Chiral-Phonon Assisted Spin Current Model

• The chiral-phonon-assisted spin current model is a mechanism where lattice vibrations with circular polarization transfer angular momentum to electrons to generate spin currents.
• It employs external drives like electric fields or temperature gradients to create a helicity imbalance in phonons, yielding effective Zeeman fields and spin splitting in various systems.
• Key predictions include quadratic low-field scaling, nonreciprocal behavior, and temperature-dependent peaks near phase transitions, offering new avenues for spin transport control.

The chiral-phonon-assisted spin current model is a class of microscopic transport theories in which nonequilibrium chiral phonons transfer angular momentum to electronic spins and thereby generate spin current or spin accumulation. In these formulations, phonons in chiral crystals possess definite circular polarization and carry angular momentum; when their populations are driven out of equilibrium by an electric field or a temperature gradient, they act either as an effective Zeeman field in the electronic sector or as a spin-flip channel mediated by lattice microrotation. The version formulated for chiral-structure superconductors explains electric-field-induced spin transport that is not captured by the conventional Edelstein effect, predicting a bulk spin current along the screw axis with quadratic low-field scaling, nonreciprocity, and a temperature maximum near the superconducting transition (Yao et al., 2024). Related constructions extend the same conversion principle to chiral insulator-normal metal interfaces, nonmagnetic chiral crystals, halide perovskites, DNA, and first-principles descriptions of chirality-induced spin selectivity (CISS) (Funato et al., 2024, Li et al., 2021, Gupta et al., 5 Aug 2025).

1. Conceptual basis: chiral phonons, angular momentum, and spin conversion

A chiral phonon is a lattice vibrational mode with circular polarization and a definite handedness. In the formulations considered here, such modes arise in crystals lacking inversion, mirror, or roto-reflection symmetries, and they carry angular momentum that can be represented either through a branch helicity label or through a phonon angular-momentum operator. In one compact notation, the phonon angular momentum is written as

$$L_{\rm ph}^z=\hbar\sum_{\mathbf q,\lambda}\lambda\,a_{\mathbf q\lambda}^\dagger a_{\mathbf q\lambda},$$

with $\lambda=\pm$ denoting opposite circular polarizations (Yao et al., 2024, Nishimura et al., 29 May 2025).

A complementary continuum description replaces the angular-momentum language by lattice microrotation or vorticity. In that representation, the local rotational motion is

$$\boldsymbol\Omega(\mathbf r,t)=\nabla\times \dot{\mathbf u}(\mathbf r,t),$$

so that a chiral phonon carries a finite rotational field which couples to electron spin via spin-rotation or spin-vorticity coupling (Funato et al., 2024, Nishimura et al., 29 May 2025). This reformulation is especially important for interface problems, where the relevant observable is the spin current injected into an adjacent normal metal.

The essential mechanism is the same across bulk and interface settings. A nonequilibrium imbalance between opposite phonon helicities produces a net phonon angular momentum or microrotation. That imbalance then enters the electronic sector through an electron-phonon term that is odd under chirality reversal, so the induced spin response changes sign between enantiomers. In the achiral limit, the mechanism disappears: linearly polarized phonons do not provide the same angular-momentum transfer channel, and an equivalent spin-polarization mechanism does not arise (Fransson, 2022).

2. Minimal superconducting formulation

The best-defined electric-field-driven realization was introduced for an $s$-wave bulk superconductor with broken inversion symmetry and an external electric field $\mathcal E\parallel \hat z$, where $\hat z$ is the screw axis. In Nambu-spinor notation,

$$\Psi_{\mathbf k}^\dagger=(c_{\mathbf k,\uparrow}^\dagger,\;c_{\mathbf k,\downarrow}^\dagger,\;c_{-\mathbf k,\uparrow},\;c_{-\mathbf k,\downarrow}),$$

the mean-field Bogoliubov-de Gennes Hamiltonian is

$$H=\frac12\sum_{\mathbf k}\Psi_{\mathbf k}^\dagger \mathcal H_{\rm BdG}(\mathbf k)\Psi_{\mathbf k},$$

with

$$\mathcal H_{\rm BdG}(\mathbf k)= \begin{pmatrix} \xi_{\mathbf k+\eta \mathcal E} & 0 & 0 & \Delta \ 0 & \xi_{\mathbf k-\eta \mathcal E} & -\Delta & 0 \ 0 & -\Delta & -\xi_{-\mathbf k-\eta \mathcal E} & 0 \ \Delta & 0 & 0 & -\xi_{-\mathbf k+\eta \mathcal E} \end{pmatrix},$$

where $\xi_{\mathbf k}=\hbar^2k^2/2m-\mu$, $\lambda=\pm$0 is the $\lambda=\pm$1-wave gap, and the shifts $\lambda=\pm$2 encode an effective Zeeman field generated by chiral phonons (Yao et al., 2024).

