Chiral Phonons: Angular Momentum & Applications

• Chiral phonons are lattice vibrational modes with a well-defined circular motion and quantized angular momentum, arising from symmetry breaking in crystals.
• They are detected using advanced techniques like helicity-resolved Raman spectroscopy, resonant inelastic X-ray scattering, and torque experiments in materials such as Te and TMDs.
• Their coupling with magnetism and electronic bands enables novel applications in spintronics, topological phononic devices, and phonon diodes.

Chiral phonons are collective lattice vibrational modes whose atomic displacements form a well-defined sense of rotation—right- or left-handed circular motion—resulting in a nonzero, quantized phonon angular momentum. This intrinsic handedness is a direct consequence of crystal symmetries: absence of inversion or certain mirror operations, or the breaking of time-reversal symmetry by magnetic order. Chiral phonons carry angular momentum and, in many cases, can couple to magnetism, electronic bands, and transport, leading to novel effects in thermal, spintronic, and topological phononic devices. Their characterization, detection, and manipulation have become a highly active research frontier across materials physics, with direct experimental realizations in chiral crystals, van der Waals moiré superlattices, and magnets with nontrivial spin order.

1. Theoretical Foundations: Angular Momentum, Symmetry, and Pseudo-Angular Momentum

A phonon mode is chiral if its eigenvector possesses nonzero angular momentum,

$$L_{\mathrm{phonon}} = \sum_{q, \nu} \hbar a_{q\nu}^\dagger (i\,\partial_q) a_{q\nu}$$

or, projection onto the polarization eigenvectors $u_{q\nu}$,

$$L_{\mathrm{phonon}} = \sum_{q,\nu} u_{q\nu}^{\dagger} (i\hbar \partial_q) u_{q\nu}$$

(Ueda et al., 4 Apr 2025). For a mode at momentum $q$, the phonon angular momentum quantifies the circularity of atomic motion.

Phonon chirality is governed by the symmetries of the lattice:

• Inversion symmetry (P): $E(J, q) = E(-J, q)$. Enforces degeneracy between opposite chiralities at a given $q$ and forbids net angular momentum for each branch unless inversion is broken.
• Time-Reversal symmetry (T): $E(J, q) = E(-J, -q)$. If both P and T are preserved, $L_z(q) = -L_z(q)$, yielding $L_z(q) = 0$ (Mishra et al., 14 Aug 2025).

In noncentrosymmetric, nonmagnetic crystals, e.g., $\alpha$-quartz (SiO$u_{q\nu}$0), tellurium (Te), and chiral perovskites, circularly polarized phonons emerge at generic $u_{q\nu}$1 via mixing of degenerate transverse branches, directly leading to modes with nonzero phonon angular momentum (Ueda et al., 2023, Ishito et al., 2022).

Pseudo-angular momentum (PAM) generalizes the concept in crystals with rotation or screw axes. In such systems, chiral phonon eigenstates acquire quantized (or, for non-symmorphic symmetries, $u_{q\nu}$2-dependent and nonquantized) PAM under discrete rotations, e.g.

$u_{q\nu}$3

(Zhang et al., 2021, Ishito et al., 2021). At high-symmetry points or lines, the quantized PAM identifies each chiral branch and enters optical selection rules.

2. Symmetry Classes, Lattice Types, and Materials Platforms

Comprehensive symmetry analysis across all space groups reveals three broad classes for chiral phonon emergence (Yang et al., 16 Jun 2025):

• Type-I (achiral): All improper rotations present (inversion, roto-inversion); $u_{q\nu}$4.
• Type-II (chiral, s-wave): Only proper rotations, no inversion or mirrors; phonon angular momentum allowed at generic $u_{q\nu}$5, transforming as an s-wave.
• Type-III (locally chiral): Improper rotations but no inversion; $u_{q\nu}$6 nonzero on nodal structures of higher-order symmetry (d-, g-, i-wave).

