Symmetry Classes in Graphene Quantum Dots: Universal Spectral Statistics, Weak Localization, and Conductance Fluctuations

Abstract

We study the symmetry classes of graphene quantum dots, both open and closed, through the conductance and energy level statistics. For abrupt termination of the lattice, these properties are well described by the standard orthogonal and unitary ensembles. However, for smooth mass confinement, special time-reversal symmetries associated with the sublattice and valley degrees of freedom are critical: they lead to block diagonal Hamiltonians and scattering matrices with blocks belonging to the unitary symmetry class even at zero magnetic field. While the effect of this structure is clearly seen in the conductance of open dots, it is suppressed in the spectral statistics of closed dots, because the intervalley scattering time is shorter than the time required to resolve a level spacing in the closed systems but longer than the escape time of the open systems.

4 pages, 4 figures, RevTex, submitted to Phys. Rev. Lett

References in corpus (6)

• The electronic properties of graphene
• Chaotic Dirac billiard in graphene quantum dots
• Weak localisation in graphene flakes
• Spin currents in rough graphene nanoribbons: Universal fluctuations and spin injection
• Tunable Coulomb blockade in nanostructured graphene
• Conductivity of disordered graphene at half filling

Cited by in corpus (8)

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• Weak Localization and Transport Gap in Graphene Antidot Lattices
• Conformal mapping and shot noise in graphene
• Revivals of quantum wave-packets in graphene
• Interfaces Within Graphene Nanoribbons
• Artifical atoms in interacting graphene quantum dots
• Boundary-induced violation of the Dirac fermion parity and its signatures in local and global tunneling spectra of graphene