Microscopically, the model assumes a pair of degenerate transverse optical phonon branches with helicities $\lambda=\pm$3. Their angular momentum is

$\lambda=\pm$4

and the leading electron-phonon coupling takes the form

$\lambda=\pm$5

Because the coupling changes sign under mirror, a chiral lattice allows $\lambda=\pm$6, so an electric-field-induced helicity imbalance generates a nonzero $\lambda=\pm$7 (Yao et al., 2024).

The phonon nonequilibrium is treated with a Boltzmann equation in the relaxation-time approximation: $\lambda=\pm$8 which yields

$\lambda=\pm$9

That phonon angular momentum generates an effective Zeeman field

$$\boldsymbol\Omega(\mathbf r,t)=\nabla\times \dot{\mathbf u}(\mathbf r,t),$$0

The sign of $$\boldsymbol\Omega(\mathbf r,t)=\nabla\times \dot{\mathbf u}(\mathbf r,t),$$1 flips under mirror, consistent with opposite enantiomers of the crystal (Yao et al., 2024).

3. Quasiparticle spin splitting and spin-current response

Diagonalization of the superconducting Hamiltonian produces spin-split Bogoliubov quasiparticle branches,

$$\boldsymbol\Omega(\mathbf r,t)=\nabla\times \dot{\mathbf u}(\mathbf r,t),$$2

The nonequilibrium quasiparticle distribution is then written as

$$\boldsymbol\Omega(\mathbf r,t)=\nabla\times \dot{\mathbf u}(\mathbf r,t),$$3

with

$$\boldsymbol\Omega(\mathbf r,t)=\nabla\times \dot{\mathbf u}(\mathbf r,t),$$4

where

$$\boldsymbol\Omega(\mathbf r,t)=\nabla\times \dot{\mathbf u}(\mathbf r,t),$$5

The spin current along the screw axis is defined as

$$\boldsymbol\Omega(\mathbf r,t)=\nabla\times \dot{\mathbf u}(\mathbf r,t),$$6

Expanding for small $$\boldsymbol\Omega(\mathbf r,t)=\nabla\times \dot{\mathbf u}(\mathbf r,t),$$7 gives the central low-field result,

$$\boldsymbol\Omega(\mathbf r,t)=\nabla\times \dot{\mathbf u}(\mathbf r,t),$$8

so the response is even in the electric field and therefore nonreciprocal in the sense that $$\boldsymbol\Omega(\mathbf r,t)=\nabla\times \dot{\mathbf u}(\mathbf r,t),$$9 (Yao et al., 2024).

This quadratic scaling is the key signature of the superconducting model. The electric field has a dual role: it first drives the chiral phonons out of equilibrium, and the resulting phonon angular momentum then spin-splits the Bogoliubov spectrum. Spin current generation is therefore second order in the external field at low fields, rather than the linear-in-field response characteristic of conventional Edelstein-type spin polarization.

The same logic recurs in thermal models. In the chiral phonon activated spin Seebeck effect (CPASS), nonequilibrium chiral phonons under $s$0 generate an effective spin splitting $s$1, and the resulting spin accumulation scales as $s$2 (Li et al., 2021). Across these variants, the model class is defined less by a single Hamiltonian than by a common sequence: drive $s$3 phonon helicity imbalance $s$4 angular-momentum transfer $s$5 spin-selective transport.

4. Predicted signatures in chiral-structure superconductors

The superconducting theory was motivated by the experiment of R. Nakajima et al., which reported a pair of oppositely polarized spins under an alternating electric current in a superconductor with a chiral structure. The theory explicitly states that these behaviors cannot be explained by the conventional Edelstein effect and require a new mechanism (Yao et al., 2024). In that context, the chiral-phonon-assisted model is not a refinement of Edelstein physics but a distinct route to spin transport based on inversion breaking and electron-phonon conversion of phonon angular momentum into an effective Zeeman field.

A second defining prediction is the temperature dependence. Using typical metal parameters $s$6, cutoff $s$7, $s$8, $s$9, the superconducting gap $\mathcal E\parallel \hat z$0, and a phenomenological $\mathcal E\parallel \hat z$1 with $\mathcal E\parallel \hat z$2, the calculated $\mathcal E\parallel \hat z$3 is strongly nonmonotonic below $\mathcal E\parallel \hat z$4 and peaks near $\mathcal E\parallel \hat z$5 (Yao et al., 2024). The stated reason is twofold: as $\mathcal E\parallel \hat z$6 shrinks, more quasiparticles become available, while $\mathcal E\parallel \hat z$7 remains appreciable; above $\mathcal E\parallel \hat z$8, both tendencies reverse.

