Intelligent infrared sensing enabled by tunable moiré quantum geometry

9 also exhibiting a 2𝜓 dependence with respect to the optical field polarization. In contrast to the 𝐶3𝑧 case, the polarization for the maximum or minimum photovoltage does not change with 𝜎𝑦𝑦𝑦 or the top/bottom gate voltages in experiments. Note that the analysis for the mirror symmetry ℳ𝑦 is similar. The C3v symmetry is present in pristine graphene few-layers even with broken inversion symmetry, e.g., ABA-stack trilayer graphene (ABA-TLG) and AB-stack bilayer graphene (AB- BLG) under a D field. When inversion symmetry is broken in these non-moiré systems, an energy gap opens at K and K’ points, though nonzero, the BPVE is extremely small unless (i) the Fermi level is in the gap and (ii) the photon energy matches the gap. As shown in Fig. S4a, the band structure of ABA-TLG consists of gapped linear Dirac cones and gapped quadratic Dirac cones. One expects that its BPVE is negligible when the Fermi level is not in a sub-bandgap or the photon energy does not match the gap. This result on ABA-TLG has been demonstrated by our calculations in Fig. S4b. A comparison of the calculated nonlinear conductivity elements of ABA- TLG with that of TDBG at various 𝐸𝐹 and at infrared wavelengths is shown in Fig. S4c and S4d, from which it is evident that the magnitude of the conductivity elements in ABA-TLG (with 𝜎𝑥𝑥𝑥 ≡ 0) is significantly smaller than that in TDBG over a wide range of 𝐸𝐹 for infrared photons. Similar results on AB-BLG with broken inversion symmetry (by a vertical D field) are summarized in Fig. S4e-h. To conclude, in non-moiré pristine graphene few-layers with broken inversion symmetry, the phase of the Vph oscillations with respect to the polarization in linear BPVE cannot be tuned; meanwhile, the BPVE (to be confirmed by experiments) is appreciable only within a narrow spectral range with limited electrical tunability. Thus, they cannot be leveraged to achieve the intelligent light sensing.