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We introduce a combinatorial framework, validated by DFT calculations of SnSe, to enumerate all possible stacking and sliding configurations of identical monolayers, revealing that a limited set of point groups explains observed nonlinear optical responses. This approach predicts metastable few-homomonolayer stacks and accounts for experimental observations in layered materials. The method generalizes to arbitrary numbers of identical monolayers, offering a predictive tool for designing novel material functionalities.
A combinatorial atlas of monolayer stacking configurations explains observed nonlinear optical phenomena and predicts novel metastable structures.
Structure leads to function: Knowing all possible ways to stack and slide identical monolayers enables the design of functionalities such as nonlinear optical responses and ferroelectricity in layered materials. Besides, mounting experimental evidence points to differing stacking configurations in few-monolayer and bulk samples. To exemplify the core concepts for stacking arbitrary monolayers, ground-state and metastable non-moir\'e SnSe stacks were first identified using density functional theory and employed to validate a ``divide and conquer''combinatoral approach for determining the most probable stacking configurations in materials with an arbitrary number of identical monolayers. A small number of point groups accounts for all possible stacks, which explains experimental second-harmonic optical responses. Finite-temperature effects are also studied despite the granularity of available data. This comprehensive framework readily generalizes to provide a predictive description of arbitrary metastable few-homomonolayer stacks.