Weyl-Kondo Fermions in Heavy-Fermion Semimetals

• Weyl-Kondo fermions are Weyl quasiparticles formed through Kondo hybridization, where local moments and conduction electrons create heavy bands with topological node crossings.
• They are modeled via a periodic Anderson framework on noncentrosymmetric lattices, with symmetry and strong correlations reducing nodal velocities and pinning nodes to the Fermi energy.
• Experimental realizations in materials like Ce₃Bi₄Pd₃ and YbPtBi reveal signatures such as a T³ specific heat, anomalous Hall effects, and field-tuned Weyl node behavior.

Searching arXiv for foundational and papers on Weyl-Kondo fermions and related Kondo/Weyl impurity and lattice physics. I’ll gather a compact set of representative arXiv sources spanning the original WKSM proposal, key experimental realizations, symmetry-based generalizations, and single-impurity/Kondo-screening studies in Weyl hosts. Weyl-Kondo fermions are Weyl quasiparticles whose dispersion and, in the strongest formulation, whose very existence are generated by Kondo hybridization in heavy-fermion semimetals. In this setting, localized moments and itinerant electrons form Kondo-screened heavy bands that retain Weyl topology, so Berry-monopole band crossings and Fermi arcs occur on an energy scale set by the Kondo effect rather than by a bare conduction bandwidth. The defining consequence is a Weyl semimetallic state with strongly reduced nodal velocities, narrow heavy bands, and topological responses inherited by composite heavy quasiparticles rather than by weakly interacting Bloch electrons (Lai et al., 2016).

1. Definition and conceptual scope

The defining distinction from an ordinary Weyl semimetal is not the presence of Weyl nodes as such, but the origin of those nodes. In a conventional Weyl semimetal, the nodes are features of weakly interacting bands, typically controlled by spin-orbit coupling and inversion- or time-reversal-symmetry breaking. In a Weyl-Kondo semimetal, by contrast, the relevant bands are Kondo-hybridized heavy bands, so the low-energy Weyl fermions are heavy quasiparticles with velocities renormalized down to the Kondo scale and with spectral weight tied to the many-body Kondo singlet. The corresponding phase is therefore a topological heavy-fermion semimetal rather than a lightly renormalized topological metal (Lai et al., 2016).

This concept also differs from an ordinary heavy Fermi liquid. A conventional heavy Fermi liquid has Kondo-induced large effective masses and a large Fermi surface, but no symmetry-protected linear band touching is required. Weyl-Kondo fermions appear when the same Kondo hybridization that produces heavy quasiparticles also yields topologically protected Weyl nodes, often pinned to the Fermi energy by symmetry and filling constraints. A central implication is that low-temperature thermodynamics can be governed by an electronic $T^3$ law associated with linear Weyl dispersion, but with a prefactor strongly enhanced by the small renormalized velocity $v^*$ (Grefe et al., 2020).

The term has also broadened in the literature. In the canonical usage it refers to Weyl quasiparticles in a Kondo lattice, especially heavy-fermion systems. Closely related single-impurity, surface, and disorder-driven problems study how Kondo screening operates in Weyl or Dirac environments and supply the microscopic building blocks for lattice Weyl-Kondo phases. This broader usage does not erase the lattice definition; rather, it situates Weyl-Kondo fermions within a hierarchy ranging from impurity screening to coherent heavy Weyl bands.

