Axial Chiral Phonon Skew Scattering

Updated 1 August 2025

Axial chiral phonon skew scattering is defined by phonons with nonzero angular momentum causing asymmetric scattering that leads to transverse (Hall-like) responses.
The phenomenon is explained via mechanisms such as anharmonicity-driven modulation of spin–orbit coupling, impurity-induced interference, and Berry curvature effects.
The analysis details material platforms, symmetry constraints, and experimental strategies like Raman and RIXS for detecting chiral phonon-induced skew scattering in quantum materials.

Axial chiral phonon skew scattering refers to the phenomenon wherein phonons possessing well-defined angular momentum (i.e., chiral phonons) induce asymmetric (skewed) scattering of carriers (electrons, spins, or other phonons) or are themselves skew-scattered, resulting in the emergence of transverse (Hall-like) responses in materials. This effect is fundamentally linked to the interplay between crystal symmetry (especially lack of inversion), the quantum numbers of the phonons (angular momentum, pseudo-angular momentum, helicity), and various microscopic mechanisms such as electron-phonon coupling, spin fluctuations, or orbital magnetization. Its manifestations span the spin Hall effect, phonon Hall effects, and a variety of nonreciprocal transport and optical phenomena.

1. Fundamental Mechanisms of Axial Chiral Phonon Skew Scattering

The foundation of axial chiral phonon skew scattering is the existence of phonon modes with nonzero angular momentum—a direct consequence of chiral symmetry in the lattice. In such systems, phonons are not restricted to linearly polarized motions but can exhibit circular or elliptical polarization, yielding mechanical angular momentum (AM) and pseudo-angular momentum (PAM) defined by the eigenvalue under rotational symmetry operations (Zhang et al., 28 Mar 2025, Ishito et al., 2022, Ishito et al., 2021). The microscopic mechanisms for skew scattering can be classified as follows:

Phonon Skew Scattering via Anharmonicity: In Rashba-like and metallic systems, skew scattering arises due to the dynamical modulation of spin–orbit coupling by phonon anharmonicity, leading to a transverse spin current (i.e., spin Hall effect) (Gorini et al., 2015). The core process involves three-phonon terms (characterized by an anharmonicity parameter Λ) leading to a temperature-independent contribution to the spin Hall conductivity for $T > T_D$ (Debye temperature).
Impurity and Defect-Induced Skew Scattering: Extrinsic skew scattering can be induced when phononic Hall viscosity (often generated via coupling to electrons or broken time-reversal symmetry) combines with impurity potentials possessing channels of opposite parity. Interference between these channels yields an antisymmetric part in the scattering amplitude, responsible for generating skew scattering and thus a thermal Hall current (Guo et al., 2021).
Spin/Orbital Texture–Induced Skew Scattering: In Mott insulators and correlated systems, the scalar spin chirality $\chi = \mathbf{S}_i \cdot (\mathbf{S}_j \times \mathbf{S}_k)$ produces a Berry-phase correction in the nuclear (phonon) Hamiltonian, acting as an emergent “magnetic” field that couples to the generalized phonon angular momentum and results in a ‘Raman-like’ interaction. This, in turn, drives skew scattering of circularly polarized phonon modes (Oh et al., 3 Aug 2024).
Orbital Magnetization–Mediated Skew Scattering: In nonmagnetic insulators and Chern insulators, the orbital motion of electrons generates an emergent Berry curvature which couples to the phonon angular momentum, leading to an orbital magnetization–phonon coupling ( $V = -\sum_i b_i^z \cdot L_i/M_i$ ) that underlies a thermal Hall effect via phonon skew scattering (Oh, 30 Jul 2025).

2. Symmetry, Quantum Numbers, and the Nature of Chiral Phonons

The existence and form of chiral phonons, and thus the possibility for axial chiral skew scattering, are tightly dictated by the crystalline symmetry. In chiral (noncentrosymmetric) crystals, phonons can carry well-defined angular momentum or PAM, with the handedness defined relative to the principal rotation axis (Chen et al., 2021, Zhang et al., 28 Mar 2025, Yang et al., 16 Jun 2025):

Angular Momentum (AM): Defined via $l_{a,\nu}(\mathbf{q}) = \sum_k \hbar\,\mathrm{Im}[ \epsilon_{k,\nu}^*(\mathbf{q}) \cdot (M_a \epsilon_{k,\nu}(\mathbf{q})) ]$ .
Pseudo-Angular Momentum (PAM): Associated with the eigenvalue acquired under rotation operations (e.g., $C_n$ symmetry), crucial at high-symmetry points.
Helicity: The projection of the phonon angular momentum onto its propagation direction, $h_{\nu}(\mathbf{q}) = (\mathbf{q} \cdot \mathbf{l}_{\nu}(\mathbf{q}))/|\mathbf{q}|$ .

