Momentum–Spin-Locked Carriers in Quantum Materials

Updated 1 September 2025

Momentum–spin–locked carriers are quasiparticles defined by an intrinsic locking of spin orientation to momentum, enabling robust, unidirectional transport and protection against backscattering.
They manifest in diverse platforms such as topological insulators, Rashba interfaces, and photonic systems, with experimental evidence from spin valves and nonlocal electrical measurements.
Theoretical models using effective Hamiltonians, topological invariants, and response functions provide key insights for designing spintronic and photonic devices.

Momentum–spin–locked carriers are quasiparticles whose spin (or pseudospin, polarization, or angular momentum) is intrinsically locked to their momentum due to fundamental symmetry and microscopic mechanisms. This phenomenon underpins electronic transport in topological insulators, ultrafast spintronic responses in Rashba systems and antiferromagnets, robust optical effects in photonic and plasmonic media, and strongly chiral light–matter interactions in hybrid and quantum systems. The key feature is that for each carrier, the spin orientation is not independent: it is set by the carrier's momentum vector, often enforcing protection against certain scattering processes and enabling directional charge or spin flow.

1. Microscopic Mechanisms of Spin–Momentum Locking

The canonical examples of momentum–spin–locked carriers arise in topological insulators (TIs), Rashba interfaces, antiferromagnets, and photonic systems:

Topological Insulators: 3D TIs such as Bi $_2$ Se $_3$ host topological surface states (TSS) in which the in-plane spin $\boldsymbol{\sigma}$ of an electron is locked perpendicular to its momentum $\boldsymbol{k}_{||}$ , according to $\boldsymbol{\sigma} \propto \hat{n} \times \boldsymbol{k}$ , with $\hat{n}$ the surface normal. Reversal of $\boldsymbol{k}$ reverses $\boldsymbol{\sigma}$ (Tian et al., 2014), enforcing helical (spin-textured) currents and strong suppression of elastic backscattering.
Rashba Surfaces: At surfaces and interfaces with strong spin–orbit coupling and broken inversion symmetry, as in Sb films, the Rashba effect leads to split bands with helical spin–momentum textures. The effective Hamiltonian $H_R = \alpha_R (\hat{\sigma} \times \boldsymbol{k})\cdot\hat{z}$ describes spin–momentum locking, which forms the basis for direct and inverse Rashba–Edelstein effects in spintronics (Abrão et al., 23 Apr 2024).
Collinear Antiferromagnets and Altermagnets: Nontrivial momentum-dependent spin splitting may also arise from local anisotropic (electric) crystal fields, even in the absence of net magnetization or strong relativistic effects. In altermagnets, the spin–group symmetry allows for robust, even-integer winding of the spin texture in momentum space. In 2D antiferromagnetic Weyl semimetals, such as monolayer CrO, giant momentum-dependent spin splittings occur due to magnetic symmetry (Chen et al., 2021, Šmejkal et al., 2021).
Magnons in Noncollinear Antiferromagnets: Spin–momentum locking can generalize to magnon excitations, leading to complex spin textures in momentum space. The Poincaré–Hopf theorem constrains the sum of winding numbers (vortices) of the magnon spin textures over the Brillouin zone to vanish, resulting in exotic vortex structures not seen in electronic TIs (e.g., $Q = -2$ vs $Q = +1$ in TIs) (Okuma, 2017).
Optical and Photonic Systems: In electromagnetic fields, especially evanescent waves and surface modes (e.g., in fibers, plasmonic interfaces, and metasurfaces), the transverse spin angular momentum (SAM) is locked to the momentum direction due to intrinsic dispersion relations and causality requirements (e.g., $\mathbf{S}_t \propto \hat{n} \times \mathbf{p}$ ). This is universal for evanescent waves, plasmon modes, and photonic topological lattices (Mechelen et al., 2015, Kalhor et al., 2015, Shi et al., 2022, Qian et al., 22 Jul 2025).

