Electrochemical Measurement of the Electronic Structure of Graphene via Quantum Mechanical Rate Spectroscopy

TL;DR

This paper introduces quantum-rate spectroscopy (QRS) as a novel electrochemical method to measure the electronic structure of graphene in electrolyte environments at room temperature, offering practical advantages over traditional ARPES techniques.

Contribution

The study demonstrates that QRS can accurately determine graphene's electronic structure in situ, aligning well with ARPES and DFT results, and highlights its advantages in simplicity and operational conditions.

Findings

QRS measurements agree with ARPES and DFT results.

QRS enables in-situ electronic structure analysis at room temperature.

QRS is more practical and less costly than ARPES.

Abstract

Quantum-rate theory defines a quantum mechanical rate $\nu$ that complies with the Planck--Einstein relationship $E = h\nu$, where $\nu = e^2/hC_q$ is a frequency associated with the quantum capacitance $C_q$, and $E = e^2/C_q$ is the energy associated with $\nu$. Previously, this definition of $\nu$ was successfully employed to define a quantum mechanical meaning for the electron-transfer (ET) rate constant of redox reactions, wherein faradaic electric currents involved with ET reactions were demonstrated to be governed by relativistic quantum electrodynamics at room temperature~\citep{Bueno-2023-3}. This study demonstrated that the definition of $\nu$ entails the relativistic quantum electrodynamics phenomena intrinsically related to the perturbation of the density-of-states $\left( dn/dE \right) = C_q/e^2$ by an external harmonic oscillatory potential energy variation. On this basis, the electronic structure of graphene embedded in an electrolyte environment was computed. The electronic structure measured using quantum-rate spectroscopy (QRS) is in good agreement with that measured through angle-resolved photo-emission spectroscopy (ARPES) or calculated via computational density-functional theory (DFT) methods. Electrochemical QRS has evident experimental advantages over ARPES. For instance, QRS enables obtaining the electronic structure of graphene at room temperature and in an electrolyte environment, whereas ARPES requires low temperature and ultrahigh-vacuum conditions. Furthermore, QRS can operate \textit{in-situ} using a hand-held, inexpensive piece of equipment, whereas ARPES necessarily requires expensive and cumbersome apparatus.