Materials exhibiting robust chiral phonons include chiral trigonal, hexagonal, and cubic lattices (e.g., $u_{q\nu}$7-HgS (Ishito et al., 2021); CrSi$u_{q\nu}$8 (Kusuno et al., 19 Feb 2026); chiral MOFs (Romao et al., 2023)), nonmagnetic honeycomb monolayers and moiré superlattices (e.g., TMDs (Zhang et al., 2022), twisted bilayer MoS$u_{q\nu}$9 (Suri et al., 2021)), and systems with time-reversal-breaking magnetic order (e.g., Co$$L_{\mathrm{phonon}} = \sum_{q,\nu} u_{q\nu}^{\dagger} (i\hbar \partial_q) u_{q\nu}$$0Sn$$L_{\mathrm{phonon}} = \sum_{q,\nu} u_{q\nu}^{\dagger} (i\hbar \partial_q) u_{q\nu}$$1S$$L_{\mathrm{phonon}} = \sum_{q,\nu} u_{q\nu}^{\dagger} (i\hbar \partial_q) u_{q\nu}$$2 (Che et al., 2024), bcc Fe (Weißenhofer et al., 2024), altermagnets (Okamoto et al., 29 Nov 2025)).

For chiral phonons to appear in cubic lattices, the symmetry breaking must allow nonzero pseudoscalar coupling constants arising from the stiffness tensor structure (electric toroidal monopoles), which governs the spin-1 Weyl Hamiltonian for the optical phonon triplets near $$L_{\mathrm{phonon}} = \sum_{q,\nu} u_{q\nu}^{\dagger} (i\hbar \partial_q) u_{q\nu}$$3 (Tsunetsugu et al., 19 Aug 2025).

3. Microscopic Mechanisms: Berry Curvature, Spin–Lattice Coupling, and Doping Control

The microscopic origin of angular momentum in a chiral phonon is both geometric and topological:

• Berry curvature mechanism: The self-rotation of the phonon mode is governed by off-diagonal Berry curvature in phonon Bloch space: $$L_{\mathrm{phonon}} = \sum_{q,\nu} u_{q\nu}^{\dagger} (i\hbar \partial_q) u_{q\nu}$$4 with the phonon angular momentum for branch $$L_{\mathrm{phonon}} = \sum_{q,\nu} u_{q\nu}^{\dagger} (i\hbar \partial_q) u_{q\nu}$$5,

$$L_{\mathrm{phonon}} = \sum_{q,\nu} u_{q\nu}^{\dagger} (i\hbar \partial_q) u_{q\nu}$$6

(Ueda et al., 4 Apr 2025).

• Magnon–phonon hybridization in magnetic materials: Selective Dzyaloshinskii-Moriya coupling between circularly polarized phonons and magnons yields robust angular momentum, even in inversion-symmetric magnets, and can induce strong anomalous Hall and spin Nernst responses (Weißenhofer et al., 2024, Ma et al., 2023, Okamoto et al., 29 Nov 2025).
• Symmetry breaking via doping: Atomic-selective substitution (e.g., B, N, or BN in graphyne) removes inversion, enabling nonzero phonon angular momentum that scales with dopant electron affinity and local charge transfer (Mishra et al., 14 Aug 2025).

4. Experimental Detection and Characterization Techniques

Chiral phonons have been directly measured and characterized using:

• Helicity-resolved Raman spectroscopy: Circularly polarized input and detection channels engage selection rules set by PAM conservation, resulting in optical detection of chiral phonon branches at high-symmetry points in materials such as Te, $$L_{\mathrm{phonon}} = \sum_{q,\nu} u_{q\nu}^{\dagger} (i\hbar \partial_q) u_{q\nu}$$7-HgS, CrSi$$L_{\mathrm{phonon}} = \sum_{q,\nu} u_{q\nu}^{\dagger} (i\hbar \partial_q) u_{q\nu}$$8, and Weyl semimetals (Ishito et al., 2022, Ishito et al., 2021, Kusuno et al., 19 Feb 2026, Che et al., 2024).
• Resonant inelastic X-ray scattering (RIXS): Chiral phonon modes are selectively excited by circularly polarized X-rays, with their handedness determined by the dichroism of the inelastic spectral response (Ueda et al., 2023, Okamoto et al., 29 Nov 2025).
• Thermo-mechanical torque (Einstein–de Haas) experiments: Non-equilibrium populations of chiral phonons driven by a thermal gradient induce measurable angular momentum in the lattice (Pols et al., 2024).
• Spin current and magneto-optic detection: Spin Seebeck and CISS effects in chiral materials arise from phonon–spin angular momentum transfer, observable in metallic contacts via inverse spin Hall voltage or Kerr rotation (Fransson, 2022, Pols et al., 2024).

