Enabling the bulk photovoltaic effect in centrosymmetric materials through an external electric field

TL;DR

This work addresses enabling and tuning the bulk photovoltaic effect in centrosymmetric layered materials by applying a static out-of-plane field, implemented nonperturbatively through field dressing of a Wannier-based Hamiltonian. The authors derive a length-gauge formalism for the second-order dc response and connect its weak-field limit to the mixed third-order tensor, providing a unified view of weak and strong field regimes. They show that 2H MoS2 bilayers exhibit a strong, linear-in-field shift current once inversion is broken, while monolayers and 3R bilayers display distinct, symmetry-driven responses, including field-induced activation of out-of-plane components and polarity-driven compensation. The results establish gate-tunable nonlinear photocurrents in centrosymmetric layered materials and offer a practical framework for predicting and engineering BPVE in 2D systems.

Abstract

We develop a practical approach to electrically tuning the nonlinear photoresponse of two-dimensional semiconductors by explicitly incorporating a static out-of-plane electric field into the electronic ground state prior to optical excitation, as a gate bias. The method is implemented by dressing a Wannier-interpolated Hamiltonian with the field through its position matrix elements, which allows the gate bias to modify orbital hybridization and band dispersion beyond perturbative treatments. Within the independent-particle approximation, the resulting second-order (shift) conductivity is evaluated for both centrosymmetric and non-centrosymmetric layered systems. Applied to MoS$_2$, the approach captures the emergence of a finite shift current in centrosymmetric bilayers and the tunability of intrinsic responses in polar structures. The shift conductivity rises linearly at small fields and saturates at higher intensities, reflecting the competition between the growing shift vector and the weakening interband coupling as resonant transitions move away from high-symmetry valleys. A Taylor expansion of the field-dressed conductivity connects this behavior to the third-order optical response, revealing a unified picture of field-induced nonlinearities. These results establish field dressing of Wannier Hamiltonians as a practical route to model and predict nonlinear photocurrents in layered materials.

Figures (6)

• Figure 1: second-order conductivity $\sigma^{(2)}_{yyy}(\omega;E_{\mathrm{DC}})$ of monolayer MoS2 under static out-of-plane fields up to $0.050$ mV/Å. The top panel shows the full spectrum and the bottom panel shows the differential response $\Delta\sigma^{(2)}_{yyy}(\omega;E_{\mathrm{DC}})$. Field-induced changes remain weak, on the order of $2.5$ nm$\cdot\mu$A/V$^2$.
• Figure 2: Representative out-of-plane component of the shift conductivity tensor in monolayer MoS2 under a perpendicular static field.
• Figure 3: In-plane (top) and out-of-plane (bottom) shift conductivity for 2H-MoS2 under a perpendicular static field $E_{\mathrm{DC}}$.
• Figure 4: Field dependence of the second-order conductivity for 2H-MoS2. Left panels: $\sigma^{(2)}_{yyy}(\omega;E_{\mathrm{DC}})$ and its derivative with respect to $E_{\mathrm{DC}}$ for several photon energies near the band edge. Right panels: corresponding results for $\sigma^{(2)}_{zyy}(\omega;E_{\mathrm{DC}})$. The dashed lines show the linear behavior extracted from the derivative at $E_{\mathrm{DC}}=0$, which corresponds to the mixed third-order conductivity $\sigma^{(3)}_{abcz}(0;\omega,-\omega,0)$ through Eq. \ref{['eq:taylor']}. The linear regime around zero field verifies the Taylor expansion, while deviations at larger fields reveal the onset of higher-order field dependence.
• Figure 5: Comparison between the field-induced second-order conductivity of centrosymmetric 2H (AA$'$) bilayer MoS2 (black circles) and the intrinsic monolayer response (red squares) at $\hbar\omega\approx E_g$. The bilayer exhibits a strong (essentially) linear dependence on $E_{\mathrm{DC}}$, while the monolayer remains nearly constant. The sign reversal for opposite field polarities reflects the antisymmetric character of the field-induced shift current, which vanishes in the centrosymmetric limit.