Density of States Proportion on Electron–Hole Symmetrical-to-Asymmetrical Transport in Free-Electron Solids to Interacting Fermionic Systems: A Perspective of Entropy-Ruled Method

Conceptualization, theory/method development, and implementation are always of great importance and interesting tasks to explore a new dimension in science and technology, which is highly solicited for various functional-driven potential applications (e.g., electronic devices, charge storage devices). Numerous experimental and theoretical studies urge the necessity of a new theory or method to quantify the exact value of charge and energy transport calculations (e.g., mobility, conductivity and quantum capacitance, etc.) through the appropriate processes and methods. With this motivation, the entropy-ruled charge dynamics method has been recently proposed, which unifies the band and hopping transport mechanism via the quantum-classical transition analogy. Here, the energy (in terms of chemical potential) scaled entropy has a direct proportion with the density of states (DOS), and hence, it is termed as DOS proportion. This proportion principally acts as a key descriptor for charge transport (CT) calculations in both molecular and materials systems, which is directly connected with all CT quantities like mobility, conductivity, current density, etc. In this perspective, the breakdown of electron–hole symmetrical transport is discussed, and the possibility of electron–hole symmetrical-to-asymmetrical transition has been addressed with respect to the correlation effect between the total entropy and the chemical potential of a given system. Importantly, the charge disorder-associated Coulombic potential formalism is proposed, and its impact on the DOS proportion is described. The inverse symmetrical behavior between the energy gap and electronic states coupling (i.e., strength of orbital level interactions) is discussed, which helps to provide the charge relaxation information about any ordered and disordered molecular/material systems. Besides that, this perspective explains a unique nature of the entropy-ruled method for the entire transport range from delocalized band to localization (or hopping) transport at different physical limits. The validity and limitations of Einstein’s relation and Boltzmann approach for mobility calculation are discussed with suitable thermodynamic conditions for disordered molecules and periodic systems. Finally, the futuristic scope and expected progress are addressed for correlated electron dynamical systems and devices. It is well-noted that the new DOS proportion and related entropy-ruled transport formalism are fundamentally more important for nurturing semiconducting science and technology toward a new era.