Research Projects

In the last two years an entirely new platform for realizing topological condensed matter and correlated states has become available – rhombohedral stacked multilayer graphene. [4–9] The bands in rhombohedral n-layered graphene are also flat, E ∝ k^n , and as a result the role of interactions becomes very important as kinetic energy is quenched. This system offers a rich phase diagram 10–12 exhibiting quantum anomalous Hall (QAH), fractional quantum anomalous Hall (FQAH), multiferroicity [13] and superconductivity [7]. Moiré formed with rhombohedral quad/pentalayer systems offers additional advantages as a moiré with hBN together with a perpendicular electric field tunes a rich phase diagram with unprecedented tunability with electric field reduces/increases the relative importance of the moiré potential in the same device. Unlike traditional fractional quantum Hall systems requiring high magnetic fields, FQAH states in rhombohedral stacked multilayer graphene possibly emerge from interaction-driven topology where electron correlations spontaneously break symmetries to generate Chern bands without Landau levels. Crucially, these states persist even in the “moiréless limit”, suggesting a novel paradigm, which is theoretically proposed as topological Wigner crystals with Chern number C=1, pinned by weak external potentials. The coexistence of fractionalization, topology, and emergent superconductivity in these systems presents a unique opportunity to address fundamental questions about non-Abelian anyons and high-temperature topological order. At the same time, several key questions remain unanswered: (1) what is the origin and exact nature of such QAH and FQAH physics and their thermal crossover? (2) What are possible signatures as well as applications of the chiral superconductivity observed? (3) What are the effects of inhomogeneity, disorder and domain walls? The PI, who is an experimentalist, and the Co-PI, who is a theorist, had previously worked on twisted systems resulting in several joint publications (Nature Materials, 24 (2025) and Nature Communications 13, 7781 (2022)) on the topic of twisted multi-layer devices. The experimental techniques of the PI’s group will be complemented by theoretical understanding at the Co-PI’s group. Detailed Objectives: 1. Fabricate devices of 4- and 5-layer rhombohedral graphene in a double gate geometry and study the symmetry broken quantum anomalous Hall state and the fractional quantum anomalous state using DC transport measurements. 2. Use RF measurements to probe the density of states in rhombohedral multilayer graphene, and using DC and RF measurements to probe compressibility of the flat bands to understand why the longitudinal resistance remains finite. 3. Fabrication of disspationless transistors that work at cryogenic temperatures. 4. Demonstrate superconducting contacts to rhombohedral multilayer graphene and probe coupling between FQAH state and superconductivity. 5. Along with experiments, theoretical modelling will be done for (1) self-consistent Hatree-Fock bands (2) Transport via chiral edge based networks, and (3) Current phase relationship for Josephson devices of the proposed system.