Critical angles and one-dimensional moir\'e physics in twisted rectangular lattices

Engineering moir\'e superlattices in van der Waals heterostructures provides fundamental control over emergent electronic, structural, and optical properties allowing to affect topological and correlated phenomena. This control is achieved through imposed periodic modulation of potentials and targeted modifications of symmetries. For twisted bilayers of van der Waals materials with rectangular lattices, such as PdSe2, this work shows that one-dimensional (1D) moir\'e patterns emerge universally. This emergence is driven by a series of critical twist angles (CAs). We investigate the geometric origins of these unique 1D moir\'e patterns and develop a universal mathematical framework to predict the CAs in twisted rectangular lattices. Through a density functional theory (DFT) description of the electronic properties of twisted bilayer PdSe2, we further reveal directionally localized flat band structures, localized charge densities and strong spin-orbit coupling along the dispersive direction which points to the emergence of an effectively 1D strongly spin-orbit coupled electronic systems. This establishes twisted rectangular systems as a unique platform for engineering low-symmetry moir\'e patterns, low-dimensional strongly correlated and topological physics, and spatially selective quantum phases beyond the isotropic paradigms of hexagonal moir\'e materials.