Weyl Fermion Plasmons

• Weyl fermion plasmons are collective charge excitations in Weyl semimetals, defined by topological band structures, anisotropic dispersions, and Fermi-arc surface states.
• Bulk modes reveal unique density scaling and acoustic branches emerging from mixed linear-quadratic dispersions and multicomponent plasma behavior.
• Surface modes, including chiral Fermi-arc plasmons, exhibit nonlocal effects and directional propagation, tunable through interface geometry and finite-size confinement.

Weyl fermion plasmons are collective charge excitations in Weyl semimetals and Weyl metals whose dispersion, damping, and optical activity are controlled by Weyl-node structure, open Fermi-arc surface states, anomalous Hall response, multicomponent node inequivalence, and, in some geometries, axion-modified electrodynamics. The literature does not describe a single universal branch: it spans doped bulk plasmons with direction-dependent density scaling, chiral Fermi-arc plasmons on sharp or smooth interfaces, thin-film and edge modes, chemically tunable surface plasmons, acoustic plasmons in realistic multi-node compounds, and localized surface resonances in finite Weyl nanostructures (Wang et al., 2017, Song et al., 2017, Afanasiev et al., 2021, Pellegrino et al., 29 May 2025).

1. Electronic structure basis and mode classes

The plasmonic problem in Weyl systems is inseparable from the underlying band topology. In the minimal bulk setting, Weyl quasiparticles arise near isolated nodes with linear dispersion, but several important variants appear in the plasmon literature: anisotropic Weyl nodes that are linear in two momentum components and quadratic in the third, multi-node type-I Weyl semimetals with inequivalent $W_1$ and $W_2$ sectors, type-II systems in which Weyl and trivial carriers coexist at the Fermi surface, and time-reversal-breaking surfaces carrying open Fermi arcs (Wang et al., 2017, Afanasiev et al., 2021, Jia et al., 2020).

This diversity produces a corresponding taxonomy of collective modes. Bulk modes include conventional gapped optical plasmons, anisotropic plasmons with nontrivial density exponents, and acoustic plasmons generated by out-of-phase oscillations of inequivalent Weyl components. Surface modes include Fermi-arc plasmons, smooth-interface modes involving both chiral Fermi arcs and massive Volkov-Pankratov states, and thin-film surface plasmon polaritons shaped by hybridization between the two interfaces. Finite geometries add localized surface plasmons, while magnetic or pseudomagnetic fields generate unidirectional bulk, surface, and edge modes with explicitly topological character (Lu et al., 2021, Giri et al., 2020, Tamaya et al., 2018, Zhang et al., 2020).

A central theme across these settings is that the plasmon is not determined by dimensionality alone. The broader Weyl-plasmon literature repeatedly ties the long-wavelength mode to details of the polarization kernel: current anisotropy, Fermi-arc kinematics, interband structure, and magnetoelectric couplings all alter the collective spectrum. This is why the same label, “Weyl fermion plasmon,” covers physically distinct objects rather than a single canonical dispersion law (Wang et al., 2017).

2. Bulk plasmons: anisotropy, screening, and multicomponent acoustic branches

A paradigmatic bulk result was obtained for a doped three-dimensional anisotropic Weyl semimetal with single-particle Hamiltonian

$$H(\mathbf{k})=v k_x \sigma_x+ v k_y \sigma_y + A k_z^2 \sigma_z,$$

and dispersion

$$E_{\mathbf{k}}=\pm \sqrt{v^2 k_\perp^2 + A^2 k_z^4}.$$

In that system the carrier density obeys $n_e\propto \mu^{5/2}$, and the long-wavelength intraband polarization produces

$$\operatorname{Re}\Pi^{\mathrm{ret}}(\Omega,\mathbf q)\sim -\frac{q_\perp^2\mu^{3/2}}{\Omega^2}-\frac{q_z^2\mu^{5/2}}{\Omega^2}.$$

