Abstract
Quantum geometric properties of Bloch wave functions in solids, that is, Berry curvature and the quantum metric, are known to significantly influence the ground- and excited-state behaviour of electrons1,2,3,4,5. The bulk photovoltaic effect (BPVE), a nonlinear phenomenon depending on the polarization of excitation light, is largely governed by the quantum geometric properties in optical transitions6,7,8,9,10. Infrared BPVE has yet to be observed in graphene or moiré systems, although exciting strongly correlated phenomena related to quantum geometry have been reported in this emergent platform11,12,13,14. Here we report the observation of tunable mid-infrared BPVE at 5 µm and 7.7 µm in twisted double bilayer graphene (TDBG), arising from the moiré-induced strong symmetry breaking and quantum geometric contribution. The photoresponse depends substantially on the polarization state of the excitation light and is highly tunable by external electric fields. This wide tunability in quantum geometric properties enables us to use a convolutional neural network15,16 to achieve full-Stokes polarimetry together with wavelength detection simultaneously, using only one single TDBG device with a subwavelength footprint of merely 3 × 3 µm2. Our work not only reveals the unique role of moiré engineered quantum geometry in tunable nonlinear light–matter interactions but also identifies a pathway for future intelligent sensing technologies in an extremely compact, on-chip manner.
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Data availability
The data that support the plots within this paper are available from the corresponding authors upon request. Source data are provided with this paper.
Code availability
The code and CNN used in this paper are available from the corresponding authors upon request.
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Acknowledgements
F.X., S.Y. and C.M. acknowledge support by the National Science Foundation EFRI NewLAW programme under grant number 1741693 and the Yale Raymond John Wean Foundation. F.Z. and P.C. acknowledge the Texas Advanced Computing Center (TACC) for providing resources that have contributed to the research results reported in this work. F.Z. and P.C. acknowledge support by the Army Research Office under grant number W911NF-18-1-0416 and by the National Science Foundation under grant numbers DMR-1945351 through the CAREER program, DMR-1921581 through the DMREF program and DMR-2105139 through the CMP program. Growth of hBN crystals by K.W. and T.T. was supported by the Elemental Strategy Initiative conducted by the Japan Ministry of Education, Culture, Sports, Science and Technology (MEXT; grant number JPMXP0112101001), the Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research (JSPS KAKENHI; grant number JP20H00354) and the Japan Science and Technology Agency Core Research for Evolutional Science and Technology (CREST; grant number JPMJCR15F3).
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C.M., S.Y., F.Z. and F.X. conceived the project. C.M. and S.Y. fabricated the devices, performed the measurements and developed the program for applying CNN. P.C. and F.Z. performed the theoretical analysis and calculations. K.W. and T.T. synthesized the hBN crystals. F.Z. and F.X. supervised the project. C.M., S.Y., P.C., F.Z. and F.X. analysed the results and wrote the manuscript.
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C.M., S.Y., P.C., F.Z. and F.X. are evaluating the feasibility of a patent application based on the concepts and results in this work with their intellectual property offices.
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Extended data figures and tables
Extended Data Fig. 1 Temperature dependence of the resistance of TDBG D1.
a, Temperature coefficient of resistance mapping (the same as Fig. 1d) with the selected gate biases measured in b highlighted. b, Logarithmic values of the resistance R as a function of 100/T, measured at different sets of n and D highlighted in a.
Extended Data Fig. 2 Polarization dependence of Vph versus Ψ under 5 μm linearly polarized light in TDBG D1.
Measured photovoltage Vph as a function of the orientation angle \(\psi \) under 5 μm linearly polarized light at different sets of gate voltages. Inset: extracted amplitudes of Vc and Vs.
Extended Data Fig. 3 Power dependence of the photovoltage Vph.
a, Selected Vph oscillations as a function of Ψ, under different excitation powers. b, Amplitudes of the Vph oscillation curves, \({({V}_{{\rm{c}}}^{2}+{V}_{{\rm{s}}}^{2})}^{1/2}\), versus power on device at different sets of (VBG, VTG) combinations. The polarization-dependent components scale linearly with the power, confirming the second-order nature of the photoresponse. c and d, The overall photoresponse Vph, including both the polarization-dependent and -independent components, exhibiting a linear dependence on the power. The curves are measured at two selected polarization angles Ψ=45° and 135° with two sets of gate voltages (0V, −7.6V) and (14V, −7.6V).
