Stability of destructive quantum interference antiresonances in electron transport through graphene nanostructures

We investigate the stability of destructive quantum interference (DQI) in electron transport through graphene nanostructures connected to source and drain electrodes. The fingerprint of DQI is an antiresonance in the transmission function, and its origin is deeply connected to the topology of the atomic structure, which we discuss in terms of symmetry arguments supported by numerical simulations. A systematic analysis of the transmission function versus system size reveals that the DQI antiresonance persists for large systems in the ballistic regime and establishes the quantum confinement gap as the intrinsic resolution limit to detect QI effects. Furthermore, we consider the influence of disorder, electron-electron and electron-phonon interactions, and provide quantitative criteria for the robustness of DQI in their presence. We find that the conductance is quite sensitive to perturbations, and its value alone may not be sufficient to characterize the quantum interference properties of a junction. Instead, the characteristic behavior of the transmission function is more resilient, and we suggest it retains information on the presence of an antiresonance even if DQI is partially concealed or suppressed. At the same time, DQI results in a non-linear transport regime in the current-bias characteristics that can be possibly detected in transport experiments.