Within RPA this yields a direction-dependent plasmon frequency

$$\Omega_p = \sqrt{ \frac{4\pi e^2}{\kappa}\left( C_{++}^\perp \mu^{3/2}\sin^2\phi + C_{++}^z \mu^{5/2}\cos^2\phi \right)},$$

with the characteristic density laws

$$\Omega_p^\perp \propto n_e^{3/10},\qquad \Omega_p^z \propto n_e^{1/2}.$$

The same analysis gives Debye screening $\Pi(0,0)\sim \mu^{3/2}\sim n_e^{3/5}$ at $T=0$ and $W_2$0 at charge neutrality, emphasizing that even static screening inherits the anisotropic density of states (Wang et al., 2017).

A second bulk theme is that realistic Weyl plasmas are often multicomponent. For type-I TaAs-family materials, the $W_2$1 and $W_2$2 node groups act as distinct plasma components with different directional velocities and carrier densities. In that setting the in-phase oscillation remains an optical plasmon, but the out-of-phase oscillation generates an acoustic branch $W_2$3. The acoustic mode exists in a narrow angular sector around the $W_2$4 direction and is weakly damped because the $W_2$5 and $W_2$6 quasiparticles have a large velocity contrast along $W_2$7, with $W_2$8. The result is an effectively gapless three-dimensional plasmon spectrum in TaAs-family WSMs, in contrast with HgTe-family systems, which the same analysis leaves gapped (Afanasiev et al., 2021).

These two bulk examples delimit two complementary mechanisms. In the anisotropic-node problem, unusual exponents come from a single mixed linear-quadratic dispersion. In the TaAs-family problem, the new low-energy branch comes from multicomponent plasma composition. Both results show that “bulk Weyl plasmon” is not a universal object: node anisotropy, node multiplicity, and inequivalent Fermi-surface sectors all enter directly into the collective mode.

3. Surface-state plasmons: Fermi arcs, nonlocality, and smooth interfaces

The most distinctive surface collective modes in Weyl semimetals are Fermi-arc plasmons. In a time-reversal-breaking WSM with a semi-infinite geometry, the surface charge dynamics contains both the usual metallic surface accumulation and a chiral Fermi-arc contribution. The resulting secular equation,

$W_2$9

describes hybrid bulk-surface modes rather than a purely two-dimensional surface fluid. The constant-frequency contours of these Fermi-arc plasmons are generally open and hyperbolic, and their group velocities become collimated along a small set of directions, which is why near-field excitation is predicted to launch directional surface-plasmon beams (Song et al., 2017).

A more microscopic nonlocal formulation decomposes the response into Fermi-arc-only, bulk-only, and mixed surface-bulk channels,

$$H(\mathbf{k})=v k_x \sigma_x+ v k_y \sigma_y + A k_z^2 \sigma_z,$$0

and shows that the observable surface mode is a chiral surface-bulk hybrid plasmon. In the doped regime the long-wavelength frequency takes the form

$$H(\mathbf{k})=v k_x \sigma_x+ v k_y \sigma_y + A k_z^2 \sigma_z,$$1

while the dominant linewidth comes from decay into bulk electron-hole pairs over a continuum of $$H(\mathbf{k})=v k_x \sigma_x+ v k_y \sigma_y + A k_z^2 \sigma_z,$$2. This nonlocal damping is intrinsic to the half-space geometry and is strongest away from the forward propagation direction set by the Fermi-arc chirality (Andolina et al., 2017).

The undoped semi-infinite problem yields a different asymptotic result when the deep penetration of arc-end states into the bulk is retained explicitly. In that treatment the Fermi-arc electron liquid supports a gapless, linearly dispersing surface mode,

$$H(\mathbf{k})=v k_x \sigma_x+ v k_y \sigma_y + A k_z^2 \sigma_z,$$3

rather than a conventional $$H(\mathbf{k})=v k_x \sigma_x+ v k_y \sigma_y + A k_z^2 \sigma_z,$$4 plasmon. The paper attributes the gaplessness to the divergence of the surface-state localization length near the ends of the arc and argues that truncated or purely surface-projected theories can spuriously generate a gap (Adivehvand et al., 2019).

