Pure bulk orbital and spin photocurrent in two-dimensional ferroelectric materials

The study addresses whether nonlinear optical excitation in non-centrosymmetric 2D ferroelectrics can generate bias-free orbital and spin photocurrents, extending the bulk photovoltaic (BPV) effect beyond charge. BPV converts alternating optical fields into direct current throughout illuminated regions without contacts, offering efficiency advantages. To enhance information processing, additional electron degrees of freedom—spin and orbital angular momentum—are considered. While spintronics exploits spin-dependent transport, orbitronics focuses on orbital angular momentum, often quenched in conventional crystals but significant in low-dimensional systems with reduced symmetry. The research aims to demonstrate a second-order nonlinear bulk orbital photovoltaic (BOPV) effect producing a pure orbital current under linearly polarized light, and its conversion into a bulk spin photovoltaic (BSPV) current via spin–orbit coupling (SOC), in 2D ferroelectric group-IV monochalcogenides and Bi(110). It further explores symmetry constraints dictating current directions, valley contributions, and ferroelectric polarization control of these currents, highlighting potential for ultrafast orbitronic/spintronic applications.

Background includes foundational work on BPV as a second-order nonlinear optical effect generating charge current in noncentrosymmetric crystals and its enhancement in polar materials. Spintronics literature establishes spin currents arising from spin-dependent velocities. Orbitronics literature notes orbital moments in low-dimensional or symmetry-reduced systems and predicts orbital current and orbital Hall effects in linear response, alongside spin and valley Hall effects. Prior reports established robust in-plane ferroelectricity in group-IV monochalcogenide monolayers and Bi(110), and that symmetry (mirror, glide) constrains spin/orbital components. The present work builds on these by proposing a second-order nonlinear bulk orbital and spin photovoltaic response and relating it to symmetry, SOC, and valley physics.

- Theoretical framework: Second-order nonlinear response (Kubo formalism) under closed-circuit boundary conditions, using electric field as perturbation. Currents J^c (charge), J^l (orbital, with Lz), and J^s (spin, with Sz) are expressed via photoconductivity tensors σ^c, σ^l, σ^s contracted with optical field components for ω and −ω. Focus is on out-of-plane angular momentum components (z) and in-plane current directions (x,y). - Symmetry analysis: For materials with vertical mirror Mx and time-reversal symmetry, under linearly polarized light (LPL) along x or y (which preserves Mx), charge current along x is forbidden (Jx=0), while charge BPV flows along y. Because Lz and Sz are pseudovectors flipping under Mx, σ_xx^l, σ_yy^l, σ_xx^s, σ_yy^s can be nonzero whereas σ_xz and σ_yz components vanish, implying hidden counterflow along x carrying angular momentum but zero net charge—i.e., pure orbital (and via SOC, spin) current. Under circularly polarized light (CPL), directions are interchanged (charge along x; orbital/spin along y). - Nonlinear conductivity evaluation: Within independent-particle approximation and a three-band model, the complex second-order conductivity is integrated over the Brillouin zone using band velocities and current operators. The orbital/spin current operator uses the symmetrized product with Lz or Sz; charge current uses ev^c. A phenomenological carrier lifetime τ = 0.2 ps controls relaxation/broadening. Contributions are dominated by resonant interband transitions, analyzed via k-resolved integrands and joint density of states (jDOS). - Materials: 2D nonmagnetic ferroelectrics: group-IV monochalcogenide monolayers (GeS, SnS, GeSe, SnSe, GeTe, SnTe) and Bi(110). All have in-plane ferroelectric polarization and belong to space group Pmn2_1 with vertical mirror symmetry. - First-principles calculations: DFT with VASP using GGA-PBE, PAW potentials, 350 eV plane-wave cutoff, 9x9x1 k-mesh, 12 Å vacuum, convergence criteria 1e-7 eV (energy) and 0.01 eV/Å (forces). SOC included self-consistently unless noted. Electronic structures are Wannierized (s and p orbitals) using Wannier90; optical conductivities integrated on dense 901x901x1 k-grid with convergence checks. Intra-atomic Lz matrix elements constructed from spherical-harmonic-based s,p basis; spin operators from Pauli matrices. - 2D normalization: To remove artificial vacuum contribution, 3D conductivities are rescaled to effective 2D values using an estimated effective thickness deff (≈0.6 nm, corresponding to interlayer spacing of stacked bulk analogs). - SOC tuning: SOC strength scaled by a prefactor λ∈[0,1] to assess its role in BSPV vs BOPV. - Ferroelectric polarization control: Conductivities computed for P=+P0, −P0, and centrosymmetric P=0 states to probe symmetry-imposed behavior (sign reversal and suppression at P=0). - Additional considerations: CPL responses discussed in supplementary; injection vs shift character analyzed (BOPV/BSPV under LPL show injection-like dependence on τ; CPL induces shift-type contributions).

