Quantization Mapping on Dirac Dynamics via Voltage-Driven Charge Density in Monolayer Graphene: A Klein Paradox and Entropy-Ruled Wavevector Mechanics Study
Thermodynamics coupled quantum features on electron and hole dynamics in Dirac materials is quite interesting and crucial for real device applications such as electronic, thermoelectric, energy devices, and quantum circuits. The correlation between the formation of electron-hole puddles near the charge neutrality point (CNP) and the role of disorder in terms of differential entropy is fundamentally important for the Dirac transport mechanism in graphene systems, but not yet well-established. With this motivation, we map the energy quantization for Dirac materials through the empirical relation of voltage-driven charge density in monolayer graphene, using the differential entropy (h)-ruled wavevector (k) mechanics. For this work, we propose the four postulates which are the key observable descriptions of earlier research reports, to study the precise electronic transport via an entropy-guided wavevector propagation approach, along with the Klein paradox, which pertains to the ultrafast dynamics in the Dirac or quasi-Dirac systems. The introduced h-ruled k and h-ruled N relations generalize the electron dynamics in both the unbounded and potentially bounded Dirac systems. Through the quantization mapping procedure under different voltage-driven potential (U=eV) boundary conditions, the observed energy shift from lower to excited quantum state obeys the relation of N(k)=N(U)^3; here, N(U) is the voltage-driven potential energy contribution factor for the quantum state existence. In such a way, the mapped electron density, diffusion coefficient, and mobility for bounded Dirac materials are increased by orders of N^3, N^2, and N, respectively. This study reveals information about the interaction potential-DOS relationship in the Dirac materials.