Surface smoothness further enriches the problem. For a smooth Weyl-semimetal–insulator interface, the chiral $$H(\mathbf{k})=v k_x \sigma_x+ v k_y \sigma_y + A k_z^2 \sigma_z,$$5 Fermi arc coexists with a ladder of massive Volkov-Pankratov states. The FA branch supports the usual nonreciprocal plasmon, with long-wavelength form

$$H(\mathbf{k})=v k_x \sigma_x+ v k_y \sigma_y + A k_z^2 \sigma_z,$$6

and gap

$$H(\mathbf{k})=v k_x \sigma_x+ v k_y \sigma_y + A k_z^2 \sigma_z,$$7

But the VP ladder adds a damped VP interband plasmon and, when the first VP conduction band is occupied, a VP intraband plasmon that is approximately linear and becomes nonreciprocal through coupling to the FA sector. The same model yields a singularly direction-dependent FA-plasmon gap,

$$H(\mathbf{k})=v k_x \sigma_x+ v k_y \sigma_y + A k_z^2 \sigma_z,$$8

which vanishes along the $$H(\mathbf{k})=v k_x \sigma_x+ v k_y \sigma_y + A k_z^2 \sigma_z,$$9 direction (Lu et al., 2021).

Taken together, these results show that the surface sector does not admit a single universal low-$$E_{\mathbf{k}}=\pm \sqrt{v^2 k_\perp^2 + A^2 k_z^4}.$$0 law. Sharp versus smooth interfaces, doped versus undoped regimes, and local versus fully nonlocal treatments produce distinct asymptotics because they probe different combinations of Fermi-arc, bulk, and massive surface-state physics.

4. Thin films, finite-size structures, and localized resonances

Confinement across the sample thickness fundamentally reorganizes Weyl plasmonics. In a thin-film WSM slab, Coulomb coupling between the two surfaces does not reproduce the ordinary bilayer pattern. Instead, the low-energy collective mode is a single optical branch

$$E_{\mathbf{k}}=\pm \sqrt{v^2 k_\perp^2 + A^2 k_z^4}.$$1

with an anti-symmetric charge profile across the film,

$$E_{\mathbf{k}}=\pm \sqrt{v^2 k_\perp^2 + A^2 k_z^4}.$$2

This “dipolar optical plasmon” is the opposite of the standard bilayer assignment, where the $$E_{\mathbf{k}}=\pm \sqrt{v^2 k_\perp^2 + A^2 k_z^4}.$$3 mode is symmetric and the anti-symmetric mode is acoustic. The inversion is traced directly to the opposite chiralities of the Fermi arcs on the two surfaces (Giri et al., 2020).

A complementary thin-film problem treats the WSM as an axion-electrodynamic medium of thickness $$E_{\mathbf{k}}=\pm \sqrt{v^2 k_\perp^2 + A^2 k_z^4}.$$4, embedded between dielectrics with $$E_{\mathbf{k}}=\pm \sqrt{v^2 k_\perp^2 + A^2 k_z^4}.$$5 and $$E_{\mathbf{k}}=\pm \sqrt{v^2 k_\perp^2 + A^2 k_z^4}.$$6. Hybridization of the two interface SPPs produces short-range and long-range surface plasmons, but their reciprocity depends on the orientation of the axion vector $$E_{\mathbf{k}}=\pm \sqrt{v^2 k_\perp^2 + A^2 k_z^4}.$$7. In the perpendicular and Faraday configurations the spectrum is reciprocal, while in the Voigt configuration

$$E_{\mathbf{k}}=\pm \sqrt{v^2 k_\perp^2 + A^2 k_z^4}.$$8

The same formalism predicts a partial lack of dispersion, complex decay constants in the Faraday case, and strong control of mode existence and nonreciprocity through thickness, dielectric asymmetry, and the direction of $$E_{\mathbf{k}}=\pm \sqrt{v^2 k_\perp^2 + A^2 k_z^4}.$$9 (Tamaya et al., 2018).

