Gauge-independent Wannier parametrization for the ab-initio simulations of sub-µm-wide nanoribbons

Simulation of mesoscopic nanostructures is a central challenge in condensed matter physics and device applications. First-principles methods provide accurate electronic structures but are computationally too demanding to simulate mesoscopic nanostructures. Though empirical band theories are efficient for the simulation of nanostructures, their validities are limited by the empirical parametrization that usually lacks the consideration of microscopic wavefunctions and do not hold the transferability. In this work, we propose a methodology that bridges these approaches, achieving first-principles-level reliability with computational efficiency through a tight-binding framework. Our approach starts with Wannier tight-binding (WTB) parameters from small nanostructures, which serve as training data for fitting. To remove the gauge freedom of Wannier functions that obscures size- and geometry-dependent parameter trends, we construct gauge-independent (GI) bases and transform the WTB model into a gauge-independent WTB (GI-WTB) model. This enables robust parameter fitting and prediction of parameter variations, yielding the parametrized GI-WTB (P-GI-WTB) model. Applied to MoS₂ armchair-edge nanoribbons, the P-GI-WTB model shows excellent agreement with first-principles results and enables reliable simulations of sub-µm-wide nanoribbons. This framework offers a scalable approach for predicting the electronic properties of realistic nanostructures at a computational cost far lower than that of conventional first-principles methods.