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

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.