2. Mathematical Frameworks and Topological Constraints

A variety of theoretical approaches quantify and classify spin–momentum locking:

Effective Hamiltonians and Spin–Group Theory: In TIs and Rashba interfaces, effective Hamiltonians with momentum–spin coupling terms (e.g., $H_\mathrm{SO} = \alpha (\boldsymbol{\sigma} \times \boldsymbol{k})\cdot\hat{n}$ ) describe the locking. In altermagnets, spin–group symmetries involving decoupled spin and crystal spaces yield distinct momentum-dependent splitting with even-integer winding (Šmejkal et al., 2021).
Poincaré–Hopf Index Theorem: For magnon bands, the Poincaré–Hopf theorem applies to the spin vector field $S_{\boldsymbol{k},\alpha}$ across the Brillouin zone ( $\mathbb{T}^2$ ), enforcing the sum rule $\sum_i Q_i = 0$ on winding numbers ( $Q_i$ ) at singularities, leading to compensation of exotic spin vortices in the band structure (Okuma, 2017).
Response Theory and Chern–Simons Terms: In systems with commuting pseudospins (spin–momentum locking with preserved conservation), the mixed spin–momentum quadrupole moment in Weyl semimetals underpins a bulk Chern–Simons response term, facilitating the cancellation of surface anomalies and giving rise to a giant spin Hall effect (Hwang et al., 2023).
Dispersive Maxwellian Equations: For surface EM waves, dispersive materials require extended Maxwell-like equations for momentum density and SAM, revealing that while the transverse spin always locks to momentum (via right- or left-hand rules depending on material dispersion), an extraordinary longitudinal (coupling-induced) spin may arise (Shi et al., 2022).

3. Experimental Manifestations and Observables

Momentum–spin–locked carriers have been detected through diverse experimental modalities:

Spin Valves and Magnetotransport: In TI-based spin-valve devices, the measured magnetoresistance exhibits a polarity that is reversed by changing current direction, a direct signature of spin–momentum locking. The asymmetry and its dependence on current and field confirm spin-polarized, momentum–spin–locked currents (Tian et al., 2014).
Nonlocal Electrical Probes: By employing local and nonlocal configurations with spin-sensitive ferromagnetic contacts (e.g., Co/Al $_2$ O $_3$ ), TIs reveal spin-momentum locked surface state currents, distinguishable from bulk contributions. Temperature dependence further separates surface and bulk effects (Jafarpisheh et al., 2019).
Spin–Photon and Spin–Magnon Interactions: Directional photocurrents are generated in integrated TI–photonic waveguide devices via the CPGE mechanism, mapping the momentum-locked SAM of photons to a spin-polarized electronic current (Luo et al., 2017). NV centers coupled to ferromagnetic nanowires can drive unidirectional magnon excitation and entanglement through their spin–momentum locked stray magnetic field (Xue et al., 12 May 2025).
Spin–Momentum-locked Optical Forces: Chiral and achiral particles placed in evanescent or plasmonic fields experience lateral forces determined by the transverse spin of the near field, with the directionality set by the momentum–spin locking of the electromagnetic field (Kalhor et al., 2015).
Unidirectional Perfect Absorption: In YIG–SSPP hybrid devices, chiral photon–magnon coupling via spin–momentum locked waveguide modes enables unidirectional perfect absorption due to selective coupling with matching transverse SAM, achievable at a critical coupling condition (Qian et al., 22 Jul 2025).

4. Material Realizations and Tunability

The robustness and flexibility of spin–momentum locking hinge on material structure, symmetry, and external controls:

Topological and Rashba Systems: Spin–momentum locking is maximized at the surface of well-characterized TIs (Bi $_2$ Se $_3$ , BSTS), Rashba metals and 2DEGs (e.g., Sb, BiTeI), and at oxide interfaces. The magnitude of locking and spin splitting is tunable by electric fields, mechanical strain, or alloying (Tian et al., 2014, Abrão et al., 23 Apr 2024).
Antiferromagnetic and Altermagnetic Materials: Collinear antiferromagnets (monolayer CrO) and altermagnets (KRu $_4$ O $_8$ , CrSb, La $_2$ CuO $_4$ ) exhibit large spin splitting and even-integer winding textures, enabling high-speed, robust, and stray-field–free spintronic functionalities (Chen et al., 2021, Šmejkal et al., 2021).
Photonic and Plasmonic Architectures: Spin–momentum locking is engineered through symmetry in metasurfaces and SSPP waveguides, and by tailoring the dispersion and interface geometry in photonic and plasmonic lattices (Revah et al., 2018, Shi et al., 2022, Qian et al., 22 Jul 2025).
Hybrid and Quantum Optics Platforms: The combination of chiral excitations (from, e.g., chiral molecules on TMDs, or engineered NV–magnon interactions) extends spin–momentum locking into valleytronics, quantum communication, and robust on-chip entanglement (Bhattacharya, 2021, Xue et al., 12 May 2025).

