered as vortex-like topological defects. We find that a simple analogy to common topological systems with an S 1 order parameter, such as a superconductor or planar ferromagnet, cannot correctly capture the topological nature of these defects. For example, in twisted bilayer graphene, the order parameter space for the relaxed moiré system is homotopy equivalent to a punctured torus. Here, the nodes of the 2D dislocation network can be characterized as elements of the fundamental group of the punctured torus, the free group on two generators, endowing these network nodes with non-Abelian properties. Extending this analysis to consider moiré patterns generated from any relative strain, we find that antivortices occur in the presence of anisotropic heterostrain, such as shear or anisotropic expansion, while arrays of vortices appear under twist or isotropic expansion between vdW materials. Experimentally, utilizing the dark field imaging capability of transmission electron microscopy (TEM), we demonstrate the existence of vortex and antivortex pair formation in a moiré system, caused by competition between different types of heterostrains in the vdW interfaces. We also present a methodology for mapping the underlying heterostrain of a moiré structure from experimental TEM data, which provides a quantitative relation between the various components of heterostrain and vortex-antivortex density in moiré systems.

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Section: Introductionmentioning

confidence: 57%

Non-Abelian topological defects and strain mapping in 2D moiré materials

Engelke¹,

Carr²,

Xu³

et al. 2022

Preprint

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“…1.1 o , which leads to the formation of electronic bands with very weak dispersion in momentum space, so-called 'flat' bands 47 . In a recent seminal work, Yu et al 48 established the fundamental baseline for the understanding of the heterogeneous kinetics at the twisted bilayer graphene/aqueous electrolyte interface, by probing the dependence of the heterogeneous electron transfer rate on the twist angle using both electrochemical methods and theoretical calculations. This was achieved by investigating the effect of the twist angle on graphene DOS in the vicinity of the Fermi level.…”

Section: % (mentioning

confidence: 99%

The electrochemical double layer at the graphene/aqueous electrolyte interface: what we can learn from simulations, experiments, and theory

et al. 2022

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“…It is clearly resembling Equation ( 4) apart from the term F c,v,v,c . As noted, the exchange energy correction to the bare electronic bands was neglected in Equation (19). This correction turns out to be important at k ¼ 0, as it renormalizes the bare bandgap.…”

Section: Bsementioning

confidence: 99%

“…As graphene physics matured, the interest in other 2D materials grew and novel physical properties were found. The existence of correlated phases in twisted graphene layers, [16][17][18][19][20][21] valley physics and excitons in TMDs, [3,[22][23][24][25][26][27] 2D superconductivity, [28][29][30][31][32] 2D magnetic materials, and the myriad of heterostructures made of these materials has created a new and exciting research field in condensed matter physics and materials science alike.…”

Section: Introductionmentioning

confidence: 99%

Theoretical Methods for Excitonic Physics in 2D Materials

Quintela

Henriques

Tenório

et al. 2022

Physica Status Solidi (b)

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In this Perspective article, the reader is introduced to several theoretical methods of determining the exciton wave functions and the corresponding eigenenergies. The methods covered are either analytical, semianalytical, or numeric. All the details associated with the different methods are made explicit, thus allowing newcomers to do research on their own, without experiencing a steep learning curve. The Perspective starts with a variational method and ends with a simple semianalytical approach to solve the Bethe–Salpeter equation (BSE) in gapped 2D materials. For the first methods addressed in this Perspective, the authors focus on a single layer of hexagonal boron nitride (hBN) and of transition metal dichalcogenide (TMD), as these are exemplary materials in the field of 2D excitons. For explaining the Bethe–Salpeter method, the biased bilayer graphene, which presents a tunable bandgap is chosen. The system has the right amount of complexity (without being excessive). This allows the presentation of the solution in a context that can be easily generalized to more complex systems or to apply it to simpler models.

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Tunable angle-dependent electrochemistry at twisted bilayer graphene with moiré flat bands

Cited by 88 publications

References 59 publications

Non-Abelian topological defects and strain mapping in 2D moiré materials

Non-Abelian topological defects and strain mapping in 2D moiré materials

The electrochemical double layer at the graphene/aqueous electrolyte interface: what we can learn from simulations, experiments, and theory

Theoretical Methods for Excitonic Physics in 2D Materials

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