Session D55: Physical Properties of Twisted Transition Metal Dichalcogenides

Smectic phases in moire patterns of bilayer graphene

We study the possibility of smectic phases in biased bilayer graphene under electron-electron interaction effects. When one layer is deformed by strain, this system can be modeled as a single graphene layer with a periodic moire potential, which derives from integrating out the deformed layer. Under an appropriately chosen deformation, the effective model describes an array of parallel of one dimensional wires describing coupled Luttinger liquids. We investigate how to realistically engineer various experimentally observable smectic phases that have been predicted in the context of doped Mott insulators by controlling the amount of strain and bias voltage in this system.   

Low-energy moiré phonons in twisted bilayer heterostructures

We develop a continuum model for low-energy phonon modes in moiré bilayers based on force fields computed from first-principles Density Functional Theory (DFT) in local stacking configurations. Applied directly, DFT calculations of moiré phonons are intractable, and while empirical continuum models are efficient, they are crude and ignore important details. The model we propose is based on first-principles DFT while remaining efficient to compute. We show that the low-energy phonon modes sensitively depend on the twist angle, which dictates the interlayer coupling strength and relaxation . As the twist angle becomes small, the frequencies of low-energy modes reorder and several mode symmetries in real space break. We exemplify our findings on twisted bilayer graphene, molybdenum disulfide (MoS₂), and Janus heterostructures.   

Measurement of the chemical potential in angle-aligned WS2/WSe2 moire superlattice

Recently, TMD moire superlattices have been demonstrated as a highly tunable platform with strong electron correlation. Various 2D quantum phases have been reported in this system, such as Mott insulator, generalized Wigner crystal states and quantum anomalous effect. With the ability to detect sample’s local conductivity, microwave impedance microscopy (MIM) has been used to observe a series of correlated insulating states at both integer and fractional fillings of the moire superlattice. Here, we report measurement of the chemical potential in moire heterobilayer devices (WS₂/WSe₂) with a dual gate geometry. A monolayer graphene is used as the top gate and its carrier density is determined by the potential difference with the moire heterobilayer. With the graphene’s local carrier density and conductivity probed with MIM and fixed by adjusting the gate voltage, the change in the chemical potential of the moire heterobilayer can be detected. We will discuss measurement results of its chemical potential when the moire heterobilayer is tuned through various correlated insulating states.   

Spin and layer pseudospin order in transition metal dichalcogenide double-moire systems

We study the competition between spin, layer polarization, and layer coherence order in transition metal dichalcogenidie double-moiré systems by performing self-consistent unrestricted Hartree-Fock calculations. Spontaneous layer coherence states are counter-flow superfluids, whereas spontaneous layer polarization states are expected to lead to a hysteric dependence of layer polarization on external displacement field. At integer moiré filling factors we find that the dependence of the ground state on displacement field exhibits a series of generalized Wigner crystal states at rational layer polarizations, separated by intervals of spontaneous interlayer phase coherence. We comment on the relationship between our theoretical results and the recent experimental identification of a dipolar exciton insulator in a moire lattice [Gu, et al. arXiv:2108.06588; Zhang, et al. arXiv:2108.07131].   

Twisted Janus TMDs as moiré quantum simulators

We investigate the moiré bandstructure of twisted polar transition metal dichalcogenides bilayers (Janus TMDs). These systems exhibit a set of extremely narrow bands over a broad range of twist angles. The dispersion is computed using a continuum model instructed by ab-initio calculations and accounts for lattice relaxation, spin-orbit coupling (SOC), and effective mass variations on the moiré scale. In homobilayers, the moirè pattern localizes holes/electrons in triangular, honeycomb, and  Kagomè lattices while in heterobilayers Rashba SOC generates non-trivial spin textures.   

Atomic reconstruction and flat bands in strain engineered transition metal dichalcogenide bilayer moiré systems

Strain-induced lattice mismatch leads to moiré patterns in homobilayer transition metal dichalcogenides (TMDs). We investigate the structural and electronic properties of such strained moiré patterns in TMD homobilayers. The moiré patterns in strained TMDs consist of several stacking domains which are separated by tensile solitons. The order parameter distribution shows the formation of aster topological defects at the highest energy stackings. In contrast, twisted TMDs host shear solitons at the domain walls, and the order parameter distribution shows the formation of vortex defects. The strained moiré systems also host several well-separated flat bands at both the valence and conduction band edges. The flat bands in these strained moiré superlattices provide platforms for studying the Hubbard model on a triangular lattice as well as the ionic Hubbard model on a honeycomb lattice. The wavefunction localization, which is different from twisted TMDs, is in excellent agreement with recent spectroscopic experiments [1].

