The discovery of dynamic chiral anomaly in a Weyl semimetal NbAs

Chiral anomaly refers to the breaking of chiral symmetry upon quantization, leading to non-conservation of chiral charge. Weyl semimetals, which host low-energy excitations with definite chirality at Weyl nodes, provide a solid-state platform to study this physics. Their electromagnetic response features an axial E·B term in the effective Lagrangian, underpinning phenomena such as the anomalous Hall effect and chiral anomaly. In the DC limit with parallel electric and magnetic fields, charge pumping between opposite-chirality Weyl nodes yields negative longitudinal magnetoresistance. However, experiments have largely been limited to static E·B. Accessing the dynamic (AC) E·B regime would enable unique light–matter coupling to Weyl fermions but is challenging due to the semimetallic nature of these materials. The study aims to realize and detect a dynamic chiral anomaly in NbAs by using the internal electric field from phonon-induced deformation potentials together with an external static magnetic field, and to identify its signatures via angle-dependent magneto-infrared spectroscopy.

Prior work established Weyl and Dirac semimetals and their DC chiral anomaly signatures, including negative longitudinal magnetoresistance and chiral magnetic effects in transport and optics. The E·B term distinguishes their electromagnetic responses from conventional materials. Theoretical proposals predicted that in the presence of a magnetic field, phonon dynamics in Weyl/Dirac semimetals can exhibit signatures of the chiral anomaly, with an emergent phonon effective charge proportional to B and strong angular dependence relative to E and B. Magneto-optical spectroscopies have been successful in probing Landau quantization and topological carriers in related systems. NbAs-family compounds show strong electron–phonon coupling and well-characterized phonon modes, with previous Raman and optical studies identifying A1, B1, and E modes and Landau level spectra. These set the stage for probing dynamic E·B via phonon–electron coupling.

• Materials and characterization: High-quality NbAs single crystals were grown by chemical vapor transport. Crystal orientation was identified by X-ray diffraction to access (001) and (101) surfaces. Room-temperature Raman spectroscopy (633 nm excitation) characterized phonon modes. Zero-field infrared reflectivity was measured by in situ overcoating in a Fourier transform infrared spectrometer.
• Magneto-infrared spectroscopy: Measurements were performed at liquid helium temperature in both Voigt geometry (light propagation perpendicular to B) and Faraday geometry (propagation parallel to B), with magnetic fields up to 16 T. Infrared light was incident near normal to the sample surface. Polarization control was implemented with a linear polarizer to set E parallel or perpendicular to B. Reflectivity spectra under field were recorded and normalized to zero-field spectra; absolute reflectivity was obtained by multiplying normalized spectra by the zero-field baseline. Optical conductivity was extracted via Kramers–Kronig constrained analysis.
• Angle-dependent and geometry tests: On the (001) surface (where Q·E|| vanishes at zero field for all modes), reflectivity was recorded for unpolarized light, then with E||B and E⊥B, and after rotating the crystal by 90 degrees to rule out crystalline anisotropy. Measurements on the (101) surface served as a zero-field control where the A1 mode is IR-active.
• Spectral analysis: Inter-Landau-level absorption features were identified by their B-dependent energies and broad widths, while phonon resonances were identified by narrow Lorentzian lines with B-invariant frequency. Line shapes were fit to Lorentzians; field dependence of intensities was analyzed. Theoretical modeling and symmetry analysis connected observed angle dependence to dynamic chiral anomaly and magnetic-field-induced symmetry breaking.