2. Microscopic lattice constructions

The foundational microscopic construction is a periodic Anderson model on a noncentrosymmetric diamond lattice. In its minimal form,

$H = H_d + H_{cd} + H_c,$

with

$$H_d = E_d \sum_{i,\sigma} d_{i\sigma}^\dagger d_{i\sigma} + U \sum_i n^d_{i\uparrow} n^d_{i\downarrow},$$

$$H_{cd} = V \sum_{i,\sigma} \left(d_{i\sigma}^\dagger c_{i\sigma} + c_{i\sigma}^\dagger d_{i\sigma}\right),$$

and a conduction Hamiltonian of Fu-Kane-Mele type with inversion breaking,

$$h_{\mathbf{k}} = \sigma_0\big[u_1(\mathbf{k})\tau_x + u_2(\mathbf{k})\tau_y + m\tau_z\big] + \lambda \big(\mathbf{D}(\mathbf{k})\cdot\boldsymbol{\sigma}\big)\tau_z .$$

Here $m\tau_z$ differentiates the two sublattices and breaks inversion symmetry, while $\lambda$ is the spin-orbit scale. In the large-$U$ limit, a slave-boson saddle point introduces a Kondo-hybridization amplitude $V_s=rV$ and a shifted $v^*$0-level $v^*$1, so that the low-energy quasiparticle bands are genuinely Kondo-generated (Lai et al., 2016).

After diagonalizing the spin-orbit texture into pseudospin sectors, the conduction problem separates into

$v^*$2

and the hybridized quasiparticle energies become

$v^*$3

Within this solution, the $v^*$4 sector remains gapped near the Fermi level, while the $v^*$5 sector can host Weyl nodes for

$v^*$6

with the chemical potential pinned by

$v^*$7

A crucial point is that without Kondo hybridization the reference state is a trivial insulator with localized moments and an empty conduction band. The semimetallic Weyl nodes therefore emerge from Kondo screening rather than merely surviving it (Lai et al., 2016).

This framework was generalized to multi-Dirac and multi-Weyl Kondo lattices with arbitrary topological charge $v^*$8, using a $v^*$9 low-energy conduction Hamiltonian

$H = H_d + H_{cd} + H_c,$0

At particle-hole symmetry, multi-Dirac and time-reversal-breaking multi-Weyl lattices inherit a pseudogap density of states

$H = H_d + H_{cd} + H_c,$1

which produces a critical Kondo coupling

$H = H_d + H_{cd} + H_c,$2

Below $H = H_d + H_{cd} + H_c,$3 there is no Kondo quenching; above it, Kondo-insulating or heavy semimetallic phases appear. By contrast, in inversion-breaking multi-Weyl systems the $H = H_d + H_{cd} + H_c,$4 term generates a finite density of states at the Fermi level, eliminating the critical coupling. Depending on filling, the mean-field phase can be a Kondo insulator, a heavy-fermion metal, or a heavy-fermion semimetal, and the renormalizations of opposite chirality sectors can differ widely (Silva et al., 2024).

3. Symmetry, topology, and node taxonomy

Nonsymmorphic symmetry is central to the Weyl-Kondo mechanism because it constrains the heavy bands after Kondo hybridization, not only the bare conduction bands. In the diamond-lattice formulation, strong correlations and nonsymmorphic space-group symmetry cooperate to form Weyl nodal excitations with highly reduced velocity and to pin the resulting Weyl nodes to the Fermi energy. In the corresponding heavy-fermion phase, the low-energy scale is $H = H_d + H_{cd} + H_c,$5, and the renormalized velocity obeys the schematic reduction $H = H_d + H_{cd} + H_c,$6. The same symmetry logic also permits tilted Weyl-Kondo solutions, described near a node by

$H = H_d + H_{cd} + H_c,$7

so that a type-I to type-II transition can occur within the heavy bands while the nodes remain pinned to the Fermi energy (Grefe et al., 2019).

Topological characterization proceeds in the standard Weyl language, but now for heavy bands. The Berry curvature

$H = H_d + H_{cd} + H_c,$8

has monopole sources and sinks at the Weyl-Kondo nodes, with Chern number

$H = H_d + H_{cd} + H_c,$9

for a simple node. Surface Fermi arcs are the corresponding boundary manifestation. The distinctive feature is not a modified topological invariant, but the fact that these invariants are carried by Kondo-hybridized heavy quasiparticles.

