Universal scaling of weak localization in graphene due to bias-induced dispersion decoherence

The differential conductance of graphene is shown to exhibit a zero-bias anomaly at low temperatures, arising from a suppression of the quantum corrections due to weak localization and electron interactions. A simple rescaling of these data, free of any adjustable parameters, shows that this anomaly exhibits a universal, temperature- (T) independent form. According to this, the differential conductance is approximately constant at small voltages (V kBT/e), while at larger voltages it increases logarithmically with the applied bias. For theoretical insight into the origins of this behaviour, which is inconsistent with electron heating, we formulate a model for weak-localization in the presence of nonequilibrium transport. According to this model, the applied voltage causes unavoidable dispersion decoherence, which arises as diffusing electron partial waves, with a spread of energies defined by the value of the applied voltage, gradually decohere with one another as they diffuse through the system. The decoherence yields a universal scaling of the conductance as a function of eV/kBT, with a logarithmic variation for eV/kBT > 1, variations in accordance with the results of experiment. Our theoretical description of nonequilibrium transport in the presence of this source of decoherence exhibits strong similarities with the results of experiment, including the aforementioned rescaling of the conductance and its logarithmic variation as a function of the applied voltage.