Moiré quantum geometry: from fundamentals to intelligent sensing

Overlaying two atomic layers with a slight lattice mismatch or at a small rotation angle creates a moiré superlattice with properties that are markedly modified from and at times entirely absent in the ‘parent’ materials. In a series of studies that combine experiments and theories, we have shown that moiré systems are fertile ground for tunable, substantial, rich quantum geometric properties.

First, I will introduce that the superlattice gap of twisted bilayer graphene is associated with unusual Z₂ band topology originating from the (single-state) quantum metric instead of (abelian) Berry curvature, by using K-theory, nonlocal transport, and superconducting quantum interferometry. This resolves the puzzle of flat-band superfluid weight in the magic-angle limit. Further, I will show that for graphene moiré systems the linear resonant optical responses and second-order bulk photovoltaic effects (BPVE), as manifestations of the Hermitian (double-state) metric and connection, are particularly strong and tunable in the infrared range. In the BPVE rendered by moiré quantum geometry, not only are the phase and amplitude of the photovoltage substantially dependent on the excitation light polarization, but they are also highly tunable by external electric fields. This has enabled us to utilize the BPVE as an encoder and a convolutional neural network as a decoder to achieve full-Stokes polarimetry together with wavelength and power detections simultaneously using only one single moiré device with a subwavelength footprint of merely 3 × 3 μm² .

These results not only reveal the significant roles of moiré engineered quantum geometry in strongly correlated phases and in tunable light–matter interactions but also identify a pathway for future intelligent quantum geometric sensing technologies in an extremely compact, on-chip manner across a broad spectral range.