Research Projects

Moiré superlattices in twisted two-dimensional crystals undergo pronounced in-plane lattice relaxation, leading to the formation of large, triangular domains separated by narrow domain walls. Notable examples of relaxation-induced moiré systems include minimally twisted bilayer graphene (MTBG), where the twist angle between the graphene layers is much smaller than 1 degree. Due to lattice relaxation, the moiré pattern relaxes into a triangular tiling of AB and BA Bernal-stacked regions. Additionally, helical trilayer graphene (HTG), another member of the moiré family, features a supermoiré structure, which relaxes into domains consisting of a single moiré pattern and its mirror-symmetric counterpart. When these domains and rendered incompressible and topological (e.g., by external gates), the resulting domain walls host chiral one-dimensional modes. At low temperatures, the electronic properties of such systems are governed by the network formed by these one-dimensional modes. In MTBG, researchers have observed magneto-oscillations in conductance, which have been qualitatively explained by non-interacting network models. Theoretical studies have also proposed that this system could serve as a tunable Josephson junction. Similar experimental and theoretical investigations are yet to be performed for helical trilayer graphene. However, a key missing piece across these systems is the role of electron interactions on the network of one-dimensional domain wall modes, which remains uncharacterised. In the presence of electron interactions, each domain wall mode realizes a Luttinger Liquid (LL), which is a theoretical description of interacting electron fluid confined to move in one dimension. While the LL formed in at a domain wall has been studied previously, the collective behavior of a network where such LL wires are coupled remains largely unexplored. In particular, multiple upstream and downstream modes along domain walls and coupling between the wires can destabilize the LL phase and potentially lead to qualitatively different phases than those found on a single domain wall. The central goal of this project is to determine whether the network of LL wires remains stable and to identify the resulting transport signatures. A deeper understanding of these interaction effects is essential for harnessing the potential of moiré materials in advancing applications in quantum metrology and sensing, one of the key focus areas of the National Quantum Mission.