Finite-size quantization becomes even more explicit in a sub-wavelength Weyl-semimetal nanosphere. There the axion-induced Hall term generates a gyrotropic permittivity tensor with off-diagonal component

$n_e\propto \mu^{5/2}$0

and the conventional Fröhlich conditions split into

$n_e\propto \mu^{5/2}$1

for dipoles and

$n_e\propto \mu^{5/2}$2

for quadrupoles. The former triply degenerate dipole resonance becomes three nondegenerate branches; the conventional fivefold $n_e\propto \mu^{5/2}$3 quadrupole degeneracy is fully lifted; and a TE excitation can generate a localized quadrupole plasmon through the axion magnetoelectric effect. In this regime Weyl topology does not merely shift resonance energies; it changes degeneracies and optical selection rules of the localized modes themselves (Pellegrino et al., 29 May 2025).

5. Experimental realizations and spectroscopic signatures

Electron-energy-loss spectroscopy is the dominant experimental probe in the present literature. It was proposed early as a way to access the anisotropic bulk plasmon laws of mixed linear-quadratic Weyl dispersion, and later became the principal tool for both surface and interband mode detection in real materials (Wang et al., 2017, Lu et al., 2021).

The clearest direct surface-plasmon experiment to date is the HREELS study of the $n_e\propto \mu^{5/2}$4 surfaces of NbAs and TaAs. At room temperature the pristine surfaces exhibit gapped low-energy loss peaks at $n_e\propto \mu^{5/2}$5 in NbAs and $n_e\propto \mu^{5/2}$6 in TaAs. Interpreted with finite-temperature Weyl-semimetal RPA theory in the high-temperature regime, these values correspond to $n_e\propto \mu^{5/2}$7. Surface chemistry strongly shifts the same mode: oxygen adsorption red-shifts it to $n_e\propto \mu^{5/2}$8 in both compounds and lowers the inferred coupling to $n_e\propto \mu^{5/2}$9 in NbAs and $$\operatorname{Re}\Pi^{\mathrm{ret}}(\Omega,\mathbf q)\sim -\frac{q_\perp^2\mu^{3/2}}{\Omega^2}-\frac{q_z^2\mu^{5/2}}{\Omega^2}.$$0 in TaAs, whereas hydrocarbon fragments blue-shift it to $$\operatorname{Re}\Pi^{\mathrm{ret}}(\Omega,\mathbf q)\sim -\frac{q_\perp^2\mu^{3/2}}{\Omega^2}-\frac{q_z^2\mu^{5/2}}{\Omega^2}.$$1 in NbAs and $$\operatorname{Re}\Pi^{\mathrm{ret}}(\Omega,\mathbf q)\sim -\frac{q_\perp^2\mu^{3/2}}{\Omega^2}-\frac{q_z^2\mu^{5/2}}{\Omega^2}.$$2 in TaAs, with $$\operatorname{Re}\Pi^{\mathrm{ret}}(\Omega,\mathbf q)\sim -\frac{q_\perp^2\mu^{3/2}}{\Omega^2}-\frac{q_z^2\mu^{5/2}}{\Omega^2}.$$3 and $$\operatorname{Re}\Pi^{\mathrm{ret}}(\Omega,\mathbf q)\sim -\frac{q_\perp^2\mu^{3/2}}{\Omega^2}-\frac{q_z^2\mu^{5/2}}{\Omega^2}.$$4, respectively. The reported $$\operatorname{Re}\Pi^{\mathrm{ret}}(\Omega,\mathbf q)\sim -\frac{q_\perp^2\mu^{3/2}}{\Omega^2}-\frac{q_z^2\mu^{5/2}}{\Omega^2}.$$5 range is therefore approximately $$\operatorname{Re}\Pi^{\mathrm{ret}}(\Omega,\mathbf q)\sim -\frac{q_\perp^2\mu^{3/2}}{\Omega^2}-\frac{q_z^2\mu^{5/2}}{\Omega^2}.$$6 to $$\operatorname{Re}\Pi^{\mathrm{ret}}(\Omega,\mathbf q)\sim -\frac{q_\perp^2\mu^{3/2}}{\Omega^2}-\frac{q_z^2\mu^{5/2}}{\Omega^2}.$$7, depending on surface condition (Chiarello et al., 2018).

