Characterization of 2D materials using complex-amplitude nonlinear spectroscopy

The stacking order of two-dimensional (2D) materials profoundly influences their optical and electronic properties, yet unambiguously identifying the absolute stacking configuration remains a challenge due to the symmetry of layered systems and limitations of conventional probes. Here we demonstrate a novel, robust approach to decode the absolute stacking order of bilayer 2D materials using complex-amplitude nonlinear spectroscopy (CANS). By measuring both the amplitude and phase of the second-harmonic generation (SHG) signal, CANS captures subtle phase differences arising from broken inversion symmetry and interlayer registry. We apply this technique to twisted and untwisted bilayer transition metal dichalcogenides, revealing clear signatures that distinguish 2H and 3R stacking as well as twist-induced domains with opposite chirality. Our results establish CANS as a powerful and generalizable tool for characterizing stacking orders in van der Waals heterostructures, enabling precise control of 2D material properties for next-generation photonic and electronic devices.