| This thesis is focused on an experimental study of the fluctuations in the conductance of disordered graphene flakes. Conductance fluctuations (CF) are generated by varying either magnetic field (+/-8 T) or Fermi energy (via back-gate voltage) in both bilayer and single-layer graphene devices. A detailed comparative study of the conductance fluctuations at ultra-low temperatures (≤ 0.1 K), as a function of magnetic field and Fermi energy, is performed to address the question of whether mesoscopic transport in graphene is governed by similar theoretical principles as in regular dirty metals and semiconductors. This study reveals a dramatic deviation from ergodicity for the CF in graphene, according to which fluctuations generated by varying magnetic field are found to be much smaller than those obtained when sweeping Fermi energy. The CF also show a strongly anisotropic response to the symmetry-breaking effects of a magnetic field, applied perpendicular or parallel to the plane of the graphene sheet. An extensive study of the temperature dependence of CF is also performed (0.03 -- 100 K), and further confirms the non-ergodic character of the CF in disordered graphene by showing two separate temperature cut-offs for magneto-CF and density-induced CF. The non-ergodic character and robust nature of density-induced CF suggests the complex and challenging nature of quantum interference in graphene, as compared to that in non-Dirac materials, emphasizing the need for development of more sophisticated theoretical models and a better understanding of substrate-induced disorder. |
