Valley-Polarized Spin Current

• Valley-polarized spin current is an electronic transport phenomenon where carriers are selectively filtered by both valley and spin indices in multi-valley materials.
• Generation mechanisms such as circular photogalvanic effect and electric-field tuning achieve nearly 100% polarization in systems like TMDs and silicene.
• Experimental methods and theoretical models demonstrate robust control and detection through optical, electric, and nonlinear techniques in engineered 2D systems.

A valley-polarized spin current is an electronic transport phenomenon in which the flow of carriers is simultaneously polarized in both the valley and spin degrees of freedom. In multi-valley materials—such as monolayer transition-metal dichalcogenides (TMDs), silicene, bilayer graphene, and certain engineered 2D systems—the presence of strong spin–orbit coupling and broken inversion symmetry leads to spin–valley locking, enabling control and isolation of carriers based on both spin orientation and crystal momentum valley index. The controlled generation, detection, and manipulation of valley-polarized spin currents underpins much of the emerging field of valleytronics and valley-spintronic device engineering.

1. Fundamentals: Spin–Valley Coupling and Selection Rules

In materials possessing multiple inequivalent energy extrema in momentum space ("valleys"), such as the K and K′ points in TMDs or the Dirac points in silicene and graphene derivatives, the valley index τ = ±1 serves as a pseudospin. Strong atomic spin–orbit coupling (SOC)—notably in transition-metal elements—breaks the spin degeneracy near the band edges, leading to spin–valley locking: each valley hosts a distinct spin state. For example, in monolayer WSe₂, the K valley bears s_z = +½, while K′ carries s_z = –½ (Yuan et al., 2014, Sousa et al., 2022).

The presence of large Berry curvature in each valley (with opposite sign for K and K′) generates valley-dependent optical selection rules: right-circularly polarized photons (σ⁺) couple exclusively to K, left-circularly polarized (σ⁻) to K′. As a result, σ⁺ (σ⁻) excitation selectively populates spin-up (spin-down) carriers in K (K′), producing both a valley and spin population imbalance (Yuan et al., 2014, Yu et al., 2017, Yuan et al., 2021). This dual selectivity is the microscopic origin of valley-polarized spin current generation in photo-excited 2D crystals, laying the foundation for opto-valleytronic control.

2. Generation Mechanisms of Valley-Polarized Spin Currents

2.1 Photogalvanic and Optical Control

Under circularly polarized illumination and broken inversion symmetry (via gating or structural engineering), monolayer TMDs and their analogs can generate transverse valley-polarized spin photocurrents via the circular photogalvanic effect (CPGE). In WSe₂, the CPGE current density is described by

$j(α,E_z) = J_0(E_z)\,\sin(2α)$

where $\alpha$ is the polarization rotation angle (with $\sin 2\alpha = +1$ for σ⁺, $–1$ for σ⁻), and $J_0(E_z)$ is tuned by the perpendicular electric field $E_z$. The measured photocurrent is both valley-polarized and spin-polarized up to $P_s\approx100\%$ (Yuan et al., 2014). In monolayer MoS₂, NEGF-DFT calculations confirm that photoinduced currents under σ⁺ (σ⁻) illumination are fully valley- and spin-polarized at K (K′), i.e., $P_v\to\pm1$ over the entire gate voltage window (Yu et al., 2017).

2.2 Electric Field and Disorder-Driven Schemes

Electric (gate) fields independently modulate the degree of inversion symmetry and tune the band-structure splitting, thus enabling electric control of valley-polarized spin transport. In ferromagnetic silicene, an out-of-plane field $\Delta_z$ and exchange field $M$ combine to isolate a single spin–valley sector, producing fully valley- and spin-polarized dc Hall currents. The controlled conductivity is given by

$$\sigma_{xy}^{\eta,s_z}=-\eta\,\frac{e^2}{4\pi\hbar}\times \begin{cases} \mathrm{sgn}(\Delta_{\eta,s_z}) & |\mu+s_z M|<|\Delta_{\eta,s_z}| \ \dfrac{\Delta_{\eta,s_z}}{|\mu+s_z M|} & |\mu+s_z M|>|\Delta_{\eta,s_z}| \ \end{cases}$$

and the degree of polarization jumps to $\pm1$ in the fully filtered regime (Mohammadi et al., 2015, Yokoyama, 2013).

Elastic backscattering on sharp nonmagnetic disorder in TMD nanoribbons can also yield a net valley-polarized spin current due to the momentum-space asymmetry in intervalley reflection rates. The spin-pump efficiency can reach 10–15% in practical nanoribbon geometries, and is robust to device orientation and disorder type (An et al., 2016).

2.3 Nonlinear and Floquet Regimes

Nonlinear transport, mediated by Berry curvature dipoles and enhanced by inversion-symmetry breaking and magnetic proximity, leads to second-order (quadratic) valley-polarized spin currents. In bilayer graphene devices with ferromagnetic Fe₃GeTe₂ contacts, the measured second-harmonic spin current exhibits spin-valve-like switching and persists with pronounced valley polarization due to large orbital magnetic moments (up to 30 μ_B per carrier) (Liao et al., 2024). Floquet engineering in valley-polarized metals (graphene on honeycomb lattices with staggered SOC) under circularly polarized drive can generate robust, unidirectional, spin-polarized edge currents, even in the absence of net charge flow (Luo, 2018).

