Photogalvanic effect in few layer graphene

Abstract

We systematically investigate the nonlinear photogalvanic effect in few-layer graphene with various stacking orders, including AA- and AB-stacked bilayers, and AAA-, ABA-, and ABC-stacked trilayers. Using a tight-binding model to describe the electronic states, the shift current conductivity and jerk current conductivity are calculated over a broad spectral range from terahertz to visible frequencies. Our symmetry analysis reveals that a nonvanishing shift current emerges only in ABA-stacked trilayer graphene due to its broken inversion symmetry, with a peak conductivity reaching approximately $1.21 \times 10^{-13}$ A$\cdot$m/V$^2$ at optimal doping. In contrast, the jerk current, permitted in all structures, requires an in-plane static electric field and exhibits pronounced spectral tunability with chemical potential. These findings establish a comprehensive symmetry-band-field coupling paradigm for nonlinear photocurrents in layered graphene and provide design principles for tunable, polarization-sensitive photodetection and energy-harvesting devices based on van der Waals heterostructures.

Figures (5)

• Figure 1: (a) Schematic of the shift current response collected by electrodes along the $x$- and $y$-directions. (b) Electronic band structure of ABA-TG. Insert is a magnification of the middle part. Spectra of the shift conductivity $\sigma^{(2);xxy}$ for ABA-TG at (c) discrete chemical potentials $\mu =0, 0.2, 0.6$ eV and (d) at continuously varying chemical potentials, with $\gamma=33$ meV. (e) The lower half is similar to (c), but with $\gamma=5$ meV, and the upper half is JDOS of ABA-TG.
• Figure 2: (a) Schematic of the jerk current response collected by electrodes along the $x$- and $y$-directions under an electrostatic field applied along the $y$-direction. (b) Two groups of considered few-layer graphene with structural diagrams. (c) Electronic band structure of AA-BG. (d) Spectra of the jerk conductivities Re[$\sigma^{(3);xxyy}$], Im[$\sigma^{(3);xxyy}$], and Re[$\sigma^{(3);xyyx}$] for AA-BG at a chemical potential $\mu=0$ eV (black lines), and for the combined two layers of monolayer graphene denoted Gr* (red lines). (e) Electronic band structure of AAA-BG. (f) Spectra of the jerk conductivities Re[$\sigma^{(3);xxyy}$], Im[$\sigma^{(3);xxyy}$], and Re[$\sigma^{(3);xyyx}$] for AAA-BG at a chemical potential $\mu=0$ eV (black lines), and for the combined three layers of monolayer graphene denoted Gr** (red lines). Note, the superimposed spectra are given by Eqs. \ref{['Gr-AA']} and \ref{['Gr-AAA']}.
• Figure 3: Electronic band structures of (a) AB-BG, (c) ABC-TG, and (e) ABC-TG. Spectra of the jerk conductivities Re[$\sigma^{(3);xxyy}$], Im[$\sigma^{(3);xxyy}$], and Re[$\sigma^{(3);xyyx}$] at a chemical potential $\mu=0$ eV for (b) AB-BG, (d) ABC-TG, and (e) ABA-TG, with insets for small damping of $\gamma=5$ meV.
• Figure 4: Schematic diagram of different chemical potentials in (a) AA-BG and (c) AAA-TG. Spectra of the jerk conductivities Re[$\sigma^{(3);xxyy}$], Im[$\sigma^{(3);xxyy}$], and Re[$\sigma^{(3);xyyx}$] continuously changing with chemical potential in (b) AA-BG and (d) AAA-TG.
• Figure 5: Schematic diagram of different chemical potentials in (a) AB-BG, (c) ABA-TG, and (e) ABC-TG. Spectra of the jerk conductivities Re[$\sigma^{(3);xxyy}$], Im[$\sigma^{(3);xxyy}$], and Re[$\sigma^{(3);xyyx}$] continuously changing with chemical potential in (b) AB-BG, (d) ABA-TG, and (f) ABC-TG.