Optical Signature of Moir\'e Superlattices Formed by Twisted SrTiO$_3$ Membranes
Moir\'e superlattices formed at the interfaces of mismatched lattices have attracted significant interest over the past decade due to their large tunability of band parameters and interactions among electrons, spins, and lattices. Superlattices made from twisted perovskite oxides may have strong structure and potential modulation, but evidence of such modulation over macroscopic areas, particularly at large twisting angles, has not been clearly demonstrated so far. Here, we fabricated millimeter-scale twisted oxide bilayers at $36^\circ$ angle, close to the simple coincidence site lattice condition $\Sigma5$, from freestanding SrTiO$_3$ membranes. We discovered new low-frequency vibrational modes whose Raman activity, according to molecular dynamics simulations, is greatly enhanced by an asymmetric, twisted interface between the SrO and TiO$_2$ layers. Such an interface is energetically favorable from first-principles calculations and is corroborated by the observation of strong second harmonic generation from the interface comparable to that from the SrTiO$_3$ surface throughout the bilayer region. The results are consistent with interlayer coupling enhanced by high-temperature annealing and confirmed by cross-sectional scanning transmission electron microscopy imaging. Our work sheds light on the structural behavior of twisted oxides and provides directions for tuning their phononic and nonlinear optical properties in future studies.