The same parameter set gives an order-of-magnitude estimate for the induced effective field and the spin current. At $\mathcal E\parallel \hat z$9 and $\hat z$0, one has $\hat z$1, corresponding to $\hat z$2, and the predicted spin current is $\hat z$3, described as well within reach of present spin-detection schemes (Yao et al., 2024).

The distinction from more conventional current-induced spin effects is reinforced by later first-principles work on trigonal Se, which identifies a key difference between CISS and the colinear Edelstein effect in spin-dependent electron-phonon scatterings. In that framework, the spin polarization increases with device length, which is presented as a unique feature in CISS and not a prediction of the relaxation-time description of the colinear Edelstein effect (Gupta et al., 5 Aug 2025). This does not duplicate the superconducting BdG construction, but it places the superconducting model within a broader trend: chirality-dependent electron-phonon processes produce transport signatures that are not reducible to standard Edelstein phenomenology.

5. Extensions to interfaces, semiconductors, and molecular systems

At chiral-insulator/normal-metal interfaces, the same mechanism is reformulated as phonon-spin conversion by spin-microrotation coupling. One microscopic Hamiltonian contains a normal metal, a chiral-insulator phonon sector, spin-conserving electron tunneling, and a spin-microrotation coupling $\hat z$4. After perturbative elimination of the interfacial electronic states, the effective interfacial electron-phonon Hamiltonian produces a spin injection rate that depends on the nonequilibrium phonon occupation $\hat z$5, the normal-metal spin susceptibility, and the phonon circularity factor $\hat z$6 (Funato et al., 2024). A related theory incorporates heat-current continuity through the chiral insulator and the Kapitza conductance at the interface, giving a compact spin-current formula in which geometry enters via $\hat z$7, with $\hat z$8 (Nishimura et al., 29 May 2025).

A nonequilibrium Green’s function variant for a normal-metal/chiral-insulator heterostructure generalizes the interfacial problem beyond linear response. In that treatment, the spin current is controlled by an effective interfacial spectral density $\hat z$9, and the theory predicts two nonlinear phenomena: negative differential spin Seebeck effect and spin-current rectification. The negative differential regime is attributed to competition between thermal bias and the thermally excited electron density, while the rectification asymmetry $$\Psi_{\mathbf k}^\dagger=(c_{\mathbf k,\uparrow}^\dagger,\;c_{\mathbf k,\downarrow}^\dagger,\;c_{-\mathbf k,\uparrow},\;c_{-\mathbf k,\downarrow}),$$0 is interpreted as a route to a thermally controlled spin diode (Zhang et al., 25 Apr 2026).

Bulk thermal formulations provide another major branch of the model family. The CPASS theory describes a nonmagnetic chiral material without magnetic order nor spin-orbit coupling, where nonequilibrium chiral phonons under $$\Psi_{\mathbf k}^\dagger=(c_{\mathbf k,\uparrow}^\dagger,\;c_{\mathbf k,\downarrow}^\dagger,\;c_{-\mathbf k,\uparrow},\;c_{-\mathbf k,\downarrow}),$$1 generate an effective Zeeman splitting and produce spin accumulation through both phonon-drag and band transport terms; the resulting spin accumulation quadratically increases with temperature gradient and can change sign under chemical-potential tuning (Li et al., 2021). In 2D halide perovskites, DFT plus on-the-fly machine-learning force fields confirm the presence of chiral phonons, identify low-energy inorganic phonons as the primary carriers of chirality, and motivate a spin-Seebeck response tensor $$\Psi_{\mathbf k}^\dagger=(c_{\mathbf k,\uparrow}^\dagger,\;c_{\mathbf k,\downarrow}^\dagger,\;c_{-\mathbf k,\uparrow},\;c_{-\mathbf k,\downarrow}),$$2 under $$\Psi_{\mathbf k}^\dagger=(c_{\mathbf k,\uparrow}^\dagger,\;c_{\mathbf k,\downarrow}^\dagger,\;c_{-\mathbf k,\uparrow},\;c_{-\mathbf k,\downarrow}),$$3 (Pols et al., 2024).

