Flexible long period moiré superlattices form in two-dimensional van der Waals crystals containing layers that differ slightly in lattice constant or orientation. In this Letter we show theoretically that isolated flat moiré bands described by generalized triangular lattice Hubbard models are present in twisted transition metal dichalcogenide heterobilayers. The hopping and interaction strength parameters of the Hubbard model can be tuned by varying the twist angle and the three-dimensional dielectric environment. When the flat moiré bands are partially filled, candidate many-body ground states at some special filling factors include spin-liquid states, quantum anomalous Hall insulators, and chiral d-wave superconductors.

We show that moiré bands of twisted homobilayers can be topologically nontrivial, and illustrate the tendency by studying valence band states in ±K valleys of twisted bilayer transition metal dichalcogenides, in particular, bilayer MoTe2. Because of the large spin-orbit splitting at the monolayer valence band maxima, the low energy valence states of the twisted bilayer MoTe2 at +K (−K) valley can be described using a two-band model with a layer-pseudospin magnetic field ∆(r) that has the moiré period. We show that ∆(r) has a topologically non-trivial skyrmion lattice texture in real space, and that the topmost moiré valence bands provide a realization of the Kane-Mele quantum spin-Hall model, i.e., the two-dimensional time-reversal-invariant topological insulator. Because the bands narrow at small twist angles, a rich set of broken symmetry insulating states can occur at integer numbers of electrons per moiré cell. arXiv:1807.03311v2 [cond-mat.mes-hall]

We present a theory of optical absorption by interlayer excitons in a heterobilayer formed from transition metal dichalcogenides. The theory accounts for the presence of small relative rotations that produce a momentum shift between electron and hole bands located in different layers, and a moiré pattern in real space. Because of the momentum shift, the optically active interlayer excitons are located at the moiré Brillouin zone's corners, instead of at its center, and would have elliptical optical selection rules if the individual layers were translationally invariant. We show that the exciton moiré potential energy restores circular optical selection rules by coupling excitons with different center of mass momenta. A variety of interlayer excitons with both senses of circular optical activity, and energies that are tunable by twist angle, are present at each valley. The lowest energy exciton states are generally localized near the exciton potential energy minima. We discuss the possibility of using the moiré pattern to achieve scalable two-dimensional arrays of nearly identical quantum dots.arXiv:1710.10278v2 [cond-mat.mes-hall]

Moiré patterns are common in van der Waals heterostructures and can be used to apply periodic potentials to elementary excitations. We show that the optical absorption spectrum of transition metal dichalcogenide bilayers is profoundly altered by long period moiré patterns that introduce twist-angle dependent satellite excitonic peaks. Topological exciton bands with non-zero Chern numbers that support chiral excitonic edge states can be engineered by combining three ingredients: i) the valley Berry phase induced by electron-hole exchange interactions, ii) the moiré potential, and iii) the valley Zeeman field.Stacking two-dimensional (2D) materials into van der Waals heterostructures opens up new strategies for materials property engineering. One increasingly important example is the possibility of using the relative orientation (twist) angle between two 2D crystals to tune electronic properties. For small twist angles and latticeconstant mismatches, heterostructures exhibit long period moiré patterns that can yield dramatic changes. Moiré pattern formed in graphene-based heterostructures has been extensively studied, and many interesting phenomena have been observed, for example gap opening at graphene's Dirac point [1,2], generation of secondary Dirac points [3,4] and Hofstadter-butterfly spectra in a strong magnetic field [1,5,6].In this Letter, we study the influence of moiré patterns on collective excitations, focusing on the important case of excitons in the transition metal dichalcogenide (TMD) 2D semiconductors [7,8] like MoS 2 and WS 2 . Exciton features dominate the optical response of these materials because electron-hole pairs are strongly bound by the Coulomb interaction [9][10][11][12]. An exciton inherits a pseudospin-1/2 valley degree of freedom from its constituent electron and hole, and the exciton valley pseudospin can be optically addressed [13][14][15][16], providing access to the valley Hall effect [17] and the valley selective optical Stark effect [18,19].As in the case of graphene/hexagonal-boron-nitride and graphene/graphene bilayers, a moiré pattern can be established in TMD bilayers by using two different materials with a small lattice mismatch, by applying a small twist, or by combining both effects. TMD heterostructures have been realized [20][21][22] experimentally and can host interesting effects, for example the observation of valley polarized interlayer excitons with long lifetimes [23], the theoretical prediction of multiple degenerate interlayer excitons [24], and the possibility of achieving spatially indirect exciton condensation [25,26]. Our focus here is instead on the intralayer excitons that are more strongly coupled to light. As we explain below, the moiré pattern produces a periodic potential, mixing momentum states separated by moiré reciprocal lattice vectors and producing satellite optical absorption peaks that are revealing. The exciton energy-momentum dispersion can be measured by tracking the dependence of satellite peak energies on twist angle.The valley pseudospin...

In minimally twisted bilayer graphene, a moiré pattern consisting of AB and BA stacking regions separated by domain walls forms. These domain walls are predicted to support counterpropogating topologically protected helical (TPH) edge states when the AB and BA regions are gapped. We fabricate designer moiré crystals with wavelengths longer than 50 nm and demonstrate the emergence of TPH states on the domain wall network by scanning tunneling spectroscopy measurements. We observe a double-line profile of the TPH states on the domain walls, only occurring when the AB and BA regions are gapped. Our results demonstrate a practical and flexible method for TPH state network construction.