Quantum Rate Theory for Graphene

The quantum rate theory predicts the electron transfer rate between quantum states governed by the ratio between the quantum conductance and capacitance (Phys. Chem. Chem. Phys. 2020, 22, 26109-26112). This rate is important not only for describing the quantumness of the electron transfer of electrochemical reactions but also for understanding electron transport in molecular electronics (Phys. Chem. Chem. Phys. 2020, 22 (19), 10828-10832). Additionally, this quantum rate principle is applicable for describing conductive and capacitive V-shapes of graphene (Carbon 2021, 184 821-827). In the present work, we demonstrate the relationship between the quantum rate theory for a single-layer graphene and the relativistic quantum mechanical theory of electrons according to the Dirac equation. As the merger of quantum mechanics and relativity theory, quantum rate theory is the key to analyzing quantum electrodynamics in two-dimensional structures (e.g., honeycomb-like carbon such as graphene) using an inexpensive benchtop electrochemical setup. In this study, the quantum rate model for graphene is introduced along with its applicability to the diffusionless electrochemical transport of electrons, as exemplified for molecular films comprising redox switches. This didactic approach demonstrates that the best means of conducting electron transport in graphene is the AC mode of electric current modulation, in which electric displacement current is imperative. A maximum quantum rate of electron transport occurs at the Dirac point, where net carrier concentrations are at their minimum, in contrast to the traditional DC mode of modulating conductance. This analysis opens an avenue of possibilities for fabricating quantum devices with electronic semiconducting accuracy, for example, biological sensors in complex environments.