The electronic capacitance of a one-dimensional system such as a carbon nanotube is a thermodynamic quantity that contains fundamental information about the ground state1. It is composed of an electrostatic component describing the interactions between electrons and their correlations, and a kinetic term given by the electronic density of states. Here, we use a field-effect transistor geometry to obtain the first direct capacitance measurement of individual carbon nanotubes, as a function of the carrier density. Our measurements detect the electrostatic part of the capacitance as well as the quantum corrections arising from the electronic density of states. We identify the van-Hove singularities that correspond to the one-dimensional electron and hole sub-bands and show that the measured capacitance exhibits clear electron–hole symmetry. Finally, our measurements suggest the existence of a negative capacitance, which has recently been predicted to exist in one dimension as a result of interactions between electrons2,3,4.

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Measurement of the quantum capacitance of interacting electrons in carbon nanotubes

The equation describing the capacitance of capacitors is determined. It is shown that by optimizing the material of the conducting electrodes, the capacitance of capacitors reaching the quantum regime can be substantially enhanced or reduced. Dielectric capacitors with negative total capacitances are suggested and their properties analyzed. Resulting perspectives to enhance the performance of electronic devices are discussed.

Calculation of the capacitances of conductors: Perspectives for the optimization of electronic devices

Calculation of the Capacitances of Conductors -- Perspectives for the Optimization of Electronic Devices

We measure the quantum capacitance and probe thus directly the electronic density of states of the high mobility, Dirac type two-dimensional electron system, which forms on the surface of strained HgTe. Here we show that observed magnetocapacitance oscillations probe-in contrast to magnetotransport-primarily the top surface. Capacitance measurements constitute thus a powerful tool to probe only one topological surface and to reconstruct its Landau level spectrum for different positions of the Fermi energy.

/pdf/probing-quantum-capacitance-in-a-3d-topological-insulator-s1r2ezqx9o.pdf

Probing Quantum Capacitance in a 3D Topological Insulator

Experimental and theoretical research on the integer quantum Hall effect is reviewed, together with other transport phenomena in a two-dimensional electron gas in a quantizing magnetic field. Particular emphasis is placed on primary experimental data, on the comparison of experimental and theoretical results, and on the analysis of theoretical predictions from the point of view of their experimental verification. Among experiments conducted in recent years, those that have raised questions to be resolved are highlighted. Possible directions of further research are suggested.

https://iopscience.iop.org/article/10.3367/UFNe.0184.201402a.0113/pdf

V. Mosser

Papers

Density of states of GaAs-AlGaAs-heterostructures deduced from temperature dependent magnetocapacitance measurements