Recent work extended the taxonomy from cubic noncentrosymmetric settings to hexagonal heavy-fermion systems with chiral and achiral nonsymmorphic space groups. In chiral SG 173 ($$H_d = E_d \sum_{i,\sigma} d_{i\sigma}^\dagger d_{i\sigma} + U \sum_i n^d_{i\uparrow} n^d_{i\downarrow},$$0), the heavy-fermion sector hosts hourglass-type Weyl crossings on $$H_d = E_d \sum_{i,\sigma} d_{i\sigma}^\dagger d_{i\sigma} + U \sum_i n^d_{i\uparrow} n^d_{i\downarrow},$$1 and $$H_d = E_d \sum_{i,\sigma} d_{i\sigma}^\dagger d_{i\sigma} + U \sum_i n^d_{i\uparrow} n^d_{i\downarrow},$$2, with reported charges $$H_d = E_d \sum_{i,\sigma} d_{i\sigma}^\dagger d_{i\sigma} + U \sum_i n^d_{i\uparrow} n^d_{i\downarrow},$$3 and $$H_d = E_d \sum_{i,\sigma} d_{i\sigma}^\dagger d_{i\sigma} + U \sum_i n^d_{i\uparrow} n^d_{i\downarrow},$$4, and also Kramers-Weyl fermions. In chiral SG 180 ($$H_d = E_d \sum_{i,\sigma} d_{i\sigma}^\dagger d_{i\sigma} + U \sum_i n^d_{i\uparrow} n^d_{i\downarrow},$$5), the heavy bands host double-charge Weyl nodes on $$H_d = E_d \sum_{i,\sigma} d_{i\sigma}^\dagger d_{i\sigma} + U \sum_i n^d_{i\uparrow} n^d_{i\downarrow},$$6. In achiral SG 176 ($$H_d = E_d \sum_{i,\sigma} d_{i\sigma}^\dagger d_{i\sigma} + U \sum_i n^d_{i\uparrow} n^d_{i\downarrow},$$7), the heavy-fermion state realizes a Dirac-Kondo nodal-line semimetal with non-Abelian Wilson-loop phases pinned at $$H_d = E_d \sum_{i,\sigma} d_{i\sigma}^\dagger d_{i\sigma} + U \sum_i n^d_{i\uparrow} n^d_{i\downarrow},$$8, implying drumhead surface states. In achiral SG 190 ($$H_d = E_d \sum_{i,\sigma} d_{i\sigma}^\dagger d_{i\sigma} + U \sum_i n^d_{i\uparrow} n^d_{i\downarrow},$$9), the heavy bands realize a Weyl-Kondo nodal-line semimetal with symmetry-enforced nodal lines on Brillouin-zone boundary planes and additional linked nodal lines, each carrying an Abelian Berry phase of $$H_{cd} = V \sum_{i,\sigma} \left(d_{i\sigma}^\dagger c_{i\sigma} + c_{i\sigma}^\dagger d_{i\sigma}\right),$$0 (Lin et al., 25 Feb 2026).

4. Experimental realizations and candidate materials

The nonmagnetic noncentrosymmetric heavy-fermion semimetal Ce$$H_{cd} = V \sum_{i,\sigma} \left(d_{i\sigma}^\dagger c_{i\sigma} + c_{i\sigma}^\dagger d_{i\sigma}\right),$$1Bi$$H_{cd} = V \sum_{i,\sigma} \left(d_{i\sigma}^\dagger c_{i\sigma} + c_{i\sigma}^\dagger d_{i\sigma}\right),$$2Pd$$H_{cd} = V \sum_{i,\sigma} \left(d_{i\sigma}^\dagger c_{i\sigma} + c_{i\sigma}^\dagger d_{i\sigma}\right),$$3 is the canonical Weyl-Kondo material. Theoretical work on the periodic Anderson model and the concurrent experimental identification of a Weyl-Kondo semimetal in this compound established the basic phenomenology: heavy Weyl nodes pinned near the Fermi energy, a low-temperature specific heat

