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In heterostructures consisting of atomically thin crystals layered on top of one another, lattice mismatch or rotation between the layers results in long-wavelength moiré superlattices. These moiré patterns can drive significant band structure reconstruction of the composite material, leading to a wide range of emergent phenomena including superconductivity [1][2][3], magnetism [4], fractional Chern insulating states [5], and moiré excitons [6][7][8][9]. Here, we investigate monolayer graphene encapsulated between two crystals of boron nitride (BN), where the rotational alignment between all three components can be varied. We find that band gaps in the graphene arising from perfect rotational alignment with both BN layers can be modified substantially depending on whether the relative orientation of the two BN layers is 0 or 60 degrees, suggesting a tunable transition between the absence or presence of inversion symmetry in the heterostructure. Small deviations (< 1 • ) from perfect alignment of all three layers leads to coexisting longwavelength moiré potentials, resulting in a highly reconstructed graphene band structure featuring multiple secondary Dirac points. Our results demonstrate that the interplay between multiple moiré patterns can be utilized to controllably modify the electronic properties of the composite heterostructure.The ability to combine diverse vdW materials into a heterostructure enables engineering of new properties not observed in the constituent materials alone. A unique degree of freedom within these vdW heterostructures is the twist angle between layers, and changing this angle can strongly modify the material properties owing to the formation of moiré patterns. In graphene-BN heterostructures, the moiré pattern introduces a spatiallyperiodic effective potential that modifies the graphene band structure, giving rise to emergent secondary Dirac points (SDPs) at finite energy [10][11][12][13] and band gaps at the charge neutrality point and valence band SDP [13][14][15][16][17][18][19][20][21][22][23][24][25][26]. In twisted bilayer graphene (tBLG), correlated insulating states and superconductivity emerge at a twist angle of ∼1.1 • where the lowest energy moiré bands be-come exceptionally flat [1,2,4,27,28]. However, typical vdW heterostructures comprising many flakes possess numerous crystal interfaces, and in principle multiple long-wavelength moiré patterns may coexist within a single heterostructure, likely with profound consequences on moiré-driven physics. For example, topological bands have been shown to potentially arise in tBLG aligned to BN [4]. So far, little has been done to controllably tune the alignment of multiple pairs of crystals within a single device, and it is not well understood how multiple moiré patterns interact to influence the properties of the vdW heterostructure.In a heterostructure where graphene is encapsulated on both sides by BN, there are a number of qualitatively distinct stacking orders that can be realized by independently controlling the twist angle ...

MoTe2 is an exfoliable transition metal dichalcogenide (TMD) which crystallizes in three symmetries; the semiconducting trigonal-prismatic 2H−phase, the semimetallic 1T ′ monoclinic phase, and the semimetallic orthorhombic T d structure 1-4 . The 2H−phase displays a band gap of ∼ 1 eV 5 making it appealing for flexible and transparent optoelectronics. The T d−phase is predicted to possess unique topological properties 6-9 which might lead to topologically protected non-dissipative transport channels 9 . Recently, it was argued that it is possible to locally induce phasetransformations in TMDs 3,10,11,14 , through chemical doping 12 , local heating 13 , or electric-field 14,15 to achieve ohmic contacts or to induce useful functionalities such as electronic phase-change memory elements 11 . The combination of semiconducting and topological elements based upon the same compound, might produce a new generation of high performance, low dissipation optoelectronic elements. Here, we show that it is possible to engineer the phases of MoTe2 through W substitution by unveiling the phase-diagram of the Mo1−xWxTe2 solid solution which displays a semiconducting to semimetallic transition as a function of x. We find that only ∼ 8 % of W stabilizes the T d−phase at room temperature. Photoemission spectroscopy, indicates that this phase possesses a Fermi surface akin to that of WTe2 16 .The properties of semiconducting and of semimetallic MoTe 2 are of fundamental interest in their own right, but are also for their potential technological relevance. In the mono-or few-layer limit it is a direct-gap semiconductor, while the bulk has an indirect bandgap 5,17,18 of ∼ 1 eV. The size of the gap is similar to that of Si, making 2H−MoTe 2 particularly appealing for both purely electronic devices 19,20 and optoelectronic applications 21 . Moreover, the existence of different phases opens up the possibility for many novel devices and architectures. For example, controlled conversion of the 1T ′ −MoTe 2 phase to the 2H−phase, as recently reported 22 , could