Extended Data Fig. 4 Spatial dependence of the photovoltage Vph.
a, Spatial dependence of Vph as a function of the beam spot position x under linear polarized, 7.7 μm light excitation with Ψ = 135° and (VBG, VTG) = (0 V, −7.6 V). Blue, black, and red curves represent the photo-thermal effect, linear BPVE, and their summation, respectively. Inset: Optical image of the TDBG photodetector with the x- and y- axes. The device center is defined to be the origin (x, y = 0). b, Spatial dependence of the Vph along the y-axis (perpendicular to the Vph collection path) measured at (VBG, VTG) = (0 V, −7.6 V) under linearly polarized light with Ψ = 135° in TDBG D1, which can be fitted by a Gaussian peak function \({A}^{{\prime} }{e}^{-\frac{{y}^{2}}{2{{w}^{{\prime} }}^{2}}}\) (black curve).
Extended Data Fig. 5 Temperature dependence of the photovoltage Vph.
a, Temperature dependence of Vph oscillation curves at different sets of gate voltage combinations under the excitation of 7.7 μm linearly polarized light. b, Extracted oscillation amplitudes, \({({V}_{{\rm{c}}}^{2}+{V}_{{\rm{s}}}^{2})}^{1/2}\), versus temperature at different sets of gate voltage combinations.
Extended Data Fig. 6 Linear BPVE in TDBG D2.
a-d, Photovoltage Vph mappings as functions of top- (VTG) and back- (VBG) gate biases under the excitation of 5 μm linearly polarized light with orientation angles Ψ = 40°, 130°, 0° and 90°, measured at T = 79 K. Inset: optical image of D2 and schematic of the orientation angle Ψ of the incident light. D2 has a dimension of 2.2 μm \(\times \) 2 μm. e, Polarization dependence of Vph at different gate biases. Insets: extracted polarization-dependent components Vs and Vc. f, Linear dependence of the Vph amplitudes on the power at selected gate biases. g, Temperature dependence of the amplitudes of Vph.
Extended Data Fig. 7 Twist angle-dependence of the linear bulk photovoltaic effect in TDBG.
a-d, Nonlinear conductivity elements σxxx (red) and σyyy (blue) as functions of the incident photon energy ħω when the Fermi level is placed in the CNP gap (top) and the electron-side superlattice gap (bottom) in TDBG with ΔV = 50 meV and the twist angle of 1.2°, 1.4°, 1.6° and 1.8°. Extracted σxxx and σyyy at e, ħω = 161 meV and f, 248 meV, corresponding to the wavelengths of 7.7 μm and 5 μm used in our experiments, respectively.
Extended Data Fig. 8 Complete plots of the polarization outputs from the total 91 training and 12 test data sets.
Complete polarization outputs from the total 103 CNN data sets projected to a, \({S}_{1}\)-\({S}_{2}\) and b, \({S}_{2}\)-\({S}_{3}\) planes. Blue circles are measured values with error bars determined by the errors in measuring the orientation angle Ψ and the ellipticity angle χ (Methods). Red (Orange) spheres are corresponding outputs from CNN training (test) data sets.
Extended Data Fig. 9 Speed and noise characterizations of the TDBG as a photodetector.
a, Photovoltage Vph as a function of the chopping frequency measured under the excitation of 7.7 μm linearly polarized light with Ψ = 45°. b, Voltage noise spectral density measured with zero in-plane electric bias without light illumination. Noise density spikes at multiples of 60 Hz are caused by the power line “hums” in the ground loop. Both measurements were taken at T = 79 K and (VBG, VTG) = (2 V, −7.6 V) in TDBG D1.
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Ma, C., Yuan, S., Cheung, P. et al. Intelligent infrared sensing enabled by tunable moiré quantum geometry. Nature 604, 266–272 (2022). https://doi.org/10.1038/s41586-022-04548-w
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DOI: https://doi.org/10.1038/s41586-022-04548-w
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