Executive Summary : | Topological phases of matter are crucial for the future of quantum technology, as they are insensitive to smooth variation in material parameters, making them robust against disorders and perturbations. Emerging quantum materials, such as graphene and twisted bilayer graphene, are expected to host exotic quasiparticles like anyons, coherent neutral states, Majorana fermions, and para-fermions. Exploring emergent quasiparticles with topological properties is exciting in tabletop condensed matter experiments. The key questions in this area are creating emerging quasiparticles and identifying them. Integer and fractional quantum Hall (QH) states of two-dimensional (2D) graphene are ideal platforms for creating emerging quasiparticles due to their unique Landau level structure, new fractions, and enriched QH states due to the interplay of many degrees of freedom. Graphene-based hybrid structures like twisted bilayer graphene with flat band also offer richer tunability, with interaction and correlation driven topological states like Chern insulator (CI) and fractional CI expected even at zero magnetic fields. Detecting emerging quasiparticles remains a challenge due to the lack of conclusive evidence using conventional electrical measurement. Cutting-edge probes like thermal conductance and shot-noise spectroscopy are unique in identifying exotic quasiparticles. Measurements of the half-integer of G_Q and shot-noise generated by anyon collision can directly demonstrate the quantum statistics of the quasiparticles. Recent experiments by PI's group have shown evidence of quantized G_Q and high precision noise measurements. |