Statistical properties of electrochemical capacitance in disordered mesoscopic capacitors

TL;DR

This study numerically analyzes the statistical behavior of electrochemical capacitance in disordered mesoscopic capacitors, revealing universal fluctuations and the influence of necklace states across different symmetry classes.

Contribution

It uncovers the universal electrochemical capacitance fluctuation and the role of necklace states in disordered mesoscopic systems across various symmetry ensembles.

Findings

Capacitance follows Gaussian distribution at weak disorder.

Strong disorder leads to one-sided distribution due to necklace states.

Universal capacitance fluctuation is independent of system parameters.

Abstract

We numerically investigate the statistical properties of electrochemical capacitance in disordered two-dimensional mesoscopic capacitors. Based on the tight-binding Hamiltonian, the Green's function formalism is adopted to study the average electrochemical capacitance, its fluctuation as well as the distribution of capacitance of the disordered mesoscopic capacitors for three different ensembles: orthogonal (symmetry index \beta=1), unitary (\beta=2), and symplectic (\beta=4). It is found that the electrochemical capacitance in the disordered systems exhibits universal behavior. In the case of single conducting channel, the electrochemical capacitance follows a symmetric Gaussian distribution at weak disorders as expected from the random matrix theory. In the strongly disordered regime, the distribution is found to be a sharply one-sided form with a nearly-constant tail in the large capacitance region. This behavior is due to the existence of the necklace states in disordered systems, which is characterized by the multi-resonance that gives rise to a large density of states. In addition, it is found that the necklace state also enhances the fluctuation of electrochemical capacitance in the case of single conducting channel. When the number of conducting channels increases, the influence of necklace states becomes less important. For large number of conducting channels, the electrochemical capacitance fluctuation develops a plateau region in the strongly disordered regime. The plateau value is identified as universal electrochemical capacitance fluctuation, which is independent of system parameters such as disorder strength, Fermi energy, geometric capacitance, and system size. Importantly, the universal electrochemical capacitance fluctuation is the same for all three ensembles, suggesting a super-universal behavior.