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Register a new userChiral valley phonons and flat phonon bands in moire materials
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We investigate the chirality of phonon modes in twisted bilayer WSe2. We demonstrate distinct chiral behavior of the K/K valley phonon modes for twist angles close to 0 degrees and close to 60 degrees. Moreover, we discover two sets of well-separated chiral valley modes in moire lattices for angles close to 60 degrees. These emergent moire chiral valley phonons originate from inversion symmetry breaking at the moire scale. We also find similar emergent chiral modes in moire patterns of strain-engineered bilayer WSe2 and MoSe2/WSe2 heterostructure. Furthermore, we observe the flattening of bands near the phononic band-gap edges for a broad range of twist angles in twisted bilayer WSe2. Our findings, which are expected to be generic for moire systems composed of two-dimensional materials that break inversion symmetry, are relevant for understanding electron-phonon and exciton-phonon scattering, and for designing phononic crystals to mimic behaviors of electrons in moire materials.
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We demonstrate that the concept of moire flat bands can be generalized to achieve electronic band engineering in all three spatial dimensions. For many two dimensional van der Waals materials, twisting two adjacent layers with respect to each other leads to flat electronic bands in the two corresponding spatial directions -- a notion sometimes referred to as twistronics as it enables a wealth of physical phenomena. Within this two dimensional plane, large moire patterns of nanometer size form. The basic concept we propose here is to stack multiple twisted layers on top of each other in a predefined pattern. If the pattern is chosen such that with respect to the stacking direction of layers, the large spatial moire features are spatially shifted from one twisted layer to the next, the system exhibits twist angle controlled flat bands in all of the three spatial directions. With this, our proposal extends the use of twistronic to three dimensions. We exemplify the general concept by considering graphitic systems, boron nitride and WSe$_2$ as candidate materials, but the approach is applicable to any two-dimensional van der Waals material. For hexagonal boron nitride we develope an ab initio fitted tight binding model that captures the corresponding three dimensional low-energy electronic structure. We outline that interesting three dimensional correlated phases of matter can be induced and controlled following this route, including quantum magnets and unconventional superconducting states.
We present a low-energy model describing the reconstruction of the electronic spectrum in twisted bilayers of honeycomb crystals with broken sublattice symmetry. The resulting moire patterns are classified into two families with different symmetry. In both cases, flat bands appear at relatively large angles, without any magic angle condition. Transitions between them give rise to sharp resonances in the optical absorption spectrum at frequencies well below the gap of the monolayer. Owing to their chiral symmetry, twisted bilayers display circular dichroism, i.e., different absorption of left and right circularly-polarized light. This optical activity is a nonlocal property determined by the stacking. In hexagonal boron nitride, sensitivity to the stacking leads to strikingly different circular dichroism in the two types of moires. Our calculations exemplify how subtle properties of the electronic wavefunctions encoded in current correlations between the layers control physical observables of moire materials.
We theoretically demonstrate that moire phonons at the lowest-energy bands can become chiral. A general symmetry analysis reveals that they originate from stacking configurations leading to an asymmetric interlayer binding energy that breaks the $C_{2z}$ symmetry on the moire length scale. Within elastic theory, we provide a complete classification of van der Waals heterostructures in respect to hosting moire chiral phonons and discuss their emergence in twisted bilayer MoS$_2$ as an example. The formation of the chiral phonons can be qualitatively understood using an effective model, which emphasizes their origin in the energy difference between stacking domains. Since moire chiral phonons are highly tunable, with excitation energies in only a few meV, and moire scale wavelengths, they might find potential applications in phononic twistronic devices.
Collective plasma excitations in moire flat bands display unique properties reflecting strong electron-electron interactions and unusual carrier dynamics in these systems. Unlike the conventional two-dimensional plasmon modes, dispersing as $sqrt{k}$ at low frequencies and plunging into particle-hole continuum at higher frequencies, the moire plasmons pierce through the flat-band continuum and acquire a strong over-the-band character. Due to the complex structure of the moire superlattice unit cell, the over-the-band plasmons feature several distinct branches connected through zone folding in the superlattice Brillouin zone. Using a toy Hubbard model for the correlated insulating order in a flat band, we predict that these high-frequency modes become strongly dipole-active upon the system undergoing charge ordering, with the low-frequency modes gapped out within the correlated insulator gap. Strong dipole moments and sensitivity to charge order make these modes readily accessible by optical measurements, providing a convenient diagnostic of the correlated states.
We introduce and study a minimum two-orbital Hubbard model on a triangular lattice, which captures the key features of both the trilayer ABC-stacked graphene-boron nitride heterostructure and twisted transition metal dichalcogenides in a broad parameter range. Our model comprises first- and second-nearest neighbor hoppings with valley-contrasting flux that accounts for trigonal warping in the band structure. For the strong-coupling regime with one electron per site, we derive a spin-orbital exchange Hamiltonian and find the semiclassical ground state to be a spin-valley density wave. We show that a relatively small second-neighbor exchange interaction is sufficient to stabilize the ordered state against quantum fluctuations. Effects of spin- and valley Zeeman fields as well as thermal fluctuations are also examined.
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