Tunable Layer Circular Photogalvanic Effect in Twisted Bilayers

We develop a general theory of the layer circular photogalvanic effect (LCPGE) in quasi-two-dimensional chiral bilayers, which refers to the appearance of a polarization-dependent, out-of-plane static dipole moment induced by circularly polarized light. We elucidate the geometric origin of the LCPGE as two types of interlayer coordinate shift weighted by the quantum metric tensor and the Berry curvature, respectively. As a concrete example, we calculate the LCPGE in twisted bilayer graphene, and find that it exhibits a resonance peak whose frequency can be tuned from visible to infrared as the twisting angle varies. The LCPGE thus provides a promising route toward frequency-sensitive, circularly polarized light detection, particularly in the infrared range.

Figure 1

(a) Schematic illustration of the LCPGE. Circularly polarized light induces a static out-of-plane dipole, whose direction flips when the circular polarization of light is reversed. Red and blue disks stand for negative and positive charges, respectively. (b) Origin of the LCPGE. The incident light excites an electron from the valence band to the conduction band, while simultaneously causing a change in the dipole moment. Such a transition process is dependent on the light chirality through the geometric factor ${\beta }_G$ in Eq. (5).

Figure 2

The LCPGE coefficient ${\beta }_0$ and the joint density of states (JDOS) in twisted bilayer graphene with twisting angle $\theta =21.8°$. ${\beta }_0$ is in units of $e/{\hslash }^2$. The joint density of states is in units of $1/3a^2$ per electron volts with $a$ being the lattice constant of the bilayer graphene. The phenomenological relaxation parameters are chosen as ${\eta }_1={\eta }_2=0.02\mathrm{eV}$. The Fermi level is taken at the Dirac point.

Figure 3

Geometric origin of the peak at 2.8 eV in Fig. 2. We plot the band spectrum in (a), the quantum geometric tensor $(\mathrm{Tr}{g}_{ij}{)}_{n\ell }$ in (b), and the interlayer coordinate shift $R_{\text{as}}$ in (c), along the high symmetry line shown in black in the inset of (a). In (a), we include the spectrum from 13th to 18th band. The red and blue arrows in (a) show the optical transition with a photon energy 2.8 eV, which are also shown as dots in the inset plot of the Brillouin zone. For $(\mathrm{Tr}{g}_{ij}{)}_{n\ell }$ and $(R_{\text{as}}{)}_{n\ell }$, we consider the quantities with $n=14$ and $\ell =15$, and with $n=13$ and $\ell =15$, which correspond to the red and blue transitions shown in (a). The blue and red dashed lines in (b) and (c) are at the same position in the Brillouin zone with the blue and red arrows in (a).

Figure 4

The peak position (black) and the corresponding potential difference (red) generated by the LCPGE at different twisting angles. We have assumed a laser power $1\mathrm{mW}/\mu {\mathrm{m}}^2$.

Figure 5

The real-space resolved layer potential difference ($\mu \mathrm{V}$) induced by the LCPGE in the moiré supercell at the twisting angle, $\theta =2.87°$, and the peak frequency, $\omega =0.34\mathrm{eV}$.