Glass patterns: a single moiré spot in twisted amorphous materials and twisted disordered crystals

Twisting and stacking two copies of a 2D crystal can produce a long-wavelength periodic interference pattern known as a moiré pattern. Performing the same procedure with an aperiodic structure instead generates a single moiré spot at the rotation center, known as a Glass pattern. I will first provide some simple examples of how this can produce specific impacts in twisted amorphous materials and disordered crystals. Then, I will consider each layer a 2DEG with (pre-twist) interlayer-correlated Anderson disorder, and show how in the Born approximation the scattering rates as a function of distance serve as a way to measure the real-space interlayer component of the Green's function on mesoscopic scales: Σ(R,k)~G₀(θR).