- Symmetry-driven directions: Under LPL, charge BPV flows parallel to polarization (y), while charge current along x is symmetry-forbidden. Nevertheless, hidden electron motion along ±x exists, carrying opposite angular momenta, producing a pure orbital current (BOPV) and, via SOC, a pure spin current (BSPV) along x. - Quantitative BOPV in GeS monolayer: BOPV conductivity along x is zero below the direct bandgap (~1.91 eV). It exhibits strong frequency dependence with peaks at specific energies. Notably, at ħω=2.83 eV, σ_xx^l reaches a negative peak of approximately −636.2 (in the same unit convention as nonlinear charge BPV). For y-polarized LPL, a peak of about 913.95 occurs at ħω=2.17 eV. k-resolved analyses show dominant contributions near valleys ±Vx (near X) and ±Vy (near Y), respecting Mx symmetry; Γ contributes little. At ħω≈2.63 eV, opposing valley contributions cancel, yielding near-zero net BOPV but implying valley-polarized responses. - BSPV magnitude and scaling: BSPV conductivities are generally ~an order of magnitude smaller than BOPV. For GeS, at ħω=2.83 eV, σ_xx^s≈113.37; at 2.17 eV, ≈3.60. Momentum-space distributions mirror BOPV with contributions from the same valleys. Tuning SOC with λ shows BSPV scales approximately linearly to zero as λ→0, confirming SOC necessity for BSPV; BOPV is largely insensitive to λ. - Pure-current character: Along x, electric charge current sums to zero while equal and opposite angular-momentum-carrying electron flows exist, demonstrating pure orbital (and spin) photocurrents. Along y, the photocurrent is a pure charge current with vanishing orbital current under LPL. - Polarization control: In centrosymmetric high-symmetry structure (P=0), all BPV/BOPV/BSPV conductivities vanish by inversion symmetry. Reversing polarization (P0→−P0) reverses current direction with similar magnitude. A 90° rotation of polarization rotates current directions accordingly (e.g., BOPV/BSPV switch between x and y depending on light polarization and P orientation). - Materials generality: Across GeSe, SnS, SnSe, GeTe, SnTe, and Bi(110), BOPV responses show similar spectral features due to shared low-energy electronic structure; magnitudes vary, with monolayer GeTe exhibiting the largest peaks (>10,000 µA/V^2 in figures), while SnS is smaller. BSPV magnitudes vary with SOC strength (∝Z^2), lacking a uniform trend across compounds. - Mechanism insight: Larger BOPV than BSPV arises because orbital textures set by crystal field are similar across Rashba-split bands (contributing constructively), whereas spin textures flip sign between Rashba partners and partially cancel, leaving smaller net BSPV. Velocity textures are similar but not identical, preventing complete cancellation. - Device concept: A four-terminal structure can separately detect charge (along y) and angular momentum (along x) photocurrents; magnetic contacts can transduce orbital-to-spin signals via interfacial SOC. Domain boundaries in ferroelectrics may act as angular-momentum current filters/valves due to 90° polarization rotations.

The work demonstrates that the conventional symmetry-forbidden transverse charge BPV channel hides robust angular-momentum-carrying electron flows, establishing a second-order bulk orbital photovoltaic effect. This directly addresses the question of generating and controlling pure orbital and spin photocurrents with light in nonmagnetic 2D ferroelectrics. The results show: (1) current directions are dictated by mirror symmetry and light polarization, enabling simultaneous orthogonal detection of charge and angular-momentum currents; (2) SOC converts orbital to spin currents, but BOPV persists even without SOC, highlighting orbitals as primary carriers; (3) ferroelectric polarization provides a handle to switch and rotate currents, suggesting nonvolatile, reconfigurable photonic control of orbitronics/spintronics. Valley-selective contributions open avenues for valley-orbit-spin intertwined functionalities. Proposed detection strategies (magneto-optical Kerr/Faraday, inverse spin Hall via interfacial SOC) make experimental verification feasible. The findings expand BPV from charge-only effects to a broader framework encompassing orbital and spin degrees of freedom, with implications for ultrafast, low-power, on-chip opto-spintronic/orbitronic devices and domain-boundary current routing.

This study predicts and quantifies pure bulk orbital (BOPV) and spin (BSPV) photocurrents in 2D nonmagnetic ferroelectric materials under linearly polarized light. Owing to mirror symmetry, charge current along x is forbidden, yet hidden counter-propagating electron flows with opposite angular momenta produce a pure orbital current; SOC converts it into a smaller pure spin current. These currents are orthogonal to conventional charge BPV and are tunable by ferroelectric polarization, vanishing in the centrosymmetric state and reversing with polarization switching. First-principles and k·space analyses identify valley origins and explain why BOPV exceeds BSPV via crystal-field-determined orbital textures and Rashba spin cancellation. The concept generalizes across group-IV monochalcogenides and Bi(110), with GeTe showing particularly large responses. A four-terminal device is proposed for simultaneous charge/orbital/spin current detection, and ferroelectric domain boundaries are suggested as angular-momentum current filters. Future directions include: experimental detection of BOPV/BSPV via interfacial SOC conversion and magneto-optical probes; incorporation of many-body and excitonic effects in nonlinear response; systematic studies of carrier lifetimes and disorder; engineering materials with enhanced orbital textures and SOC; and device-level exploration of domain-boundary routing and polarization-controlled current logic.

- Many-body and excitonic effects are not explicitly included; computations rely on DFT electronic structures (with scissor-like considerations referenced) and are expected to be qualitatively reliable for ultrathin 2D systems but may differ quantitatively near resonances. - A constant phenomenological relaxation time τ=0.2 ps is used; real τ is band-, k-, and condition-dependent, impacting injection-like currents’ magnitudes. - Instantaneous (nonsequential) contributions from diagrammatic expansions are neglected, typically small in time-reversal-symmetric bulk photogalvanics. - Orbital angular momentum Lz is not strictly conserved; a projected operator approach maintains effective conservation, yielding qualitatively similar results, but exact classification of orbital current remains theoretically subtle. - Detection of orbital currents is challenging due to orbital hybridization; proposals rely on interfacial SOC conversion to spin signals. - Very strong SOC can alter band dispersions, potentially breaking linear BSPV–SOC scaling; material-dependent details may vary. - Multi-domain ferroelectric samples may complicate macroscopic current readout due to local coordinate rotations at domain boundaries, though this can be leveraged for current filtering.