Conductance fluctuations in graphene systems: The relevance of classical dynamics

Conductance fluctuations associated with transport through quantum-dot systems are currently understood to depend on the nature of the corresponding classical dynamics, i.e., integrable or chaotic. However, we find that in graphene quantum-dot systems, when a magnetic field is present, signatures of classical dynamics can disappear and universal scaling behaviors emerge. In particular, as the Fermi energy or the magnetic flux is varied, both regular oscillations and random fluctuations in the conductance can occur, with alternating transitions between the two. By carrying out a detailed analysis of two types of integrable (hexagonal and square) and one type of chaotic (stadium) graphene dot system, we uncover a universal scaling law among the critical Fermi energy, the critical magnetic flux, and the dot size. We develop a physical theory based on the emergence of edge states and the evolution of Landau levels (as in quantum Hall effect) to understand these experimentally testable behaviors.