Intrinsic and extrinsic photogalvanic effects in twisted bilayer graphene

Abstract

The chiral lattice structure of twisted bilayer graphene with D6 symmetry allows for intrinsic photogalvanic effects only at off-normal incidence, while additional extrinsic effects are known to be induced by a substrate or a gate potential. In this work, we first compute the intrinsic effects and show they reverse sign at the magic angle, revealing a band inversion at the Γ point. We next consider different extrinsic effects, showing how they can be used to track the strengths of the substrate coupling or displacement field. We also show that the approximate particle-hole symmetry implies stringent constraints on the chemical potential dependence of all photocurrents. A detailed comparison of intrinsic vs. extrinsic photocurrents therefore reveals a wealth of information about the band structure and can also serve as a benchmark to constrain the symmetry breaking patterns of correlated states.

Figures (4)

• Figure 1: (a) Sketch of a TBG flake under out-of-plane EM radiation. An off-normal incident field $\boldsymbol E = E_i \boldsymbol e_i$ with $E_z \neq 0$ and associated second-order DC current $\boldsymbol J$ are shown in yellow and purple, respectively. (b) Brillouin zone of TBG. The moiré Brillouin zone is highlighted in black. Black and gray dashed hexagons refer to the first Brillouin zone of top and bottom graphene monolayers, respectively. (c) Band structure of the $\nu=+1$ valley of TBG Hamiltonian in Eq. \ref{['continuummodel']} with $\theta = 1.05^\circ$. Bands are labeled according to their $D_3$ irreducible representation at $\Gamma$. (d) Joint density of states for vertical interband transitions at the two $\mu$ values indicated by dashed lines in (c), with shaded regions representing involved transitions as a function of $\omega$.
• Figure 2: Intrinsic photogalvanic tensors at off-normal incidence. (a) Shift current $\sigma_{xyz}$ at neutrality ($\mu = \mu_1$ in Fig. \ref{['Fig1']}c). (b) $\sigma_{xyz}$ for fully filled flat bands ($\mu = \mu_2$). (c,d) Same for the injection current $\eta_{xyz}$. Only the case $\mu>0$ is shown in b) and d); $\mu<0$ is the same by PHS. Different colors refer to different $\theta$. A characteristic sign reversal when $\theta = \theta_M$ is observed in all cases.
• Figure 3: Photogalvanic components induced by the three symmetry-breaking perturbations in Table \ref{['components']}: (a) $\sigma_{yyy}$ with a $\Delta_1 \sigma_z$ term, (b) $\sigma_{xxx}$ with a $\Delta_2 \sigma_z \tau_z$ term, and (c) $\sigma_{xxz}$ and (d) $\eta_{xxz}$ with a $\Delta_3 \tau_z$ term. Red (blue) encodes $\theta<\theta_M$ ($\theta>\theta_M$), while solid, dashed, and dotted lines refer to $\mu_1$ and $\pm \mu_2$ in Fig. \ref{['Fig1']}c, respectively. $\Delta_1 = \Delta_2 = 10$ meV and $\Delta_3 =15$ meV.
• Figure 4: $\sigma_{yyy}$ in the presence of PHS breaking perturbations at neutrality. A $\Delta_1\sigma_z$ mass in all simulations allows for a finite extrinsic response. Two types of PHS breaking terms are considered: a layered-resolved sublattice perturbation, $\Delta_1 \sigma_z + \Delta_2 \sigma_z\tau_z$, with $\Delta_1 = -\Delta_2 = 10$ meV (gray), and the Kang-Vafek term in Eq. \ref{['kangvafek']} (red). Solid and dashed red lines correspond to $\omega_3 = \pm0.9$ meV, respectively. The PHS preserving case is displayed in black as reference. We set $\theta = 1.05^\circ$.