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

TL;DR

This paper investigates the symmetry classes of graphene quantum dots, revealing how different confinement types influence spectral statistics, conductance, and the role of valley symmetries, with implications for quantum transport properties.

Contribution

It uncovers the impact of smooth mass confinement on symmetry classes and spectral statistics in graphene quantum dots, highlighting the importance of valley and sublattice symmetries.

Findings

Abrupt termination leads to orthogonal and unitary ensemble behavior.

Smooth mass confinement introduces block diagonal Hamiltonians with unitary symmetry.

Spectral statistics in closed dots are affected by intervalley scattering times.

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.