Phonons in chiral crystals (Type II in the classification of (Yang et al., 16 Jun 2025)) generically possess nonzero AM on general $\mathbf{q}$ -points as an s-wave–like helicity pattern, whereas crystals with improper operations (Type III) exhibit a higher-order helicity texture. By contrast, in centrosymmetric (Type I) crystals, the combined effect of inversion and time-reversal forces all phonon angular momenta to vanish identically, precluding the possibility of chiral phonon–mediated skew scattering.

The labeling of phonon modes by crystal momentum and CAM is formalized for systems with symmetry lines (e.g., chiral helical crystals with line groups such as $L3_1$ ), resulting in strict conservation rules governing both indices in phonon–carrier or phonon–phonon interactions (Tateishi et al., 18 Mar 2025).

3. Theoretical Models and Quantitative Frameworks

Quantitative theory of axial chiral phonon skew scattering employs several key formulations for the computation of conductivities and scattering rates:

Spin Hall Conductivity via Phonon Skew Scattering: For $T > T_D$ ,

$\sigma_{ss}^{(sH)} = -3\left(\frac{\lambda k_F}{4}\right)^2 \frac{e n}{m} \frac{\hbar \Lambda}{g}$

with all symbols as defined in (Gorini et al., 2015). The $T$ -independence arises from the thermal averaging of the anharmonic phonon field.

Thermal Hall Conductivity from Impurity Interference:

$\kappa_{yx} \sim \frac{1}{n_i} T^{d+2} \quad \text{(for %%%%10%%%%)}$

where $n_i$ is the impurity density, $d$ the system’s dimension, and $T_\mathrm{imp}$ the temperature threshold set by scattering channel strengths (Guo et al., 2021).

Emergent Berry Curvature–Induced Phonon Skew Scattering:

$H_R = (const) \cdot \chi \cdot \frac{L_2}{M}, \quad L_2 = U_{2x} P_{2y} - U_{2y} P_{2x}$

The resulting antisymmetric scattering rates appear in the Boltzmann equation and lead to

$\kappa_{yx} \propto \tau^2 T^3, \quad \theta_H \propto \tau T$

with $\theta_H$ the thermal Hall angle, $\tau$ the phonon relaxation time (Oh et al., 3 Aug 2024).

Symmetry Classification and Screening:

Analyses of the velocity–angular momentum tensor $\mathbf{v}(\mathbf{q}) \otimes \mathbf{J}^{\text{ph}}(\mathbf{q})$ permit direct inference of which tensor elements in the thermomagnetic response are allowed, dictating detection strategies and material selection (Yang et al., 16 Jun 2025).

4. Experimental Manifestations and Observable Consequences

Chiral phonon skew scattering is associated with robust and, in some materials, surprisingly large transverse responses in charge-neutral and spin systems:

Spin Hall Effects in Metals and Rashba Systems: The temperature independence of the skew scattering term at $T > T_D$ is critical for interpreting spin Hall angle measurements. Linear $T$ -dependence in $\theta^{(sH)}$ at high $T$ can signal extrinsic dominance, contingent on the intrinsic spin splitting $\Delta$ being less than $k_B T$ (Gorini et al., 2015).
Phonon Hall Effects in Insulators, Mott Systems, and Topological Materials: Skew scattering by spin chirality, orbital magnetization, or impurity-induced Hall viscosity can generate a phonon-driven thermal Hall angle on the order of $10^{-3}$ – $10^{-2}$ , in some cases comparable to or exceeding magnonic contributions (Oh et al., 3 Aug 2024, Oh, 30 Jul 2025, Yang et al., 16 Jun 2025).
Raman and RIXS Techniques: Conservation laws of PAM and AM are evident in circularly polarized Raman experiments, providing benchmarks for chiral phonon detection and permitting assignment of absolute crystal handedness (Ishito et al., 2022, Ishito et al., 2021, Ueda et al., 2023).
Control via Nonlinear Phonon Rectification: The light–induced breaking of mirror and inversion symmetries in achiral crystals, leveraging nonlinear interaction between driven IR-active phonons and silent geometric chiral phonons, enables transient creation and switching of chiral enantiomers through polarization selectivity (Romao et al., 2023). This directly links controllable geometric chirality to downstream skew scattering and transport effects.

