Interlayer stacking controls the electronic properties of the van der Waals material <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mi>T</mml:mi> </mml:mrow> <mml:mo>−</mml:mo> <mml:msub> <mml:mi>TaS</mml

Controlled stacking of van der Waals materials is a powerful tool for exploring the physics of quantum condensed matter. Given the small binding between layers, exploitation for engineering will require a breakthrough in stacking methodology or an ability to take advantage of thicker defective stacks. Here, we describe computational groundwork for the latter, using—on account of its promise for cold memory applications— <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>1</a:mn> <a:mi>T</a:mi> </a:mrow> <a:mo>−</a:mo> <a:msub> <a:mi>TaS</a:mi> <a:mn>2</a:mn> </a:msub> </a:math> as a model system. Comparing recursive Hendricks-Teller calculations and Monte Carlo simulations to published x-ray diffraction data, we obtain the key parameters describing the random stacking in mesoscopic flakes. These then regulate the electronic structures via specification of the random stacks in dynamical mean-field theory simulations. Hubbard repulsion induces strongly correlated metallic, band, and Mott insulating layers, providing compelling evidence that electronic properties follow from the coexistence of more than the metallic and insulating planes associated with ordinary band theory.