Moiré amplification of highly tunable shift current response in twisted trilayer graphene

TL;DR

This work analyzes shift current conductivity in helical twisted trilayer graphene (hTTG), establishing an upper bound tied to the two-band density of states and showing moiré amplification that scales as $|oldsymbol{ extsigma}^{a;bc}( u)| \,\propto\, oldsymbol{ extigma}_0/ heta^{2}$ with a dimensionless geometry factor, $oldsymbol{ extTheta}^{a;bc}( u)$. It demonstrates that ABA-stacked hTTG at the magic angle can yield colossal THz photoconductivity (up to ~$10^{4}$–$10^{5}$ μA·nm·V$^{-2}$ in THz) due to transitions between nearly flat middle bands, while chiral sublattice polarization can suppress such responses and AAA stacking can further enhance them (up to ~$10^{5}$ μA·nm·V$^{-2}$). The analysis integrates a gauge-free formulation of interband connections, a dimensionless quantum-geometry measure, and a continuum Hamiltonian that captures stacking phases $oldsymbol{ amephi}$, corrugation $r$, and sublattice offsets. The results highlight the synergy of high DOS, small twist angles, and layer stacking for scalable, tunable shift current photoconductivity with potential photovoltaic applications in moiré heterostructures. Finite-temperature behavior indicates resilience up to room temperature, supporting practical relevance for THz optoelectronics and energy-harvesting devices.

Abstract

In this work we analyze the shift current conductivity in helical twisted trilayer graphene. Without loss of generality, we show that the density of states and the twist angle set an upper bound for this response, which is inversely proportional to the square of the twist angle. For the case of ABA stacking and at the magic angle, the shift photoconductivity can reach values of order $10^4~\mathrm{μA \cdot nm \cdot V}^{-2}$ for frequencies below 50 meV, which can be attributed to the interband transitions between the two flattened middle bands close to the Fermi level. By tuning the twist angle, we demonstrate that the photoconductivity is shifted in the frequency range and it is further influenced by two additional factors: The magnitude of the shift vector and the energy separation between the bands. Furthermore, we propose a scenario in the AAA stacked configuration, where the photoconductivity can be of order $10^5~\mathrm{μA \cdot nm \cdot V}^{-2}$ in the THz regime, revealing a potential influence of the stacking in the optimization of the shift current conductivity. Therefore, a large density of states, a small twist angle and the layer stacking are ingredients that hold promising functionality for photovoltaic applications in moiré heterostructures.

Figures (14)

• Figure 1: (a) Band structure and the associated density of states of an equal-twist ABA-hTTG at the first magic angle ($1.95^\circ$), where the two middle bands are not completely flat due to the deviation from the chiral limit. (b) The shift-current conductivity computed with $T = 0$ and $\mu = 0$ for $\sigma^{x;yy}$ (blue lines) and $\sigma^{y;xx}$ (red lines) as functions of the incident photon energy. The plot zooms in the THz photon energy range below $0.1$ eV. The inset plot zooms in the conductivity plot within the gray rectangle.
• Figure 2: SC conductivity from transitions between flat bands, with $\sigma^{x;yy}(\omega)$ and $\sigma^{y;xx}(\omega)$ colored in blue and red lines, respectively. The inset presents schematically the band structure, highlighting the two bands involved in the main plot, with the occupied band colored in light blue and the unoccupied band in orange.
• Figure 3: SC conductivity coefficients $\sigma^{x;yy}$ (blue line) and $\sigma^{y;xx}$ (red line) from transitions between flat bands and dispersive bands. The first row shows the SC contribution by transition from the occupied flat band to unoccupied dispersive bands, while the the SC conductivity presented in the second row is from the transition from occupied dispersive bands to the unoccupied flat bands. The insets show schematically the band structure while highlighting the bands involved in each main plot. The occupied and the unoccupied bands are colored in light blue and orange, respectively.
• Figure 4: Dimensionless quantum geometry measure $\tilde{X}^{x;yy}(\bm{k})$ within the moiré Brillouin zone computed for (a) the two middle flattened bands and (b) a middle flat band to dispersive band. Both color plots uses different color scales as indicated by the colorbar beneath each subfigure. The bands contributing to the quantum geometry measure are highlighted with red color in each inset. In both color plots, the moiré Brillouin Zone is marked with gray lines.
• Figure 5: (a) Band structure and the associated density of states of an equal-twist ABA-hTTG with equal twist angles being $1.5^\circ$. (b) The shift-current conductivity computed with $T = 0$ and $\mu = 0$ for $\sigma^{x;yy}$ (blue lines) and $\sigma^{y;xx}$ (red lines) as functions of the incident photon energy. The plot zooms in the THz photon energy range below $0.1$ eV. The inset plot zooms in the conductivity plot within the gray rectangle.