5. Materials Platforms and Material Engineering

Chiral phonon execution and skew scattering can be tailored by material choice and symmetry engineering:

Material Classes: Systematic symmetry-based high-throughput searches have identified Type II (pure rotation, noncentrosymmetric) and Type III (improper rotation, no inversion) crystals as hosting possible axial chiral phonon modes (Yang et al., 16 Jun 2025).
Doped Laves-Phase Systems: Substitutional doping in compounds such as KRbBi $_4$ and RbCsBi $_4$ breaks inversion symmetry, lifting cancellation of atomic circular polarization, and enables net nonzero PAM essential for observing and exploiting phonon Hall effects and skew scattering (Basak et al., 2022).
Layered and Reduced-Dimensional Systems: Chiral phonon skew scattering plays a key role in relaxation and valley depolarization processes in monolayer transition metal dichalcogenides after valley-polarized photoexcitation; ultrafast phonon-diffuse scattering provides direct access to nonequilibrium chiral phonon populations (Britt et al., 2023).
Helical and Screw–Symmetry Systems: In chiral helical crystals with line-group symmetry (e.g., Te, in which $C_3$ and translation along c occurs), the explicit conservation of both linear ( $q$ ) and angular ( $m$ ) momentum at the electron–phonon vertex ensures that axial chiral phonon skew scattering is sharply quantized and symmetry-protected (Tateishi et al., 18 Mar 2025).

6. Theoretical and Experimental Challenges, Open Problems, and Directions

Identification and exploitation of axial chiral phonon skew scattering require addressing several conceptual and experimental issues:

AM vs. PAM: Determining true phonon angular momentum experimentally is challenging, as PAM is manifest only at high-symmetry points, and there is often no simple mapping to AM. In complex materials, hybridization of chiral and nonchiral modes further complicates unambiguous assignment (Zhang et al., 28 Mar 2025).
Symmetry Constraints and Mapping: A universal symmetry-based framework, provided in (Yang et al., 16 Jun 2025), enables material screening and classification, explicitly linking allowed phonon magnetization and skew-scattering responses to space-group symmetry.
Spectroscopy and Imaging: Phase-sensitive Raman, momentum-resolved RIXS with circular polarization, and ultrafast X-ray/electron diffuse scattering are frontier methods for resolving chiral phonon populations and their dynamics at atomic or ultrafast temporal scales (Ueda et al., 2023, Ishito et al., 2022, Britt et al., 2023).
Control of Chiral Populations: All-optical methods exploiting nonlinear phonon coupling can not only generate geometric chirality but also allow deterministic switching between enantiomers, potentially allowing for real-time chiral phonon-based devices (Romao et al., 2023).
Open Theoretical Issues: Disentangling orbital from spin contributions in skew scattering, understanding the interplay with topological magnon bands or Chern insulator phases, and quantifying the impact of time-reversal and inversion breaking present major avenues for further exploration (Oh, 30 Jul 2025, Oh et al., 3 Aug 2024).

7. Outlook and Applications

The field has matured toward systematic identification (as with the Chiral Phonon Materials Database (Yang et al., 16 Jun 2025)), predictable modeling, and precise detection of chiral phonon–induced skew scattering. Prospective applications include:

Nonreciprocal Thermal Transport: Chiral phonon skew scattering can be exploited for phonon Hall effect–based thermal diodes or rectifiers.
Spin-Phonon Conversion and Spintronics: Chiral phonons may mediate or amplify CISS effects and enable phonon-induced spin polarization transfer (Tateishi et al., 18 Mar 2025, Ishito et al., 2021).
Metamaterial and Valleytronic Devices: Monolayer materials show valley-locked chiral phonon populations, allowing for new information storage and manipulation paradigms (Britt et al., 2023).
Chiral Optoelectronics: Geometric chirality induction and chiral phonon–optical responses open platforms for gyrotropic or chiroptical devices (Romao et al., 2023).

As ongoing theoretical advances clarify the symmetry and microscopic rules for chiral phonon generation and scattering, and as spectroscopic techniques become more refined, axial chiral phonon skew scattering stands at the nexus of condensed matter, spintronics, phonon engineering, and quantum materials research.