Super Moir\'e Domain Tessellations, Sliding Ferroelectricity, and Reconfigurable Quantum Dot Arrays in Twisted Trilayer Hexagonal Boron Nitride

Abstract

At very small twist angles, bilayer moir\'e systems exhibit characteristic stacking domain patterns, where the moir\'e length scale is determined solely by the twist angle. In contrast, the additional stacking and twisting degrees of freedom in twisted trilayer systems give rise to richer and more intricate domain tessellations. In twisted trilayer hexagonal boron nitride (TTBN), the interplay between polar and nonpolar domains and their domain walls is shown to result in unconventional responses to external electric fields, including electric-field tunability of the moir\'e-of-moir\'e or super moir\'e pattern--features absent in bilayer counterparts. We demonstrate that at the vertices of super moir\'e domains, TTBN can support arrays of quantum dots hosting localized quantum harmonic oscillator (QHO) states with diverse spatial symmetries. Futhermore, we show that the shape of the array and the spacing between the localized QHO states can be dynamically reconfigured by electric fields, enabling facile switching between fully isolated and strongly coupled regimes. The local potentials for the quantum dot state are predicted to be sufficiently deep to support a series of QHO states with nonzero angular momentum. This tunability enables control over the transport of quantum dot states and their interdot coupling, facillitating long-range quantum state transfer. Combined with the feasibility of large-scale fabrication of homogeneous twisted trilayer materials, these properties position TTBN as a promising platform for a wide range of quantum technologies.