A different experimental regime appears in type-II MoTe$$\operatorname{Re}\Pi^{\mathrm{ret}}(\Omega,\mathbf q)\sim -\frac{q_\perp^2\mu^{3/2}}{\Omega^2}-\frac{q_z^2\mu^{5/2}}{\Omega^2}.$$8, studied across the $$\operatorname{Re}\Pi^{\mathrm{ret}}(\Omega,\mathbf q)\sim -\frac{q_\perp^2\mu^{3/2}}{\Omega^2}-\frac{q_z^2\mu^{5/2}}{\Omega^2}.$$9 to $$\Omega_p = \sqrt{ \frac{4\pi e^2}{\kappa}\left( C_{++}^\perp \mu^{3/2}\sin^2\phi + C_{++}^z \mu^{5/2}\cos^2\phi \right)},$$0 structural transition by momentum-resolved HREELS. In the centrosymmetric high-temperature $$\Omega_p = \sqrt{ \frac{4\pi e^2}{\kappa}\left( C_{++}^\perp \mu^{3/2}\sin^2\phi + C_{++}^z \mu^{5/2}\cos^2\phi \right)},$$1 phase, a single mode $$\Omega_p = \sqrt{ \frac{4\pi e^2}{\kappa}\left( C_{++}^\perp \mu^{3/2}\sin^2\phi + C_{++}^z \mu^{5/2}\cos^2\phi \right)},$$2 appears near $$\Omega_p = \sqrt{ \frac{4\pi e^2}{\kappa}\left( C_{++}^\perp \mu^{3/2}\sin^2\phi + C_{++}^z \mu^{5/2}\cos^2\phi \right)},$$3. In the low-temperature topological $$\Omega_p = \sqrt{ \frac{4\pi e^2}{\kappa}\left( C_{++}^\perp \mu^{3/2}\sin^2\phi + C_{++}^z \mu^{5/2}\cos^2\phi \right)},$$4 phase, two modes are observed instead: $$\Omega_p = \sqrt{ \frac{4\pi e^2}{\kappa}\left( C_{++}^\perp \mu^{3/2}\sin^2\phi + C_{++}^z \mu^{5/2}\cos^2\phi \right)},$$5 and $$\Omega_p = \sqrt{ \frac{4\pi e^2}{\kappa}\left( C_{++}^\perp \mu^{3/2}\sin^2\phi + C_{++}^z \mu^{5/2}\cos^2\phi \right)},$$6. All are nearly dispersionless in the accessible small-$$\Omega_p = \sqrt{ \frac{4\pi e^2}{\kappa}\left( C_{++}^\perp \mu^{3/2}\sin^2\phi + C_{++}^z \mu^{5/2}\cos^2\phi \right)},$$7 window and rapidly damp above $$\Omega_p = \sqrt{ \frac{4\pi e^2}{\kappa}\left( C_{++}^\perp \mu^{3/2}\sin^2\phi + C_{++}^z \mu^{5/2}\cos^2\phi \right)},$$8. First-principles RPA analysis assigns these not to a simple bulk/surface plasmon pair but to interband correlations of the inverted bands; in the $$\Omega_p = \sqrt{ \frac{4\pi e^2}{\kappa}\left( C_{++}^\perp \mu^{3/2}\sin^2\phi + C_{++}^z \mu^{5/2}\cos^2\phi \right)},$$9 phase the dominant transitions involve topological Weyl bands and trivial nonrelativistic bands simultaneously (Jia et al., 2020).

