Correlated Low-Energy Model of Monolayer 1H-NbS 2: A cRPA+DMFT Study

Monolayer 1 H-NbS 2 hosts a well-separated metallic band of predominant Nb- d z squared character, providing an ideal platform to probe electronic correlations within a single-band setting. In this work, we present a comprehensive study of 1 H-NbS 2 by combining first-principles Wannier interpolation, constrained random-phase approximation (cRPA), and DFT+DMFT. We show that an effective single-band model accurately captures the low-energy electronic structure, reproducing key experimental features from ARPES and STS dI/dV spectra, including a characteristic Van Hove singularity. While static DFT+ U fails to describe the correlated metallic nature of the system, DFT+DMFT successfully accounts for the spectral weight redistribution and dynamic correlations. By defining the cRPA target subspace directly within the isolated Nb- d z squared band, we obtain a renormalized local interaction of U cRPA = 1.138 eV. This interaction stabilizes a strongly correlated metallic state that remains robust upon cooling. Remarkably, this minimal single-band model captures a spectral broadening similar to that previously reported in more elaborate treatments - incorporating larger local interactions (U about 1.8 eV, derived from a multiorbital cRPA construction), intersite Coulomb terms (V), and electron-phonon coupling - demonstrating that a consistently downfolded local interaction alone can already capture key aspects of the experimentally observed low-energy behavior of monolayer 1 H-NbS 2.