A First-Principles Field Theory of Fluctuation Phenomena and Dielectric Screening in Two-Dimensional van der Waals Heterostructures: Keldysh-Rytova Potentials, Moiré Superlattice Corrugations, and Coherent Transport Limits

Atomically thin two-dimensional (2D) semiconductors—such as monolayer MoS2, WS2, graphene, and transition metal dichalcogenide (TMD) heterostructures—represent rigorous testbeds for condensed-matter transport. Because the entire electronic channel is confined to an atomic sheet (), the absence of bulk dielectric screening leaves carriers highly exposed to substrate impurities, interfacial traps, and moiré potential modulations. Traditional noise models rely on empirical fitting parameters that fail to capture dielectric environment-dependent screening and lattice corrugations. Here, we present a first-principles field theory of fluctuation phenomena in 2D van der Waals channels by reformulating transport across a continuous inter-site electrostatic potential manifold. Incorporating the Keldysh-Rytova non-local potential kernel proves that effective energetic disorder narrows inversely with environmental dielectric permittivity (). In atomically abrupt heterostructures where correlation lengths exceed hopping distances (), transport shifts to the coherent domain limit, replacing random point-defect scattering with deterministic moiré superlattice potentials and yielding unprecedented suppression of low-frequency excess noise (exceeding six orders of magnitude in the effective Hooge parameter). In this work, Operando Differential Noise Spectroscopy (DJS) fingerprints and companion MATLAB simulation toolboxes confirm the emergence of discrete, symmetry-protected mini-band satellite resonances, providing a robust design framework for ultra-clean 2D quantum devices, low-noise cryogenic amplifiers, and multi-millisecond quantum coherent hardware.