Resonant absorption and linear photovoltaic effect in ferroelectric moiré heterostructures

TL;DR

This work shows that electrostatic moiré potentials from interfacial ferroelectric domains in twisted bilayer vdW structures create tunable mini-bands for graphene, with resonant absorption up to about 10% arising from van Hove singularities. The authors derive effective Hamiltonians for primary and secondary massless Dirac fermions and show how carrier density, twist angle, and out-of-plane fields reshape the miniband structure, including Lifshitz transitions and anisotropic dispersion. A purely linear photovoltaic response emerges from shift photocurrents, while injection currents are symmetry-forbidden, with resonances driven by virtual interband transitions. The findings offer a route to tunable infrared optoelectronics in ferroelectric moiré heterostructures and are applicable to graphene and twisted TMD systems.

Abstract

Twisted bilayers, featuring interfacial ferroelectricity in the form of array of polar domains, combined with incommensurate two-dimensional layers in a single van der Waals heterostructures allows for generation of purely electrostatic moiré superlattice potentials in the latter. We study electronic and optoelectronic properties of such heterostructures composed of graphene stacked with the twisted ferroelectric bilayers and show that doping of graphene substantially affects mini-band structures because of screening of free carriers. We demonstrate that formation of van Hove singularities in density of states modifies linear and second-order responses of the structures leading to resonant absorption and linear photovoltaic effect, respectively. The latter is generated solely by a shift photocurrent, arising only with account of virtual optical transitions, whereas an injection photocurrent is forbidden by symmetry.

Figures (6)

• Figure 1: Low-energy mini-bands and corresponding densities of states for graphene/twisted hBN bilayer heterostructure characterized by twist angle $\theta=0.18^{\circ}$ for three values of electron doping $n=10^{10}$, $10^{11}$ and $10^{12}$ cm$^{-2}$ (red lines shows corresponding Fermi-energies $\varepsilon_F$). Blue dashed line shows density of states in an isolated graphene; arrows indicate resonant frequencies in absorption. Bottom insets show distribution of electrostatic moiré potential in graphene created by polar domains in twisted hBN bilayer and renormalization of primary mDF group velocity with electron concentration at $\theta=0.18^{\circ}$ .
• Figure 2: Frequency dependences of the absorption coefficient \ref{['Eq:absorption']} for doping levels corresponding to Fig. \ref{['fig:minibands']} at $T\ll\hbar\omega_3$. The resonances, $\omega_{1,2,3}$, corresponds to energy differences between states at peaks of DOS, shown in Fig. \ref{['fig:minibands']}, where the interband velocity matrix elements are non-zero. Dashed line indicates absorption ($2.3\%$) of an isolated graphene layer Nair2008.
• Figure 3: Frequency dependences of the shift photocurrent \ref{['Eq:jshift']} for graphene--twisted hBN bilayer with $\theta=0.18^{\circ}$ at the intensity of the incident radiation $I=0.1 {\rm W/cm^2}$ and indicated electron dopings. Insets: (Top) Dependences of $j^{x,y}_{\rm shift}(\omega_{1},\chi)$ (red) and $j^{x,y}_{\rm shift}(\omega_{3},\chi)$ (blue) on the polarisation of the incident electromagnetic wave, characterised by angle $\chi$. (Bottom) Orientation of the polarisation with respect to moiré superlattice in the twisted bilayer.
• Figure S4: (a) Sketch of the electrostatic model. In the limit $\epsilon_1\gg1$ the bottom medium simulates proximity gate electrode that doubles electrostatic moiré potential in graphene layer (at $z=z_g$).
• Figure S5: (a) Mini-band structures in graphene/twisted hBN bilayer at out-of-plane electric field $D/\epsilon_0=1.5$ V/nm across the twisted interface with $\theta=0.18^{\circ}$. Bottom inset show polar domain structure for the electric field.