Statistics of Mesoscopic Fluctuations of Quantum Capacitance

The Thouless formula $G = (e^2/h)(E_c/\Delta)$ for the two-probe dc conductance $G$ of a d-dimensional mesoscopic cube is re-analysed to relate its quantum capacitance $C_Q$ to the reciprocal of the level spacing $\Delta$. To this end, the escape time-scale $\tau$ occurring in the Thouless correlation energy $E_c = \hbar/\tau$ is interpreted as the {\em time constant} $\tau = RC_Q$ with $RG \equiv$ 1, giving at once $C_Q = (e^2/2\pi \Delta)$. Thus, the statistics of the quantum capacitance is directly related to that of the level spacing, which is well known from the Random Matrix Theory for all the three universality classes of statistical ensembles. The basic questions of how intrinsic this quantum capacitance can arise purely quantum-resistively, and of its observability {\em vis-a-vis} the external geometric capacitance that combines with it in series, are discussed

Observation of Quantum Capacitance of individual single walled carbon nanotubes

We report a measurement on quantum capacitance of individual semiconducting and small band gap SWNTs. The observed quantum capacitance is remarkably smaller than that originating from density of states and it implies a strong electron correlation in SWNTs

Mesoscopic Capacitance Oscillations

We examine oscillations as a function of Fermi energy in the capacitance of a mesoscopic cavity connected via a single quantum channel to a metallic contact and capacitively coupled to a back gate. The oscillations depend on the distribution of single levels in the cavity, the interaction strength and the transmission probability through the quantum channel. We use a Hartree-Fock approach to exclude self-interaction. The sample specific capacitance oscillations are in marked contrast to the charge relaxation resistance, which together with the capacitance defines the RC-time, and which for spin polarized electrons is quantized at half a resistance quantum. Both the capacitance oscillations and the quantized charge relaxation resistance are seen in a strikingly clear manner in a recent experiment.Comment: 9 pages, 2 figure

Quantum capacitance and density of states of graphene

We report on measurements of the quantum capacitance in graphene as a function of charge carrier density. A resonant LC-circuit giving high sensitivity to small capacitance changes is employed. The density of states, which is directly proportional to the quantum capacitance, is found to be significantly larger than zero at and around the charge neutrality point. This finding is interpreted to be a result of potential fluctuations with amplitudes of the order of 100 meV in good agreement with scanning single-electron transistor measurements on bulk graphene and transport studies on nanoribbons

Quantum capacitance of the monolayer graphene

The quantum capacitance of the monolayer graphene for arbitrary carrier density, magnetic field and temperature is found. The density dependence of the quantum capacitance is analyzed for magnetic field(temperature) is fixed(varied) and vice versa. The theory is compared with the experimental data.Comment: 5 pages, 6 figures, important changes to v

The effect of electron dielectric response on the quantum capacitance of graphene in a strong magnetic field

The quantum capacitance of graphene can be negative when the graphene is placed in a strong magnetic field, which is a clear experimental signature of positional correlations between electrons. Here we show that the quantum capacitance of graphene is also strongly affected by its dielectric polarizability, which in a magnetic field is wave vector-dependent. We study this effect both theoretically and experimentally. We develop a theory and numerical procedure for accounting for the graphene dielectric response, and we present measurements of the quantum capacitance of high-quality graphene capacitors on boron nitride. Theory and experiment are found to be in good agreement.Comment: 8+ pages, 6 figure