1. D. Edelberg et al., Nature Physics 16, 1097-1102 (2020)   

Pressuring-tuning of moiré phonons in MoS2/WSe2 heterostructures

Moiré superlattices can be created by stacking two-dimensional crystals with a small lattice mismatch or twist-angle between the layers. The associated moiré potential can give rise to new excitations in the system, such as moiré phonons: phonons from the individual layers downfolded to zone center through the periodicity of the moiré potential. Hydrostatic pressure can be a powerful tool to study and further tune those excitations. Here, we investigate the evolution of moiré phonons in a rotationally-aligned MoS₂/WSe₂ moiré heterostructure at high-pressures via Raman spectroscopy. Moiré phonons are revealed as satellite Raman peaks that appear exclusively in the heterostructure region, which are found to blueshift and increase in intensity under the application of pressure. By combining density functional theory and an effective model of the pressure-dependent moiré potential with zone folding analysis, we are able to assign the satellite peaks to downfolded MoS₂ optical phonons and accurately capture their evolution with pressure. Our theoretical analysis further illustrates the microscopic process that generates moiré phonons which can be associated to an electron-phonon scattering process within the mini-Brillouin zone. Crucially, this connection to the electronic system establishes moiré phonons as a sensitive probe of the mini-band electronic structure in moiré systems. Our work may shed light on the interplay between moiré potentials, phonons and electron-phonon scattering in novel moiré systems.   

Ultra-strong spin-orbit coupling and topological moire engineering in twisted ZrS2 bilayers

Pioneering experiments in twisted bilayer graphene and group-VI transition-metal dichalcogenide (TMD) heterostructures pave the way towards leveraging quantum interference in moiré superlattices as a broader paradigm, to quench kinetic energy scales and selectively enhance the role of competing interactions. Here, we propose twisted bilayers of the group-IV TMD ZrS₂ as a tunable platform to engineer two-dimensional topological quantum phases, instead dominated by strong spin-orbit interactions. At small twist angles, ZrS₂ heterostructures give rise to an emergent and twist-controlled moiré Kagomé lattice, combining geometric frustration and strong spin-orbit coupling to give rise to a moiré quantum spin Hall insulator with highly controllable and nearly-dispersionless bands. We study the emergence of a robust quantum anomalous Hall phase as well as possible fractional Chern insulating states from strong Coulomb repulsion at fractional fillings of the topological moiré Kagomé bands. Our results establish group-IV transition metal dichalcogenide bilayers as a novel moiré platform to realize strongly-correlated topological phases in a twist-tunable setting.   

Dynamical mean field theory of moire bilayer transition metal dichalcogenides

We present a comprehensive dynamical mean field study of the moire Hubbard model, which is believed to represent the physics of moire bilayer transition metal dichalcogenides. In these materials the band structure (including the presence or absence of a higher order van Hove singularity) can be tuned  by varying a ``displacement field". We present a magnetic and metal-insulator phase diagram and a detailed study of the dependence of the resistivity on temperature, band filling and displacement field. We find regions of strange metal behavior as well as Fermi liquid regions and show how varying the displacement field leads to actual or apparent criticality and how magnetic order affects the resistivity.  We compare our results to recent experiments.     

Thermodynamic measurements of AB-stacked twisted TMD homobilayers

Moiré superlattices composed from semiconducting transition metal dichalcogenide (TMD) layers provide a versatile platform for engineering emergent quantum phases. At low relative twist angle, these systems form flat bands in which electronic interactions dominate over kinetic energy. The resulting electronic states are predicted to depend sensitively on interlayer stacking and lattice reconstruction, with additional tunability and degrees of freedom available in twisted homobilayers. However, these systems have proved difficult to study in the small twist angle limit (<3 degrees), due in part to poor electrical contact which limits quantum transport studies. In this talk, I will describe penetration field and capacitance sensing techniques that overcome this challenge and allow us to measure the electronic compressibility of nearly-AB stacked TMD homobilayers at low twist angle. I will present thermodynamic measurements of charge-ordered states and comment on their dependence on external tuning parameters such as applied electric displacement and magnetic fields.