These experiments establish two points. First, low-energy plasmons in Weyl materials are observable with surface sensitivity and can be tuned by adsorption, temperature, and structural phase. Second, a measured plasmon in a Weyl host need not be a pure isolated-cone mode: it may be a surface plasmon governed by thermally activated Weyl carriers, or an interband plasmon generated by hybridized topological and trivial bands.

6. Topological and quantum-geometric formulations

A distinct strand of the literature treats Weyl plasmons themselves as topological bosonic bands. In a time-reversal-breaking WSM under magnetic field, the bulk current eigenstate $$\Omega_p^\perp \propto n_e^{3/10},\qquad \Omega_p^z \propto n_e^{1/2}.$$0 defines a Berry curvature

$$\Omega_p^\perp \propto n_e^{3/10},\qquad \Omega_p^z \propto n_e^{1/2}.$$1

with nonzero slice Chern numbers

$$\Omega_p^\perp \propto n_e^{3/10},\qquad \Omega_p^z \propto n_e^{1/2}.$$2

The associated surface response includes unidirectional plasmons with momentum-location lock, and opposite-surface Fermi-arc plasmons can be combined into another “3D topological plasmon” through Weyl-orbit coupling. The boundary manifestation is a gapless unidirectional edge plasmon whose location and direction are switched by reversing the magnetic field (Zhang et al., 2020).

Strain-induced pseudofields generate a different topological collective mode. In a strained type-I WSM the anomalous plasmon is governed by

$$\Omega_p^\perp \propto n_e^{3/10},\qquad \Omega_p^z \propto n_e^{1/2}.$$3

with long-wavelength gap

$$\Omega_p^\perp \propto n_e^{3/10},\qquad \Omega_p^z \propto n_e^{1/2}.$$4

Its physical origin is a modified continuity equation,

$$\Omega_p^\perp \propto n_e^{3/10},\qquad \Omega_p^z \propto n_e^{1/2}.$$5

interpreted as dynamical charge pumping between bulk and surface in the presence of a pseudomagnetic field. The mode is therefore gapped, unidirectional, and parametrically distinct from ordinary bulk plasmons (Heidari et al., 2020).

The most explicit quantum-geometric formulation appears for doped Weyl metals. There the plasmon is written as a composite particle-hole state with envelope $$\Omega_p^\perp \propto n_e^{3/10},\qquad \Omega_p^z \propto n_e^{1/2}.$$6, and its interband components inherit the Berry connection and quantum metric of the Weyl bands. The central claim is that the internal plasmon wavefunction has monopole structure and vorticity

$$\Omega_p^\perp \propto n_e^{3/10},\qquad \Omega_p^z \propto n_e^{1/2}.$$7

while the effective plasmon dipole moment is

$$\Omega_p^\perp \propto n_e^{3/10},\qquad \Omega_p^z \propto n_e^{1/2}.$$8

Because the coupling to light is proportional to $$\Omega_p^\perp \propto n_e^{3/10},\qquad \Omega_p^z \propto n_e^{1/2}.$$9, these bulk plasmons selectively absorb linearly polarized light only along the plasmon propagation direction. In this construction the topology resides in the internal relative-momentum structure of the plasmon, not in its center-of-mass Berry phase, for which

$\Pi(0,0)\sim \mu^{3/2}\sim n_e^{3/5}$0

was reported (Xie et al., 16 Jun 2026).

A recurrent conceptual boundary follows from these results. Some Weyl plasmons are explicitly topological collective bands; others are surface or interband modes strongly shaped by Weyl physics without constituting a uniquely topological fingerprint by themselves. The MoTe$\Pi(0,0)\sim \mu^{3/2}\sim n_e^{3/5}$1 study is explicit that its low-temperature plasmons are dominated by interband correlations between topological and trivial carriers (Jia et al., 2020). Conversely, the phrase “Weyl plasmons” is also used analogically in magnetized plasma, where bosonic electromagnetic/plasma modes form Weyl-point degeneracies and surface Fermi arcs; those excitations are not literal fermionic Weyl particles, but topological bosonic analogues (Gao et al., 2015).