Molecular and disordered realizations emphasize transport geometry and incoherent hopping. For DNA, a variable-range hopping model treats electrons as moving between localized states by exchange of chiral phonons; the spin-microrotation coupling generates an electric toroidal monopole $$\Psi_{\mathbf k}^\dagger=(c_{\mathbf k,\uparrow}^\dagger,\;c_{\mathbf k,\downarrow}^\dagger,\;c_{-\mathbf k,\uparrow},\;c_{-\mathbf k,\downarrow}),$$4 in the charge-to-spin conductance, and in the one-dimensional variable-range hopping regime the spin polarization follows a universal $$\Psi_{\mathbf k}^\dagger=(c_{\mathbf k,\uparrow}^\dagger,\;c_{\mathbf k,\downarrow}^\dagger,\;c_{-\mathbf k,\uparrow},\;c_{-\mathbf k,\downarrow}),$$5 law below a crossover $$\Psi_{\mathbf k}^\dagger=(c_{\mathbf k,\uparrow}^\dagger,\;c_{\mathbf k,\downarrow}^\dagger,\;c_{-\mathbf k,\uparrow},\;c_{-\mathbf k,\downarrow}),$$6 (Sano et al., 2024). By contrast, in mixed quantum-classical simulations of chiral molecular junctions, electron-phonon coupling modifies the current-voltage characteristics but does not stabilize steady-state spin filtering: transient spin polarization appears and then decays to zero at long times, while phonons mainly enhance current at intermediate bias and suppress it at high bias (Wang et al., 10 Sep 2025). This contrast is important because it shows that chiral-phonon assistance is not, by itself, a guarantee of persistent steady-state polarization in every transport regime.

6. Scope, assumptions, and recurring points of debate

The literature does not present a single universal chiral-phonon-assisted spin current model; it presents a family of models sharing a conversion mechanism but differing in drive, geometry, and electronic sector. In superconductors the drive is an electric field and the electronic theory is BdG plus Boltzmann transport (Yao et al., 2024). In interfacial spin Seebeck problems the drive is a thermal bias and the electronic response is expressed through Keldysh, Fermi-golden-rule, or nonequilibrium Green’s function formalisms (Funato et al., 2024, Zhang et al., 25 Apr 2026). In disordered molecular systems the relevant framework is variable-range hopping or mixed quantum-classical dynamics (Sano et al., 2024, Wang et al., 10 Sep 2025). This suggests that “chiral-phonon-assisted spin current model” is best understood as a mechanism family rather than a single canonical Hamiltonian.

Several assumptions recur. Interface theories often adopt weak interfacial coupling, local tunneling, long-wavelength acoustic phonons, and relaxation-time approximations for phonons (Funato et al., 2024, Nishimura et al., 29 May 2025). The 2D halide-perovskite construction assumes a single momentum-independent phonon lifetime, a free-electron-like electronic dispersion, perturbative spin-phonon coupling, and neglects magnetoelastic back-action, multiphonon processes, and interface effects (Pols et al., 2024). The superconducting model uses a minimal $$\Psi_{\mathbf k}^\dagger=(c_{\mathbf k,\uparrow}^\dagger,\;c_{\mathbf k,\downarrow}^\dagger,\;c_{-\mathbf k,\uparrow},\;c_{-\mathbf k,\downarrow}),$$7-wave BdG Hamiltonian and a phenomenological $$\Psi_{\mathbf k}^\dagger=(c_{\mathbf k,\uparrow}^\dagger,\;c_{\mathbf k,\downarrow}^\dagger,\;c_{-\mathbf k,\uparrow},\;c_{-\mathbf k,\downarrow}),$$8 to parameterize the chiral-phonon-induced effective Zeeman field (Yao et al., 2024). These approximations delimit the present quantitative predictive range.

A recurrent debate concerns the role of spin-orbit coupling. CPASS explicitly frames the effect as possible without magnetic order nor spin-orbit coupling (Li et al., 2021). In contrast, first-principles work on trigonal Se identifies the interplay of SOC, structural chirality, and spin-dependent electron-phonon interactions as central, while also showing that orbital polarization is weakly dependent on SOC compared with spin polarization (Gupta et al., 5 Aug 2025). Another recurring issue is whether standard current-induced spin physics suffices. The superconducting formulation states that the Nakajima experiment cannot be explained by the conventional Edelstein effect (Yao et al., 2024), and the trigonal Se study argues that the length dependence characteristic of CISS originates from spin-dependent electron-phonon scattering rather than the relaxation-time form of the colinear Edelstein effect (Gupta et al., 5 Aug 2025).

The most stable conclusion across the model family is therefore narrow but robust: when a chiral lattice supports phonons with finite angular momentum, and when a nonequilibrium drive creates a handedness imbalance, the resulting phonon angular momentum can be converted into spin-selective electronic transport. The detailed observable—bulk spin current, interfacial spin injection, spin accumulation, rectification, or transient polarization—depends on the specific realization, but the chirality dependence, the absence of an achiral counterpart, and the central role of electron-phonon angular-momentum transfer remain common structural features (Fransson, 2022, Yao et al., 2024).