Electrochemical Measurement of the Electronic Structure of Low-Dimensional Materials

The quantum-rate theory defines a quantum mechanical rate that complies with the Planck–Einstein relationship, permitting the study of relativistic quantum electrodynamics phenomena intrinsically related to the perturbation of the density-of-states. The electronic structure of graphene and inorganic quantum dots (within colloidal sizes) embedded in an electrolyte environment can be measured on this basis. The electronic structure measured using quantum-rate spectroscopy (QRS) is in good agreement with that measured through angle-resolved photoemission spectroscopy (ARPES) or calculated via computational density-functional theory (DFT) methods for the case of graphene and Scanning Tunneling Microscopy and Spectroscopy (STM/STS) in the case of inorganic quantum dots. Electrochemical QRS has evident experimental advantages over ARPES or STM/STS methods. 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 in situ using a hand-held, inexpensive piece of equipment, whereas ARPES necessarily requires expensive and cumbersome apparatus.