$$H_{cd} = V \sum_{i,\sigma} \left(d_{i\sigma}^\dagger c_{i\sigma} + c_{i\sigma}^\dagger d_{i\sigma}\right),$$4

and a giant spontaneous Hall response in a time-reversal-invariant heavy-fermion environment. Subsequent magnetic-field studies were interpreted as tuning and eventually annihilating Weyl-Kondo nodes, making Ce$$H_{cd} = V \sum_{i,\sigma} \left(d_{i\sigma}^\dagger c_{i\sigma} + c_{i\sigma}^\dagger d_{i\sigma}\right),$$5Bi$$H_{cd} = V \sum_{i,\sigma} \left(d_{i\sigma}^\dagger c_{i\sigma} + c_{i\sigma}^\dagger d_{i\sigma}\right),$$6Pd$$H_{cd} = V \sum_{i,\sigma} \left(d_{i\sigma}^\dagger c_{i\sigma} + c_{i\sigma}^\dagger d_{i\sigma}\right),$$7 the reference system for field control of correlated Weyl topology (Grefe et al., 2020).

YbPtBi provides a complementary case in which the Weyl physics is experimentally visible in different regimes. At elevated temperatures, where the $$H_{cd} = V \sum_{i,\sigma} \left(d_{i\sigma}^\dagger c_{i\sigma} + c_{i\sigma}^\dagger d_{i\sigma}\right),$$8 electrons are localized, triply degenerate points yield Weyl nodes in applied magnetic fields and the chiral anomaly is evident in magnetotransport. At low temperatures, where Kondo renormalization produces a heavy-fermion semimetal, the chiral-anomaly contribution becomes negligible, but Weyl fermions are inferred from a topological Hall effect and a cubic temperature dependence of the specific heat. The extracted renormalized velocities, $$H_{cd} = V \sum_{i,\sigma} \left(d_{i\sigma}^\dagger c_{i\sigma} + c_{i\sigma}^\dagger d_{i\sigma}\right),$$9 and $$h_{\mathbf{k}} = \sigma_0\big[u_1(\mathbf{k})\tau_x + u_2(\mathbf{k})\tau_y + m\tau_z\big] + \lambda \big(\mathbf{D}(\mathbf{k})\cdot\boldsymbol{\sigma}\big)\tau_z .$$0, are about three orders of magnitude smaller than the bare estimate $$h_{\mathbf{k}} = \sigma_0\big[u_1(\mathbf{k})\tau_x + u_2(\mathbf{k})\tau_y + m\tau_z\big] + \lambda \big(\mathbf{D}(\mathbf{k})\cdot\boldsymbol{\sigma}\big)\tau_z .$$1, directly illustrating the heavy Weyl regime (Guo et al., 2017).

A broader, noncanonical route was proposed for bulk WTe$$h_{\mathbf{k}} = \sigma_0\big[u_1(\mathbf{k})\tau_x + u_2(\mathbf{k})\tau_y + m\tau_z\big] + \lambda \big(\mathbf{D}(\mathbf{k})\cdot\boldsymbol{\sigma}\big)\tau_z .$$2, a nonmagnetic type-II Weyl semimetal. In that setting, disorder was argued to create local moments and enhance Kondo scattering, with anisotropic Kondo scales extracted as $$h_{\mathbf{k}} = \sigma_0\big[u_1(\mathbf{k})\tau_x + u_2(\mathbf{k})\tau_y + m\tau_z\big] + \lambda \big(\mathbf{D}(\mathbf{k})\cdot\boldsymbol{\sigma}\big)\tau_z .$$3 K for in-plane current and $$h_{\mathbf{k}} = \sigma_0\big[u_1(\mathbf{k})\tau_x + u_2(\mathbf{k})\tau_y + m\tau_z\big] + \lambda \big(\mathbf{D}(\mathbf{k})\cdot\boldsymbol{\sigma}\big)\tau_z .$$4 K for out-of-plane current. The same disordered samples showed a spontaneous Hall effect at zero magnetic field and a large second-harmonic Hall signal with quadratic current scaling. The interpretation advanced in that work is a disorder-driven Weyl-Kondo semimetal in which disorder-induced Kondo interactions pin the Fermi level near Weyl nodes and amplify Berry-curvature-driven transport (Manna et al., 12 Sep 2025).

