Giant Nonlinear Photon-Drag Currents in Centrosymmetric Moiré Bilayers

TL;DR

The paper develops a geometric-loop formalism to unify nonlinear photon-drag injection and shift currents in centrosymmetric and symmetry-broken 2D moiré materials. It casts the response in terms of gauge-invariant geometric loops and a dipole operator, enabling robust, gauge-consistent calculations on realistic continuum models. Applying the framework to an ab initio–informed continuum model of twisted bilayer graphene, the authors show that modest in-plane photon momentum can generate sizable nonlinear photon-drag currents, with magnitudes rivaling giant photogalvanic effects in noncentrosymmetric systems and tunable via twist angle, light momentum, and polarization. Inversion breaking (e.g., hBN alignment) introduces conventional shift currents and alters the relative weight of contributions, revealing distinct k-space textures that reflect the underlying quantum geometry. Overall, the work positions moiré bilayers as versatile platforms for large, tunable optoelectronic responses driven by light’s momentum.

Abstract

We present a unified microscopic theory of nonlinear photon-drag currents, formulated within a geometric-loop framework that provides both transparent quantum-geometric interpretation and numerical tractability. In this picture, the photon-drag shift current corresponds to the dipole moment of the geometric loop, while the photon-drag injection current arises from the same loop weighted by a band velocity difference. We apply the theory to an exact continuum model of twisted bilayer graphene (TBG) with ab initio accuracy. Remarkably, an in-plane wavevector only a few times larger than that of free-space photons already produces sizable photon-drag currents in centrosymmetric TBG, comparable to photogalvanic responses in typical noncentrosymmetric two-dimensional materials. These currents are broadly tunable by twist angle, photon wavevector, and light polarization. Our results establish a quantum geometric framework for nonlinear photon-drag phenomena and highlight moiré bilayers as promising platforms for large, highly tunable optoelectronic responses.

Figures (4)

• Figure 1: (a) Uniform illumination yields no photogalvanic current in a centrosymmetric medium, whereas finite $\boldsymbol{q}$ produces a nonlinear photon-drag current $J^{(2)}$ via polaritonic enhancement or spatially dispersive beams. (b) Schematic of the geometric loop $\mathcal{L}_{\beta\alpha}$. The loop connects four Bloch states $\alpha, \beta, \alpha', \beta'$, with $\alpha,\alpha'$ in the valence band and $\beta,\beta'$ in the conduction band. The momenta of $\alpha, \beta, \alpha', \beta'$ are related by $\boldsymbol{k}_\beta-\boldsymbol{k}_\alpha=\boldsymbol{k}_{\beta'}-\boldsymbol{k}_{\alpha'}=\boldsymbol{q}$ and $\boldsymbol{k}_{\beta'}-\boldsymbol{k}_\beta=\boldsymbol{k}_{\alpha'}-\boldsymbol{k}_\alpha=\boldsymbol{p}$, where $\boldsymbol{p}$ is an infinitesimal displacement.
• Figure 2: Photon-drag photoconductivity of centrosymmetric TBG. (a) $\sigma_{\mathrm{IC,L}}^{yxx}$ and (b) $\sigma_{\mathrm{SC,C}}^{xxy}$ spectra at $\theta=1.05^\circ$, showing the evolution with photon wavevector; curves from light to dark correspond to $\boldsymbol{q}_0/3, 2\boldsymbol{q}_0/3, \boldsymbol{q}_0$. Insets: magnitude of peak photoconductivity versus $\boldsymbol{q}$ over an extended range, taken at the spectral peaks $\hbar\omega = 47\mathrm{meV}$ for (a) and $\hbar\omega = 41\mathrm{meV}$ for (b). For (a), we use a moderate relaxation time $\tau=10^{-13}\,\mathrm{s}$. (c-d) Spectra at fixed $\boldsymbol{q}=\boldsymbol{q}_0$ for twist angles $\theta=1.05^\circ$, $1.15^\circ$, and $1.25^\circ$, respectively.
• Figure 3: Influence of inversion symmetry breaking on photon-drag photoconductivity in TBG. (a-c) Photoconductivity spectra in noncentrosymmetric TBG, compared with the centrosymmetric case at $\theta=1.05^\circ$: (b) $\sigma_{\mathrm{IC,L}}^{yxx}$, (c) $\sigma_{\mathrm{SC,L}}^{xxx}$, (d) $\sigma_{\mathrm{SC,C}}^{xxy}$. (d-f) $k$-resolved photoconductivity corresponding to (a-c) at the photon energies indicated by the green arrows in (a-c): (d) $\hbar\omega=58~\mathrm{meV}$, (e) $\hbar\omega=55~\mathrm{meV}$, and (f) $\hbar\omega=51~\mathrm{meV}$.
• Figure S1: Band structures from the relaxed continuum model of twisted bilayer graphene along $\rm K\!-\!\Gamma\!-\!M\!-\!K$. (a-c) Centrosymmetric TBG at twist angles $\theta=1.05^\circ$, $1.25^\circ$, and $1.15^\circ$, respectively. (d) Inversion-broken case at $\theta=1.05^\circ$.