Bulk Photovoltaic Effect Driven by Collective Excitations in a Correlated Insulator

We investigate the bulk photovoltaic effect, which rectifies light into electric current, in a collective quantum state with correlation driven electronic ferroelectricity. We show via explicit real-time dynamical calculations that the effect of the applied electric field on the electronic order parameter leads to a strong enhancement of the bulk photovoltaic effect relative to the values obtained in a conventional insulator. The enhancements include both resonant enhancements at sub-band-gap frequencies, arising from excitation of optically active collective modes, and broadband enhancements arising from nonresonant deformations of the electronic order. The deformable electronic order parameter produces an injection current contribution to the bulk photovoltaic effect that is entirely absent in a rigid-band approximation to a time-reversal symmetric material. Our findings establish that correlation effects can lead to the bulk photovoltaic effect and demonstrate that the collective behavior of ordered states can yield large nonlinear optical responses.

Figure 1

(a) Top panel: Zigzag chain model Eq. (1), where we plot an example of two orbitals that lead to hopping $t_{ab}$. Bottom panel: schematic picture of the EI state. (b) Ground-state phase diagram of Eq. (1) in the plane of interaction $V$ and interchain hopping $t_{ab}$ computed in the Hartree-Fock approximation for $D/t_h=1$. The magnitude of the order parameter ${\varphi }_{+}$ is shown in false color.

Figure 2

(a) Optical conductivity ${\sigma }_{xx}(\omega ={\omega }_p)$ of the FEI on linear (main panel) and logarithmic (inset) scales. The black dashed line indicates the band gap. (b),(c) Time evolution of the real (orange) and imaginary (blue) components of the order parameter ${\varphi }_{+}(t)$ at (b) ${\omega }_p/t_h=0.144$ and (c) ${\omega }_p/t_h=0.559$, which correspond to the phase and amplitude mode frequencies, respectively, where $\mathrm{\Delta }{\varphi }_{+}(t)={\varphi }_{+}(t)-{\varphi }_{+}(t=0)$ is plotted. $D/t_h=1$, $t_{ab}/t_h=0.2$, $V/t_h=1.1$, $E_0/t_h=0.0001$, and $\gamma /t_h=0.01$ are used.

Figure 3

(a),(b) Time evolution of the intraband current $J_{\text{intra}}^{(\mathrm{I})}(t)$ in the FEI at (a) ${\omega }_p/t_h=0.144$ and (b) ${\omega }_p/t_h=0.559$, which correspond to the collective mode frequencies in Figs. 2 and 2, respectively. (c) Conductivity ${\sigma }_{xxx}^{(\mathrm{I})}(\omega =0;{\omega }_p)$ of the shift current. The red solid and blue dashed lines indicate ${\sigma }_{xxx}^{(\mathrm{I})}(\omega =0;{\omega }_p)$ in the tdMF and IPA, respectively. The parameter set is the same as Fig. 2.

Figure 4

(a) Time evolution of the intraband current $J_{\text{intra}}^{(\mathrm{II})}(t)$ in the FEI at ${\omega }_p/t_h=0.8$. (b) Conductivity ${\sigma }_{xxx}^{(\mathrm{II})}(\omega =0;{\omega }_p)$ of the injection current with $\gamma /t_h=0.01$. $D/t_h=1$, $t_{ab}/t_h=0.2$, $V/t_h=1.1$, and $E_0/t_h=0.0001$ are used.

Figure 5

Conductivity ${\sigma }_{xxx}(\omega =0;{\omega }_p)={\sigma }_{xxx}^{(\mathrm{I})}(\omega =0;{\omega }_p)+{\sigma }_{xxx}^{(\mathrm{II})}(\omega =0;{\omega }_p)$ with changing $\gamma$. The parameter set is the same as Fig. 4.