Title: Study of Two-dimensional Correlated Quantum Fluid in Multi-layer graphene system
Description: In two dimensions, non-trivial topology and enhanced correlation lead to amazing physical phenomena. Graphene offers a high-quality, ultra-tunable and integratable two dimensional electron system in the study of interacting and topological quantum fluids. In this thesis we studied in detail various emergent quantum phenomena of electron fluids due to both strong in-plane and out-of-plane interaction between electrons in single and multi-layer graphene systems. Using magnetoresistance measurement in the corbino disk geometry, we manged to quantitatively measure the viscosity of electrons in monolayer and bilayer graphene as a function of carrier density and temperature. We demonstrated a crossover between degenerate Fermi liquid and non-degenerate electron-hole liquid. In the quantum Hall regime, we applied the corbino geometry as a probe of the incompressible sample bulk, improving significantly the resolution of fragile quantum Hall states compared to Hall bar devices. The improved resolution enables quantitative studies over a much broader parameter space in both singlelayer and multi-layer graphene system.

In double-layer graphene where two vertically stacked graphene layers are in close proximity but electrically separated by a thin hBN tunnel barrier, we observed sequence of FQHS which can be perfectly described by two-component composite fermion theory. Using a combination of different measurement configuration, we found evidence for a novel type of two-component non-abelian FQHS. At \nu = 1 in double-layer graphene where ground states of indirect excitons occur, we mappped out the entire phase diagram. We realized BEC-BCS crossover in the exciton condensation phase tunable with both magnetic field and electrostatic gating. At small exciton filling fraction, we discovered Wigner crystal of excitons. Lastly, we realized a strongly correlated triple-layer quantum Hall system with independent control of carrier density in each layer and demonstrated three-layer coherent quantum Hall effect at total integer filling fraction and possibly fractional filling fraction.