5. Theoretical and Practical Implications

Momentum–spin–locked carriers give rise to unique topological, transport, and optical behaviors:

Suppression of Backscattering and Topological Protection: In electronic TIs, backscattering by nonmagnetic disorder is forbidden due to time-reversal symmetry, enabling nearly dissipationless channels and topologically protected transport.
Charge–Spin Current Interconversion: In Rashba and TI systems, the direct and inverse Edelstein effects convert charge currents to spin accumulations and vice versa, enabling efficient spintronics without magnetic elements (Abrão et al., 23 Apr 2024, Sayed et al., 2017).
Giant and Directional Spin Hall Effects: The mixed spin–momentum quadrupole (in Weyl semimetals and CSR phases) enables bulk spin Hall currents proportional to the separation of Weyl nodes in momentum space, with no need for strong spin–orbit coupling (Hwang et al., 2023).
Optical Manipulation, Routing, and Sensing: Spin–momentum locked modes in photonic waveguides and metasurfaces underpin nonreciprocal and spin-controlled routers, unidirectional perfect absorbers, and enhanced chiral sensing in nanophotonic devices (Qian et al., 22 Jul 2025, Revah et al., 2018).
Quantum Information and Directional Entanglement: Chiral, momentum–spin–locked fields enable unidirectional magnon-mediated entanglement (e.g., NV centers exchanging virtual magnons with directionally constrained coupling), forming the basis of nonreciprocal quantum isolators (Xue et al., 12 May 2025).

6. Extensions, Limitations, and Future Directions

Material-Locked Spin and Broken Spin–Momentum Locking: In gyrotropic or gyromagnetic media, the photonic spin can be locked to the material bias rather than momentum, breaking conventional spin–momentum locking and giving rise to nonreciprocal propagation or spin-crossover phenomena (Sen et al., 2021).
Anomalies and Bulk–Surface Correspondence: Surface theories with idealized spin–momentum locking (e.g., conserved pseudospins) must be realized as boundary modes of a higher-dimensional bulk to preserve global conservation laws, bringing anomaly inflow and mixed topological responses to the forefront (Hwang et al., 2023).
Chirality Engineering and Robustness Against Scattering: The fine structure of momentum–spin–locked states may be enhanced or suppressed by substrate effects (e.g., chiral adsorbates in MoS $_2$ improve valley polarization by stabilizing in-plane magnetic fields) or by the design of nanostructure geometry for unidirectional absorption (Bhattacharya, 2021, Qian et al., 22 Jul 2025).
Interaction and Dissipation Effects: The persistence and efficiency of spin–momentum locking in practical devices depend on temperature, bulk–surface coupling, and extrinsic scattering. Many applications still require low-temperature operation to fully suppress bulk conduction or dephasing (Jafarpisheh et al., 2019, Tian et al., 2014).
Potential for New Quantum and Topological Phases: Novel classes of matter—including high-temperature antiferromagnets, altermagnets, and quantum photonic lattices—offer expanded platforms for robust, topological, and chiral spin control, with promise for scalable quantum information and ultrafast spintronic networks (Chen et al., 2021, Šmejkal et al., 2021, Shi et al., 2022).

Momentum–spin–locked carriers thus represent a unifying principle underlying a wide range of phenomena in quantum materials and photonic systems, with rigorous microscopic, topological, and device-level consequences. Their manifestations are governed by symmetry, band topology, and engineered interfaces, and they enable robust, directionally controlled charge, spin, or quantum information transport across diverse platforms.