• Field-induced phonon activation: A phonon resonance at ~275 cm^-1, absent in zero-field IR spectra on the (001) surface, becomes IR-active in the presence of a magnetic field. Its intensity increases monotonically with B and exhibits a symmetric Lorentzian line shape.
• Frequency invariance: The activated phonon peak (feature X) maintains a constant frequency with magnetic field, distinct from inter-Landau-level transitions (features A–G) whose energies increase with B and have broad (~30 cm^-1) widths.
• Mode identification: The X peak frequency matches the A1 phonon observed by Raman and the (101) surface IR mode; it is argued to be nearly degenerate with the E(3) phonons at k = 0.
• Angle dependence consistent with E·B: On the (001) surface, the phonon resonance appears in Voigt geometry when the oscillating electric field has a component parallel to B, is stronger for polarized E||B, and disappears for E⊥B and in Faraday geometry where E|| is orthogonal to B. Rotating the crystal by 90 degrees does not change the result, ruling out crystal anisotropy.
• Conductivity analysis: Kramers–Kronig-derived optical conductivity confirms the emergence and growth of a Lorentzian phonon resonance with increasing B; at high fields, the line shape is influenced by nearby Landau transitions but remains Lorentzian when those are accounted for.
• Generality to Dirac semimetals: In Cd3As2 thin flakes, a magnetic-field-induced phonon charge contribution appears in the A1g mode for E||B and disappears for E⊥B; the phonon intensity shows a B^4.3 dependence (from supplementary data), suggesting a common mechanism.
• Symmetry mechanism: Magnetic field breaks mirror symmetries (notably My) and, through formation of chiral Landau levels and anisotropic Fermi velocities, permits a pseudoscalar phonon effective charge δQ parallel to B, enabling coupling to the dynamic chiral anomaly.

The experiments directly probe the dynamic E·B term in a Weyl semimetal by using the internal electric field of phonon-induced deformation potentials under an external magnetic field. The observed activation of a phonon mode with intensity growing with B, fixed frequency, and strong dependence on the relative orientation of E and B, is consistent with a magnetic-field-induced phonon effective charge δQ ∝ B that is parallel to B. This behavior matches theoretical predictions for dynamic chiral anomaly where oscillating chiral magnetic current couples to phonons. Symmetry analysis explains why such coupling is allowed in NbAs despite zero-field mirror symmetries: the external magnetic field breaks improper rotations and specifically My, and chiral Landau levels select branches with distinct Fermi velocities, leading to non-canceling contributions from Weyl nodes. The activated mode can be viewed as a pseudoscalar descendant of the E(3) phonons near-degenerate with A1 at k = 0. The findings generalize to Dirac semimetals (Cd3As2), indicating a broader relevance of dynamic chiral anomaly in topological semimetals. The negligible coupling between the induced phonon and inter-Landau-level transitions in NbAs suggests a regime where the phonon response can be cleanly isolated, while stronger electron–phonon coupling materials may exhibit magneto-phonon resonance or anti-crossing features.

This work demonstrates an experimental pathway to access the dynamic chiral anomaly in the AC regime of a Weyl semimetal by combining internal phonon-driven electric fields with an external magnetic field. In NbAs, a phonon mode that is IR-inactive at zero field becomes active under B, with intensity controlled by the orientation of the light’s electric field relative to B and consistent with a phonon effective charge parallel to B. The approach enables coupling between Weyl fermions and electromagnetic waves beyond the DC limit and reveals characteristic angle-dependent phonon activity. The observations are supported by symmetry considerations involving magnetic-field-induced mirror-symmetry breaking and chiral Landau levels, and are echoed in a Dirac semimetal, indicating generality. Future work could explore materials with stronger electron–phonon coupling to observe magneto-phonon resonances and study detailed interplay between induced phonons and Landau transitions, as well as map frequency and temperature regimes to further elucidate dynamic electromagnetic responses in topological semimetals.

• At high magnetic fields, the phonon line shape is influenced by nearby inter-Landau-level transitions, complicating spectral analysis, though a Lorentzian profile is recovered when those contributions are removed.
• The coupling between the field-induced phonon and Landau-level transitions appears negligible in NbAs; stronger coupling regimes and potential magneto-phonon resonances were not observed here.
• The identification of the activated mode relies on near-degeneracy with E(3) phonons at k = 0 and symmetry analysis; δQ is inferred rather than directly measured.
• Access to dynamic E·B is achieved indirectly via internal phonon fields; generating a purely external oscillating E·B remains experimentally challenging.
• Measurements were performed at low temperature and specific geometries; broader temperature and frequency range studies are needed to assess generality and device relevance.