Density of states and its local fluctuations determined by capacitance of strongly disordered graphene

We demonstrate that fluctuations of the local density of states (LDOS) in strongly disordered graphene play an important role in determining the quantum capacitance of the top-gate graphene devices. Depending on the strength of the disorder induced by metal-cluster decoration, the measured quantum capacitance of disordered graphene can dramatically decrease in comparison with pristine graphene. This is opposite to the common belief that quantum capacitance should increase with disorder. To explain this counterintuitive behavior, we present a two-parameter model which incorporates both the non-universal power law behavior for the ADOS and a lognormal distribution of LDOS. We find excellent quantitative agreements between the model and measured quantum capacitance for three disordered samples in a wide range of Fermi energies. Thus, by measuring the quantum capacitance, we can simultaneously determine the ADOS and its fluctuations. It is the LDOS fluctuations that cause the dramatic reduction of the quantum capacitance.