Hexagonal heavy-fermion systems now substantially enlarge the candidate pool. A symmetry- and experiment-guided search identified chiral CePt$$h_{\mathbf{k}} = \sigma_0\big[u_1(\mathbf{k})\tau_x + u_2(\mathbf{k})\tau_y + m\tau_z\big] + \lambda \big(\mathbf{D}(\mathbf{k})\cdot\boldsymbol{\sigma}\big)\tau_z .$$5B and achiral Ce$$h_{\mathbf{k}} = \sigma_0\big[u_1(\mathbf{k})\tau_x + u_2(\mathbf{k})\tau_y + m\tau_z\big] + \lambda \big(\mathbf{D}(\mathbf{k})\cdot\boldsymbol{\sigma}\big)\tau_z .$$6NiGe$$h_{\mathbf{k}} = \sigma_0\big[u_1(\mathbf{k})\tau_x + u_2(\mathbf{k})\tau_y + m\tau_z\big] + \lambda \big(\mathbf{D}(\mathbf{k})\cdot\boldsymbol{\sigma}\big)\tau_z .$$7 and Ce$$h_{\mathbf{k}} = \sigma_0\big[u_1(\mathbf{k})\tau_x + u_2(\mathbf{k})\tau_y + m\tau_z\big] + \lambda \big(\mathbf{D}(\mathbf{k})\cdot\boldsymbol{\sigma}\big)\tau_z .$$8Co$$h_{\mathbf{k}} = \sigma_0\big[u_1(\mathbf{k})\tau_x + u_2(\mathbf{k})\tau_y + m\tau_z\big] + \lambda \big(\mathbf{D}(\mathbf{k})\cdot\boldsymbol{\sigma}\big)\tau_z .$$9Si$m\tau_z$0 as candidate topological heavy-fermion systems. In CePt$m\tau_z$1B, the relevant space group is chiral SG 180, and the material combines Kondo behavior with the symmetry setting required for chiral Weyl-Kondo nodes. In Ce$m\tau_z$2NiGe$m\tau_z$3, transport, Hall, and thermodynamic measurements support a semimetallic heavy-fermion regime with Kondo signatures and an intrinsic-dominated anomalous Hall effect compatible with Berry curvature from a Weyl-Kondo nodal-line state (Lin et al., 25 Feb 2026).

5. Relation to Kondo screening in Weyl and Dirac environments

Single-impurity studies clarify which parts of Weyl-Kondo physics are specific to coherent lattices and which already appear locally. In three-dimensional Dirac and Weyl systems, the density of states at an undoped node is pseudogapped, so Kondo screening can be suppressed or require a critical coupling. One analysis found that at the Dirac point the Kondo effect is unlikely because of the pseudogapped density of states, while time-reversal-symmetry-breaking Weyl systems preclude Kondo screening through an effective impurity magnetic field. The same work showed that long-range scalar disorder generates a distribution of Kondo temperatures rather than a single $m\tau_z$4, producing strong non-Fermi-liquid behavior (Mitchell et al., 2015).

Numerical renormalization group calculations for multi-Dirac and multi-Weyl hosts sharpened this picture. In multi-Dirac node systems the low-energy physics falls into known pseudogap Kondo classes, and Kondo screening disappears as $m\tau_z$5. In time-reversal-breaking Weyl systems, screening survives only away from particle-hole symmetry, that is, for finite chemical potential. By contrast, inversion-breaking multi-Weyl systems are qualitatively richer: double- and triple-Weyl models display two regimes, $m\tau_z$6 and $m\tau_z$7, with the latter weakly dependent on $m\tau_z$8 and resembling a flat-band single-impurity Anderson model (Pedrosa et al., 2021).

