Recent discoveries in twisted heterostructure materials have opened research directions in classical wave systems. This Letter investigates a family of double-sided pillared phononic crystal plates as the elastodynamic analog of bilayer graphene, including twisted bilayer graphene. The phononic crystal plate design is first validated by studying the basic AA- and AB-stack configurations under weak interlayer coupling. A specific commensurate twist angle giving rise to the sublattice exchange even symmetry is then studied to examine the twist-modulated band structure. Finally, this study demonstrates that the same twist angle, in concert with an ultra-strong interlayer coupling, can collectively create valley-dependent edge states that have not been previously observed in electronic bilayer graphene.
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Moiré metrology of energy landscapes in van der Waals heterostructures
Abstract The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twist-angle-induced superlattices offer means to control topology and strong correlations. At the small twist limit, and particularly under strain, as atomic relaxation prevails, the emergent moiré superlattice encodes elusive insights into the local interlayer interaction. Here we introduce moiré metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 meV/atom scale, outperforming the gold-standard of quantum chemistry. Through studying the shapes of moiré domains with numerous nano-imaging techniques, and correlating with multi-scale modelling, we assess and refine first-principle models for the interlayer interaction. We document the prowess of moiré metrology for three representative twisted systems: bilayer graphene, double bilayer graphene and H-stacked MoSe 2 /WSe 2 . Moiré metrology establishes sought after experimental benchmarks for interlayer interaction, thus enabling accurate modelling of twisted multilayers.
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- Award ID(s):
- 1922172
- NSF-PAR ID:
- 10297388
- Author(s) / Creator(s):
- ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »
- Date Published:
- Journal Name:
- Nature Communications
- Volume:
- 12
- Issue:
- 1
- ISSN:
- 2041-1723
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Twisted photonic crystals are photonic analogs of twisted monolayer materials such as graphene and their optical property studies are still in their infancy. This paper reports optical properties of twisted single-layer 2D+ moiré photonic crystals where there is a weak modulation in z direction, and bilayer moiré-overlapping-moiré photonic crystals. In weak-coupling bilayer moiré-overlapping-moiré photonic crystals, the light source is less localized with an increasing twist angle, similar to the results reported by the Harvard research group in References 37 and 38 on twisted bilayer photonic crystals, although there is a gradient pattern in the former case. In a strong-coupling case, however, the light source is tightly localized in AA-stacked region in bilayer PhCs with a large twist angle. For single-layer 2D+ moiré photonic crystals, the light source in Ex polarization can be localized and forms resonance modes when the single-layer 2D+ moiré photonic crystal is integrated on a glass substrate. This study leads to a potential application of 2D+ moiré photonic crystal in future on-chip optoelectronic integration.
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Abstract Moiré lattices formed in twisted van der Waals bilayers provide a unique, tunable platform to realize coupled electron or exciton lattices unavailable before. While twist angle between the bilayer has been shown to be a critical parameter in engineering the moiré potential and enabling novel phenomena in electronic moiré systems, a systematic experimental study as a function of twist angle is still missing. Here we show that not only are moiré excitons robust in bilayers of even large twist angles, but also properties of the moiré excitons are dependant on, and controllable by, the moiré reciprocal lattice period via twist-angle tuning. From the twist-angle dependence, we furthermore obtain the effective mass of the interlayer excitons and the electron inter-layer tunneling strength, which are difficult to measure experimentally otherwise. These findings pave the way for understanding and engineering rich moiré-lattice induced phenomena in angle-twisted semiconductor van der Waals heterostructures.
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Abstract Twisted 2D materials form complex moiré structures that spontaneously reduce symmetry through picoscale deformation within a mesoscale lattice. We show twisted 2D materials contain a torsional displacement field comprised of three transverse periodic lattice distortions (PLD). The torsional PLD amplitude provides a single order parameter that concisely describes the structural complexity of twisted bilayer moirés. Moreover, the structure and amplitude of a torsional periodic lattice distortion is quantifiable using rudimentary electron diffraction methods sensitive to reciprocal space. In twisted bilayer graphene, the torsional PLD begins to form at angles below 3.89° and the amplitude reaches 8 pm around the magic angle of 1. 1°. At extremely low twist angles (e.g. below 0.25°) the amplitude increases and additional PLD harmonics arise to expand Bernal stacked domains separated by well defined solitonic boundaries. The torsional distortion field in twisted bilayer graphene is analytically described and has an upper bound of 22.6 pm. Similar torsional distortions are observed in twisted WS 2 , CrI 3 , and WSe 2 /MoSe 2 .more » « less
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Van der Waals heterojunctions of two-dimensional transition-metal dichalcogenides are intensely investigated for multiple optoelectronics applications. Strong and adjustable interactions between layers can influence the charge and energy flow that govern material performance. We report ab initio quantum molecular dynamics investigation of the influence of the bilayer twist angle on charge transfer and recombination in MoS 2 /WS 2 heterojunctions, including high-symmetry 0° and 60° configurations, and low symmetry 9.43° and 50.57° structures with Moiré patterns. The twist angle modulates interlayer coupling, as evidenced by changes in the interlayer distance, electron-vibrational interactions, and spectral shifts in the out-of-plane vibrational frequencies. Occurring on a femtosecond timescale, the hole transfer depends weakly on the twist angle and is ultrafast due to high density of acceptor states and large nonadiabatic coupling. In contrast, the electron–hole recombination takes nanoseconds and varies by an order of magnitude depending on the twist angle. The recombination is slow because it occurs across a large energy gap. It depends on the twist angle because the nonadiabatic coupling is sensitive to the interlayer distance and overlap of electron and hole wavefunctions. The Moiré pattern systems exhibit weaker interlayer interaction, generating longer-lived charges. Both charge separation and recombination are driven by out-of-plane vibrational motions. The simulations rationalize the experimental results on the influence of the bilayer twist angle on the charge separation and recombination. The atomistic insights provide theoretical guidance for design of high-performance optoelectronic devices based on 2D van der Waals heterostructures.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1038/s41467-020-20428-1
