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1. Corrugation-driven symmetry breaking in magic-angle twisted bilayer graphene

   https://doi.org/10.1038/s42005-022-01013-y  

   Rakib, Tawfiqur ; Pochet, Pascal ; Ertekin, Elif ; Johnson, Harley T. ( October 2022 , Communications Physics)

   The discovery of unconventional superconductivity in magic-angle twisted bilayer graphene (tBLG) supported the twist-angle-induced flat band structure predictions made a decade earlier. Numerous physical properties have since been linked to the interlayer twist angle using the flat band prediction as a guideline. However, some key observations like the nematic phase and striped charge order behind the superconductivity are missing in this initial model. Here we show that a thermodynamically stable large out-of-plane displacement, or corrugation of the bilayer, induced by the interlayer twist, demonstrates partially filled states of the flat band structure, accompanied by a broken symmetry, in the magic-angle regime and the presence of symmetry breaking associated with the superconductivity in tBLG. The distinction between low and high corrugation can also explain the observed evolution of the vibrational spectra of tBLG as a function of twist angle. Our observation that large out-of-plane deformation modes enable partial filling of states near the Fermi energy may lead to a strategy for offsetting the effects of disorder in the local twist angle, which suppresses unconventional superconductivity and correlated insulator behavior in magic-angle tBLG.
2. Moiré metrology of energy landscapes in van der Waals heterostructures

   https://doi.org/10.1038/s41467-020-20428-1  

   Halbertal, Dorri ; Finney, Nathan R. ; Sunku, Sai S. ; Kerelsky, Alexander ; Rubio-Verdú, Carmen ; Shabani, Sara ; Xian, Lede ; Carr, Stephen ; Chen, Shaowen ; Zhang, Charles ; et al ( December 2021 , Nature Communications)

   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.
3. The twist angle has weak influence on charge separation and strong influence on recombination in the MoS ₂ /WS ₂ bilayer: ab initio quantum dynamics

   https://doi.org/10.1039/d1ta10788g  

   Zhu, Yonghao ; Fang, Wei-Hai ; Rubio, Angel ; Long, Run ; Prezhdo, Oleg V. ( April 2022 , Journal of Materials Chemistry A)

   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 bymore »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.« less
4. Twist-angle dependence of moiré excitons in WS2/MoSe2 heterobilayers

   https://doi.org/10.1038/s41467-020-19466-6  

   Zhang, Long ; Zhang, Zhe ; Wu, Fengcheng ; Wang, Danqing ; Gogna, Rahul ; Hou, Shaocong ; Watanabe, Kenji ; Taniguchi, Takashi ; Kulkarni, Krishnamurthy ; Kuo, Thomas ; et al ( November 2020 , Nature Communications)

   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.
5. Topological gaps by twisting

   https://doi.org/10.1038/s42005-021-00630-3  

   Rosa, Matheus I. N. ; Ruzzene, Massimo ; Prodan, Emil ( June 2021 , Communications Physics)

   Twisted bilayered systems such as bilayered graphene exhibit remarkable properties such as superconductivity at magic angles and topological insulating phases. For generic twist angles, the bilayers are truly quasiperiodic, a fact that is often overlooked and that has consequences which are largely unexplored. Herein, we uncover that twistedn-layers host intrinsic higher dimensional topological phases, and that those characterized by second Chern numbers can be found in twisted bi-layers. We employ phononic lattices with interactions modulated by a second twisted lattice and reveal Hofstadter-like spectral butterflies in terms of the twist angle, which acts as a pseudo magnetic field. The phason provided by the sliding of the layers lives on 2n-tori and can be used to access and manipulate the edge states. Our work demonstrates how multi-layered systems are virtual laboratories for studying the physics of higher dimensional quantum Hall effect, and can be employed to engineer topological pumps via simple twisting and sliding.