5. Functional Consequences: Coupling, Topological Responses, and Device Potential

Chiral phonons are central to multiple emergent phenomena:

• Phononic diode effects: In chiral materials, the directionality of phonon propagation and angular momentum are locked to the lattice handedness, enabling device concepts like the “chirality diode” where energy transmission is unidirectional for a given phonon handedness (Chen et al., 2021).
• Spin–lattice angular momentum transfer: Chiral phonons can transfer quantized angular momentum to conduction electrons, inducing net spin polarization (absent for achiral modes) and supporting phonon-generated spin currents and spin filtering (CISS effect) (Fransson, 2022, Pols et al., 2024).
• Topological phononics: Chiral phonon bands host nontrivial Berry curvature, supporting Hall-like effects for phonons, with chiral phonon magnetization responding to temperature gradients (“phonon Hall,” “phonon magnetization”) (Yang et al., 16 Jun 2025, Pols et al., 2024).
• Hybrid magnon–phonon excitations: In helical or altermagnetic states, chiral phonon–magnon coupling is amplified, leading to physically observable enhancements in RIXS intensities and mode magnetization (Weißenhofer et al., 2024, Okamoto et al., 29 Nov 2025).

6. Tunability, Materials Engineering, and High-Throughput Discovery

Advanced control over chiral phonons is achievable by:

• Twist angle engineering in moiré superlattices: The breaking of $$L_{\mathrm{phonon}} = \sum_{q,\nu} u_{q\nu}^{\dagger} (i\hbar \partial_q) u_{q\nu}$$9 symmetry in heterobilayers (e.g., twisted bilayer MoS$q$0) enables control over the magnitude, sign, and spatial distribution of chiral phonon angular momentum, scalable via the moiré period (Suri et al., 2021).
• Doping and external field tuning: The amplitude of phonon angular momentum and its interaction with other degrees of freedom in graphyne-based 2D materials is tunable via dopant selection and concentration (Mishra et al., 14 Aug 2025).
• Magnetization control: In magnetic materials (ferromagnets, altermagnets), applying and reversing magnetization directly tunes the energy splitting of chiral phonon branches and can induce hysteretic angular momentum responses (Che et al., 2024, Okamoto et al., 29 Nov 2025).
• Symmetry-guided materials search: Large-scale high-throughput phonon calculations identify thousands of candidate chiral phonon materials, now compiled into open databases for use in materials discovery and device design (Yang et al., 16 Jun 2025).

7. Broader Implications and Future Directions

Chiral phonons represent a general paradigm for quantized angular momentum in bosonic excitations and are relevant beyond phonon systems. They provide unique platforms for:

• Spintronic and opto-phononic devices: Facilitating spin–phonon transfer, dynamic control of magnetization, and information encoding in angular momentum of phonons (Fransson, 2022, Ishito et al., 2021).
• Topological transport and edge states: The spin-1 Weyl structure of chiral phonon bands in cubic and trigonal lattices yields analogues of topological fermions with protected transport signatures and surface phonon states (Tsunetsugu et al., 19 Aug 2025).
• Dark matter detection: The quantized magnetic moments of chiral phonons in chiral MOFs extend the reach of phonon-based detectors to ultralow energy scales and sub-eV dark matter candidates (Romao et al., 2023).

Chiral phononics is poised to influence quantum sensing, information transport, and energy-efficient computing, with rapid advances being driven by symmetry-based theoretical frameworks, high-throughput materials catalogues, and a growing range of direct experimental probes.