    

Friction Scaling law of two dimensional heterojunctions

The weak interlayer interaction and strong intralayer bonding in two-dimensional (2D) layered materials give rise to distinguished ultra-low friction and wear properties when two incommensurate crystalline lattices are in contact, known as structural superlubricity.  However, due to experimental restrictions, the scaling law of friction in superlubricity remains ambiguous. Specifically, the correlations between friction and the coupling effects of contact area, edge length as well as normal load are not yet fully understood.  Here, using a novel geometry that decouples bulk from edge contributions to interlayer friction, we quantitatively demonstrate the generalised scaling law of friction in 2D hetero-junctions.  Consistent with theory, friction per internal atom is at least 4 orders of magnitude smaller than that of edge atom.  Moreover, friction force within a single Moiré unit cell scales in a power law of the Moiré unit cell area f~Am^γ with 1.2≤γ≤2.7, and the overal friction from the internal atoms scales linearly with the total number of Moiré unit cells.  Finally, depending on the Moiré unit cell size and edge length, both positive and negative coefficients of friction are observed as a result of the competition between the suppression of elevated Moiré ridges and mechanical deformation contributions.    

Resonant coulomb energy transfer in transition metal dichalcogenide moirés

We report on a theoretical study of Coulomb-mediated energy transfer between electrically isolated transition metal dichalcogenide (TMD) moirés. We discuss two distinct models (approximations) intended to be accurate when the inter-moiré Coulomb interaction is either strong or weak compared to the moiré bandwidth. In the former case, which occurs when the inter-moiré spacing d is smaller than the moiré lattice constant a_M and the twist angle θ≤2º, inter-moiré energy transfer arises from interactions between nearby pairs of artificial molecules--sites of the moiré lattice where low-energy moiré band states localize. In the latter case, which occurs when θ≥2º, we describe the energy transfer with a Fermi's golden expression rule based on the random phase approximation for inter-moiré two-particle scattering amplitudes. Due to a competition between moiré lattice site densities and bandwidths, the energy transfer rate is maximized at twist angles θ≈4º, at which an interfacial thermal conductance G on the order of 100 MW/(m²K) is achievable. We relate our models of the strong and weak coupling regimes to models of the analogous regimes in photosynthetic, intermolecular energy transfer.   

Theory of near-field electrostatic effects in van der Waals heterostructures and Moiré structures

Recent advances in the fabrication and characterization of van der Waals heterostructures have demonstrated large tunability of their optoelectronic properties with respect to the relative twist and sliding of the structures. Beyond the quantum mechanical coupling between adjacent layers, 2D materials can impact the local electrostatic potential. At typical 2D-2D materials distance, near-field effects can be dominant and a multipole expansion of the potential become insufficient to capture the materials descriptors.

In this work, we develop a theory of the near-field electrostatic effects of 2D materials. We show using density functional theory that the electrostatic potential of a vast number of 2D materials is well approximated by a discretized charge density model. We derive simple analytical expressions of the electrostatic potential V(x,y,z), and show their applicability to the case of van der Waals and Moiré structures.   

Twisted Bilayer Kagome Acoustic Metamaterials

Quantum twistronics–the use of van der Waals heterostructures to create moire systems with novel electronic properties–has opened a vast parameter space of materials and assembly techniques that overwhelms the capabilities of direct exploration. Acoustic metamaterials have emerged as solutions to prototype their laborious quantum counterparts, and twisted bilayer graphene has already been successfully translated into the field of acoustics [1]. Here we reproduce similar acoustic metamaterial analogs of kagome twisted bilayers comprised of interconnected air cavities and thin interlayer membranes. Using COMSOL Multiphysics we accurately mimic both the flat band systems and real space modes of kagome twisted bilayers, and the easily tunable interlayer coupling of our metamaterials allows us to increase our magic angle to allow more computationally tractable supercell sizes. Our work demonstrates a macroscopic, continuously controllable platform for investigating twistronics beyond graphene.

[1] S Minhal Gardezi et al, 2D Materials 8, 031002 (2021)