Disorder-driven Weyl-Kondo Semimetal Phase in WTe$_2$

Technical Summary: Disorder-Driven Weyl-Kondo Semimetal Phase in WTe$_2$

Problem and Motivation
The interplay between electronic correlations and band topology is a fertile ground for emergent quantum phases, exemplified by the Weyl–Kondo semimetal (WKSM). In established WKSM systems, such as the Ce$_3$Bi$_4$(Pt$_{1-x}$Pd$_x$)$_3$ family, Kondo screening renormalizes Weyl fermions into heavy quasiparticles, pinning Weyl nodes near the Fermi level. However, these systems typically require chemical substitution, pressure, or magnetic fields to access the WKSM phase. A central question remains whether disorder alone can drive a WKSM phase in a weakly correlated, nonmagnetic Weyl semimetal. This study investigates bulk WTe$_2$, a non-centrosymmetric, type-II Weyl semimetal, to determine if disorder can induce Kondo interactions that dynamically pin the Fermi level near Weyl nodes, thereby realizing a disorder-tuned WKSM phase.

Methodology
The authors synthesized bulk single crystals of WTe$_2$ using chemical vapor transport (CVT). To systematically probe disorder effects, three representative samples (S-1, S-2, and S-3) were selected with varying residual resistivity ratios (RRR) of $\sim$51, 15, and 6, respectively, for current along the $a$-axis. Lower RRR values indicate higher disorder strength. Structural quality was verified via X-ray diffraction (XRD), and stoichiometry was confirmed by energy-dispersive spectroscopy (EDS).

Transport measurements were conducted using a six-probe lock-in technique to record longitudinal ($\rho_{xx}$) and Hall ($\rho_{xy}$) resistivities under various current ($I$) and magnetic field ($B$) orientations ($I \parallel a, c$ and $B \parallel a, c$). Nonlinear transport was probed via second-harmonic Hall measurements ($\rho_{xy}^{2\omega}$) to detect Berry curvature dipole (BCD) responses. Theoretical analysis involved fitting resistivity data to Hamann expressions for Kondo scattering and modeling the system using a tight-binding model for a time-reversal preserving, inversion-broken type-II Weyl semimetal.

Key Results

1. Anisotropic Kondo Screening:

   • Samples with higher disorder (S-2 and S-3) exhibited a low-temperature upturn in resistivity, absent in the cleaner sample (S-1). The magnitude of this upturn was $\sim$25% in S-3 and 16% in S-2 at 2 K, scaling inversely with RRR.
   • The upturn was highly anisotropic: it was $\sim$25% for in-plane current ($I \parallel a$) but reduced to only 1.7% for out-of-plane current ($I \parallel c$) in S-3.
   • Fits to the Hamann expression yielded Kondo temperatures ($T_K$) of $16 \pm 2$ K ($I \parallel a$) and $9 \pm 2$ K ($I \parallel c$), with effective spin quantum numbers $S \approx 1$. This confirms the emergence of Kondo scattering from local magnetic moments, likely associated with W$^{4+}$ ions, and demonstrates its strong directional dependence consistent with type-II Weyl dispersion.

2. Magnetoresistance (MR) Anisotropy:

   • Magnetoresistance measurements revealed a broad low-temperature peak attributed to the suppression of Kondo spin-flip scattering.
   • The difference in MR between field orientations, $\delta(\text{MR}) = \text{MR}(B \parallel c) - \text{MR}(B \parallel a)$, showed a pronounced downturn at low temperatures for disordered samples, confirming that Kondo scattering suppression is direction-dependent. This anisotropy was negligible in the clean sample S-1.

3. Spontaneous Hall Effect (SHE):

   • A spontaneous Hall effect (SHE), characterized by a non-zero Hall resistivity at zero magnetic field ($\rho_{xy}(B=0) \neq 0$), was observed in the absence of external magnetic fields.
   • The SHE signal was symmetric with respect to magnetic field reversal and grew stronger as temperature decreased.
   • Crucially, the magnitude of the SHE was significantly enhanced in the most disordered sample (S-3) compared to cleaner samples, suggesting a direct link between disorder-driven correlations and the effect.
   • Carrier density analysis via a two-band model revealed that S-3 is not charge-compensated, indicating a shift in the Fermi energy away from perfect compensation, consistent with the Fermi level being pinned near Weyl nodes by Kondo interactions.

4. Nonlinear Hall Response:

   • Second-harmonic Hall measurements revealed a robust $V_{xy}^{2\omega}$ signal exhibiting quadratic scaling with current ($I^2$), indicative of a Berry curvature dipole (BCD) driven response.
   • This nonlinear signal was markedly enhanced in the disordered S-3 sample below 50 K.
   • Theoretical modeling indicates that the BCD conductivity peaks when the Fermi level is near the Weyl nodes. The enhancement in S-3 supports the hypothesis that Kondo interactions pin the Fermi level in this region.

Significance and Claims
The paper establishes that disorder acts as an effective tuning parameter to induce a Weyl–Kondo semimetal phase in the weakly correlated, nonmagnetic material WTe$_2$. The authors claim that:

• Disorder drives the formation of local magnetic moments that undergo Kondo screening, renormalizing the electronic structure.
• These Kondo interactions dynamically pin the Fermi level near the Weyl nodes, a condition typically achieved in heavy-fermion systems via chemical substitution or pressure.
• This pinning enhances Berry curvature-driven nonequilibrium transport, accounting for both the observed linear-order spontaneous Hall effect (driven by a non-perturbative distribution function in the presence of Berry curvature) and the quadratic-order nonlinear Hall effect (driven by the Berry curvature dipole).
• The findings identify disordered WTe$_2$ as a platform hosting "Weyl–Kondo fermions" and highlight disorder as a viable mechanism for inducing correlated topological phases in nonmagnetic Weyl semimetals, opening new directions for exploring transport properties in these systems.

The work does not claim to provide a complete theoretical description of disordered type-II WKSMs but rather provides experimental evidence of the phase and its key signatures (anisotropic Kondo scattering, SHE, and nonlinear Hall response) driven by disorder.