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.
Tunable strain soliton networks confine electrons in van der Waals materials
Twisting or sliding two-dimensional crystals with respect to each other gives rise to moiré patterns determined by the difference in their periodicities. Such lattice mismatches can exist for several reasons: differences between the intrinsic lattice constants of the two layers, as is the case for graphene on BN; rotations between the two lattices, as is the case for twisted bilayer graphene; and strains between two identical layers in a bilayer. Moiré patterns are responsible for a number of new electronic phenomena observed in recent years in van der Waals heterostructures, including the observation of superlattice Dirac points for graphene on BN, collective electronic phases in twisted bilayers and twisted double bilayers, and trapping of excitons in the moiré potential. An open question is whether we can use moiré potentials to achieve strong trapping potentials for electrons. Here, we report a technique to achieve deep, deterministic trapping potentials via strain-based moiré engineering in van der Waals materials. We use strain engineering to create on-demand soliton networks in transition metal dichalcogenides. Intersecting solitons form a honeycomb-like network resulting from the three-fold symmetry of the adhesion potential between layers. The vertices of this network occur in bound pairs with different interlayer stacking arrangements. One vertex of the pair is found to be an efficient trap for electrons, displaying two states that are deeply confined within the semiconductor gap and have a spatial extent of 2 nm. Soliton networks thus provide a path to engineer deeply confined states with a strain-dependent tunable spatial separation, without the necessity of introducing chemical defects into the host materials.
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- Award ID(s):
- 1727717
- NSF-PAR ID:
- 10176487
- Date Published:
- Journal Name:
- Nature Physics
- ISSN:
- 1745-2473
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract -
null (Ed.)In moiré crystals formed by stacking van der Waals materials, surprisingly diverse correlated electronic phases and optical properties can be realized by a subtle change in the twist angle. Here, we discover that phonon spectra are also renormalized in MoS2 twisted bilayers, adding an insight to moiré physics. Over a range of small twist angles, the phonon spectra evolve rapidly owing to ultra-strong coupling between different phonon modes and atomic reconstructions of the moiré pattern. We develop a low-energy continuum model for phonons that overcomes the outstanding challenge of calculating the properties of large moiré supercells and successfully captures the essential experimental observations. Remarkably, simple optical spectroscopy experiments can provide information on strain and lattice distortions in moiré crystals with nanometre-size supercells. The model promotes a comprehensive and unified understanding of the structural, optical and electronic properties of moiré superlattices.more » « less
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We report deterministic control over a moiré superlattice interference pattern in twisted bilayer graphene by implementing designable device-level heterostrain with process-induced strain engineering, a widely used technique in industrial silicon nanofabrication processes. By depositing stressed thin films onto our twisted bilayer graphene samples, heterostrain magnitude and strain directionality can be controlled by stressor film force (film stress × film thickness) and patterned stressor geometry, respectively. We examine strain and moiré interference with Raman spectroscopy through in-plane and moiré-activated phonon mode shifts. Results support systematic C 3 rotational symmetry breaking and tunable periodicity in moiré superlattices under the application of uniaxial or biaxial heterostrain. Experimental results are validated by molecular statics simulations and density functional theory based first principles calculations. This provides a method not only to tune moiré interference without additional twisting but also to allow for a systematic pathway to explore different van der Waals based moiré superlattice symmetries by deterministic design.more » « less
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Fermi nesting Correlated states have been shown to emerge in bilayer and trilayer graphene with the two-dimensional layers at just the right angle with respect to each other. Key to the enhanced importance of interactions are the so-called moiré electronic bands that form in such systems. Rickhaus
et al . explored a related system of two graphene bilayers twisted with respect to each other. The twist angle was set so that the layer coupling was strong enough to form moiré bands but weak enough for the carrier concentration in the top and bottom bilayer to be controlled separately. Doping the top bilayer with electrons and the bottom bilayer with holes, the researchers created a correlated state with nested Fermi surfaces. —JS -
null (Ed.)Abstract The discovery of interaction-driven insulating and superconducting phases in moiré van der Waals heterostructures has sparked considerable interest in understanding the novel correlated physics of these systems. While a significant number of studies have focused on twisted bilayer graphene, correlated insulating states and a superconductivity-like transition up to 12 K have been reported in recent transport measurements of twisted double bilayer graphene. Here we present a scanning tunneling microscopy and spectroscopy study of gate-tunable twisted double bilayer graphene devices. We observe splitting of the van Hove singularity peak by ~20 meV at half-filling of the conduction flat band, with a corresponding reduction of the local density of states at the Fermi level. By mapping the tunneling differential conductance we show that this correlated system exhibits energetically split states that are spatially delocalized throughout the different regions in the moiré unit cell, inconsistent with order originating solely from onsite Coulomb repulsion within strongly-localized orbitals. We have performed self-consistent Hartree-Fock calculations that suggest exchange-driven spontaneous symmetry breaking in the degenerate conduction flat band is the origin of the observed correlated state. Our results provide new insight into the nature of electron-electron interactions in twisted double bilayer graphene and related moiré systems.more » « less
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1038/s41567-020-0953-2