A recent analytic result directly addresses the role of spin-momentum locking. For Weyl-type electrons with arbitrary spin texture $m\tau_z$9 on a spherical Fermi surface, the Kondo temperature depends only on the Fermi-surface-averaged spin

$\lambda$0

through

$\lambda$1

If $\lambda$2, the conventional Kondo scale is recovered; if $\lambda$3, $\lambda$4 vanishes. For an ideal isotropic Weyl cone, $\lambda$5, the spherical average vanishes, so perfect local spin-momentum locking does not by itself suppress the Kondo effect. The suppressing quantity is the net spin polarization of the Fermi surface, not the existence of helicity locking alone (Goto et al., 5 Jun 2025).

Surface Fermi arcs furnish another instructive limit. For a magnetic impurity on the surface of a time-reversal-invariant Weyl semimetal, a variational treatment of the Fermi-arc states found that any finite hybridization produces a positive binding energy, so the impurity is screened by surface states. The corresponding spin-spin correlation tensor $\lambda$6 is highly anisotropic, mirrors the arc spin texture, has nontrivial off-diagonal components, and changes pattern and correlation length as the chemical potential is tuned. The resulting screening cloud differs qualitatively from the Dirac-semimetal case and is a direct surface realization of Weyl-structured Kondo screening (Ma et al., 2017).

6. Field-theoretic descriptions, control parameters, and open directions

Beyond mean-field band constructions and impurity treatments, Weyl-Kondo physics has also been formulated as a continuum field theory of Dirac fermions coupled to a spin array. In that approach the fermionic action

$\lambda$7

admits an exact local chiral, Weyl, and Lorentz transformation that decouples the fermions from the spins. Because the transformation is anomalous, it generates an effective action for the spins containing kinetic terms, a long-ranged interaction, and a Wess-Zumino-like term, together with generalized chiral magnetic and Hall responses. This formulation makes explicit that anomaly physics can survive in a Kondo semimetal and that the spin sector can inherit topological terms from the Weyl or Dirac fermions it couples to (Rylands et al., 2021).

Control of Weyl-Kondo nodes by external symmetry breaking has likewise been developed at the band-structure level. A conduction-electron model with inversion breaking $\lambda$8 and Zeeman field $\lambda$9 on the diamond lattice yields a Dirac semimetal at $U$0, three distinct Weyl-semimetal phases labeled $U$1, $U$2, and $U$3, and a sequence of critical boundaries—$U$4-QBT, $U$5-ABT, $U$6-ABT, and $U$7-QBT—where Weyl nodes merge into quadratic or anisotropic band touchings before gap opening or the appearance of additional Fermi pockets. This provides the symmetry-based template for interpreting magnetic-field tuning and annihilation of Weyl-Kondo nodes in heavy-fermion materials (Grefe et al., 2020).

Several issues remain open. In YbPtBi, direct low-temperature spectroscopy of the heavy hybridized Weyl bands is still lacking, even though transport, Hall, and thermodynamic evidence strongly suggest a heavy Weyl regime (Guo et al., 2017). In the newer hexagonal candidates, the slave-boson treatment captures Kondo-driven heavy bands but neglects fluctuations, while structural ambiguities, disorder, and the proximity of frustrated magnetism complicate the identification of a fully coherent Weyl-Kondo phase (Lin et al., 25 Feb 2026). More generally, the central unresolved problem is not whether Kondo screening and Weyl topology can coexist—they clearly can—but how robust the resulting heavy Weyl quasiparticles remain near magnetic order, quantum criticality, disorder, and nonequilibrium transport regimes.