3. Detection, Characterization, and Device Integration

3.1 Experimental Signatures

Valley-polarized spin currents manifest in direct transport, nonlocal spin accumulation, and transverse Hall-like responses. Suppressed Andreev reflection in semi-Dirac NM/FM/NM/superconductor junctions provides a “zero Andreev” smoking-gun signature of spin–valley filtering (Huang et al., 2023). Nonlocal Hanle experiments in strained and adatom-decorated graphene and TMDs reveal strong, gate-tunable neutral currents with both spin and valley polarization, and the typical Hanle resistance oscillations can be strongly suppressed when the valley Hall angle is large (Zhang et al., 2018).

Optical signatures (circular dichroism, time-resolved Kerr/Faraday rotation) directly probe the valley and spin population imbalance, while angle-resolved photoemission with spin and valley resolution can resolve the Fermi-surface topology in spin-valley half-metals (Rozhkov et al., 2017).

3.2 Device Architectures

Electrically controlled EDL transistors in WSe₂ and related TMDs, magnetic tunnel junctions utilizing valley Hall–induced torques, and engineered potential barriers in BLG and monolayer TMDs all act as reconfigurable valley-polarized spin current sources, with gate-tunable on/off ratios approaching unity (Yuan et al., 2014, Ominato et al., 2020, Maksym et al., 2019, Liao et al., 2024). Multi-terminal valley and spin filters, logic gates, MRAM concepts, and high-frequency spintronic rectification circuits are enabled by these phenomena.

A representative comparison of photogalvanic and electronic generation addressing physical observables is summarized:

Material/System	Method	Max Polarization	References
Monolayer WSe₂ (EDL device)	CPGE under σ⁺/σ⁻ light	$P_s\to 100\%$	(Yuan et al., 2014)
Monolayer MoS₂	Photoexcitation + gating	$P_v\to \pm1$	(Yu et al., 2017)
Ferromagnetic silicene	E_z, M tuning (N/F/N jct.)	$|P_v|=|P_s|=1$	(Yokoyama, 2013, Mohammadi et al., 2015)
Disordered MoS₂ ribbons	Nonmagnetic impurity pump	$\eta_s\sim0.1$	(An et al., 2016)
BLG/FGT	Second-order nonlinear spin	Valley+spin	(Liao et al., 2024)

4. Theory: Models and Polarization Quantification

Theoretical modeling spans low-energy k·p Hamiltonians and tight-binding or ab initio approaches. Key ingredients are the inclusion of spin–orbit terms that lock spin and valley, electric-field–induced inversion symmetry breaking, valley-dependent optical selection rules, and exchange or proximity interactions.

Quantitative valley and spin polarizations are defined as

$$P_v = \frac{I_K - I_{K'}}{I_K + I_{K'}}, \quad P_s = \frac{I_\uparrow - I_\downarrow}{I_\uparrow + I_\downarrow}$$

where $I_K$ and $I_{K'}$ are currents at K, K′, and $I_\uparrow$, $I_\downarrow$ are spin-up, spin-down currents. In systems exhibiting perfect spin–valley locking, $P_s = P_v$. Full polarization is realized by engineering device parameters so that all active electronic states reside in just one spin–valley sector—e.g., valley half-metallicity in doped spin-density-wave systems (Rozhkov et al., 2017), or selective filtering via staggered sublattice potentials and edge termination in quantum anomalous Hall honeycomb lattices (Liu et al., 2016).

5. Material Systems, Parameter Dependence, and Robustness

Valley-polarized spin current phenomena are reported in monolayer and bilayer TMDs (WSe₂, MoS₂, WS₂), silicene, germanene, MA₂Z₄ monolayers, and semi-Dirac, spin-density-wave, or QAH candidate platforms (Yuan et al., 2021, Mohammadi et al., 2015, Yu et al., 2017, Rozhkov et al., 2017, Maksym et al., 2019).

Performance metrics—magnitude of current density, polarization, tunability, and robustness—are governed by parameters such as the magnitude of SOC, the degree of inversion symmetry breaking (applied field), disorder strength (for disorder-driven pumps), device geometry (junction length, ribbon width), proximity-induced magnetic and valley splitting, and operational temperature. For example, room-temperature operation with $j_{\textrm{CPGE}}\sim 1-3$ nA in WSe₂ is accessible (Yuan et al., 2014); nonlocal transport with $\sim$70% valley polarization is possible in WSe₂ crossbar geometries (Sousa et al., 2022); and nonlinear valley–spin currents in BLG/FGT persist up to $T\sim200$ K (Liao et al., 2024).

Robustness against disorder, electric field, and temperature depends on the topological or symmetry protection of the spin–valley channels—topological edge states and intervalley separation enhance stability, while precise gating and contact engineering can suppress charge–spin–valley leakage channels (Liu et al., 2016, Liao et al., 2024).

6. Outlook and Future Directions

Efficient generation and modulation of valley-polarized spin currents open transformative possibilities for valley-spintronic devices—including MRAM, nonvolatile logic, frequency multipliers, and optoelectronic switches—operating at low power and potentially free from the stochastic noise of classical spintronic technologies (Liao et al., 2024, Sousa et al., 2022). Integration with CMOS electronics, exploitation of large orbital g-factors for enhanced control, and operations in nonlinear or driven regimes (Floquet engineering) are prominent future avenues.

Emerging challenges include engineering materials with even larger Berry curvatures and valley splitting, scalable fabrication of disorder-robust devices, time-domain studies of coupled spin and valley relaxation, and expanding the device concepts beyond TMDs to broader classes of 2D heterostructures and quantum anomalous Hall systems. The precise control and readout of valley-polarized spin currents remain central to the realization of practical valleytronics platforms (Hu et al., 6 Feb 2026, Sousa et al., 2022, Yuan et al., 2014, Liu et al., 2016).