Data for: Correlated states in doubly-aligned hBN/graphene/hBN heterostructures

<p>Interfacial moir&eacute; superlattice in van der Waals vertical assemblies effectively reconstructs the crystal symmetry, leading to&nbsp;opportunities for investigating&nbsp;exotic quantum states. Notably, a two-dimensional nanosheet has top and bottom open surfaces, allowing the specific case of doubly aligned super-moir&eacute; lattice to serve as a toy model for studying the tunable lattice symmetry and the complexity of related electronic structures.&nbsp;Here, we show that by doubly aligning a monolayered graphene to both top and bottom encapsulating hexagonal boron nitride (h-BN), multiple conductivity minima are observed away from the main Dirac point, which are sensitively tunable with respect to the small twist angles. Moreover, our experimental evidences together with theoretical calculations suggest&nbsp;correlated insulating states at integer fillings of -5, -6, -7 electrons per moir&eacute;&nbsp;unit cell, possibly due to inter-valley coherence. Our results provide a way to construct intriguing strong correlations&nbsp;in 2D electronic systems, in the weak interaction regime.</p>