The bulk photovoltaic (BPV) effect, converting light into direct electric current in non-centrosymmetric materials, offers advantages over conventional p-n junction methods due to its bias-free nature and enhanced efficiency. This effect utilizes the electron charge degree of freedom (DOF). To enhance information processing, research has expanded to explore other DOFs, such as spin (spintronics) and orbital angular momentum (orbitronics). Spintronics leverages the different velocities of spin-up and spin-down electrons to generate spin currents. Orbitronics, focusing on electron orbital motion, is particularly relevant in low-dimensional materials where orbital moments are less quenched. This paper predicts a hidden orbital current, termed the bulk orbital photovoltaic (BOPV) effect, in 2D nonmagnetic ferroelectric materials like GeS, SnS, GeSe, SnSe, GeTe, SnTe, and Bi(110). These materials possess a vertical mirror symmetry and time-reversal symmetry but lack inversion symmetry. The study uses first-principles density functional theory (DFT) calculations to explore this effect and its interplay with spintronics via spin-orbit coupling (SOC).

The paper reviews the existing literature on the bulk photovoltaic effect, spintronics, and orbitronics. It highlights the advantages of the BPV effect for light-to-current conversion and the potential of spintronics and orbitronics for enhancing information processing. The authors discuss the limitations of relying solely on charge DOFs and the need to explore other DOFs to improve the kinetics and storage density of future devices. Previous studies on the orbital Hall effect and valley Hall effect are also reviewed, providing a context for the current work. The existing literature on 2D ferroelectric materials, especially group-IV monochalcogenides and Bi(110), is also reviewed, focusing on their experimental fabrication and ferroelectric properties.

The authors employ first-principles density functional theory (DFT) calculations using the Vienna ab initio simulation package (VASP) with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional and projector-augmented wave (PAW) method. A vacuum space of 12 Å is used to eliminate inter-image interactions, and a (9x9x1) k-mesh is used for geometric and electronic structure calculations. Convergence criteria for total energy and force are set to 1×10⁻⁷ eV and 0.01 eV Å⁻¹, respectively. Spin-orbit coupling is self-consistently included. Nonlinear optical conductivities are calculated by fitting the electronic structure to a tight-binding model using Wannier90, integrating on a denser (901x901x1) k-mesh. The BOPV and BSPV conductivities are calculated using second-order Kubo response theory within the independent particle approximation, considering a phenomenological carrier lifetime of 0.2 ps. The calculations include the effects of linearly polarized light (LPL) and circularly polarized light (CPL), focusing on the out-of-plane angular momentum current. Symmetry analysis, based on time-reversal and mirror symmetries, is used to determine the allowed and forbidden photocurrent responses. The k-resolved joint density of states (jDOS) and the integrand of the Kubo formula are analyzed to understand the momentum space contributions to the photoconductivity. The effect of varying SOC strength is investigated by scaling the SOC Hamiltonian. Polarization dependence is studied by changing the ferroelectric polarization. Calculations are performed for several analogous 2D ferroelectric materials (GeSe, SnS, SnSe, GeTe, SnTe, and Bi(110)) to assess the generality of the findings.

The study predicts the existence of a bulk orbital photovoltaic (BOPV) effect, generating a pure orbital current perpendicular to the mirror plane in 2D nonmagnetic ferroelectric materials. This pure orbital current arises from the hidden electron flow along opposite directions carrying different orbital moments, resulting in zero net charge current. The spin-orbit coupling interaction converts this orbital current into a spin current (BSPV). The authors demonstrate that the magnitude of the BOPV conductivity is significantly larger than that of the BSPV conductivity in these materials. Both BOPV and BSPV currents are shown to be strongly dependent on the direction of the ferroelectric polarization, reversing direction when polarization flips. Calculations on various analogous materials reveal similar trends for BOPV, with GeTe showing the largest photocurrent responses, while BSPV responses vary due to differences in SOC strength. The study also finds that while the BOPV effect is largely unaffected by the strength of SOC, the BSPV effect is directly proportional to the SOC strength. Importantly, the x-direction charge current is consistently zero in the calculations, further confirming the pure nature of the orbital and spin currents.

The findings address the research question by demonstrating the existence and characteristics of pure bulk orbital and spin photocurrents in 2D ferroelectric materials. This discovery extends the understanding of the bulk photovoltaic effect beyond the charge DOF, opening new avenues for orbitronics and spintronics applications. The significantly larger magnitude of the BOPV current compared to the BSPV current highlights the potential of exploiting orbital DOFs for efficient light-to-current conversion. The controllability of these currents via ferroelectric polarization switching offers a promising route for developing novel optoelectronic devices. The use of a four-terminal device to separately detect charge, orbital, and spin currents is a crucial aspect of the study, providing a pathway for experimental validation. The observed polarization dependence and the analysis of momentum space contributions provide a deeper understanding of the underlying mechanisms driving these effects.

The study successfully predicts the existence of robust and pure bulk orbital (BOPV) and spin (BSPV) photovoltaic currents in 2D ferroelectric materials. The BOPV current, characterized by its independence from charge current, arises from distinct electron movements carrying opposite orbital moments. The BSPV effect, originating from SOC interaction, is shown to be dependent on the strength of the SOC. Both effects are highly sensitive to ferroelectric polarization, offering a mechanism for manipulating current direction. This work opens up new possibilities for ultrafast spintronic and orbitronic applications using 2D in-plane ferroelectric materials. Future research may focus on experimental verification of these findings using four-terminal devices and further exploration of the impact of many-body effects and exciton interactions on the observed phenomena.

The calculations employed DFT with a phenomenological carrier relaxation time, neglecting many-body effects and exciton interactions. While the authors argue that DFT provides qualitatively correct results for this system based on previous studies, the influence of these omitted factors on the exact quantitative values of the photocurrents remains unclear. Another limitation is the simplified treatment of ferroelectric domains; the study does not model the complex interplay of polarization directions across domain boundaries comprehensively. Lastly, the choice of 0.2 ps for the carrier relaxation time might affect the exact magnitudes predicted for photoconductivities, but the general findings are qualitatively robust.