Evidence for correlation effects in noncentrosymmetric type-II Weyl semimetals

Topological fermions have mainly been addressed in the limit of weakly correlated systems, while the realization of Kondo-like physics arising from Dirac-Weyl fermions and implying strong correlations is rare. The noncentrosymmetric Weyl fermion $R\mathrm{AlGe}$ compounds (with $R=\mathrm{La} \mathrm{and} \mathrm{Ce}$) provide a promising playground for revealing the impact of electronic correlations driven by $f$-electron states on Weyl fermions. Here, we tackle their charge dynamics as a function of temperature. Besides spotting typical optical signatures of a type-II Weyl semimetal in both materials, we discover that electronic correlations at low temperatures renormalize the nontrivial bands hosting the Weyl nodes and lead to a reduction of the Fermi velocity as well as an enhancement of the charge carriers effective mass in CeAlGe with respect to LaAlGe, both being a fingerprint of a so-called Weyl-Kondo system.

Figure 1

$T$ dependence of the real part ${\sigma }_1\left(\omega \right)$ of the optical conductivity of (a) LaAlGe and (b) CeAlGe from the far-infrared up to the midinfrared frequency range (1 eV = $8.06548\times {10}^3{\mathrm{cm}}^{-1}$). The insets show ${\sigma }_1\left(\omega \right)$ in the entire measured energy interval at 300 and 5 K (please note the logarithmic energy scale).

Figure 2

Interband contribution $\mathrm{\Delta }{\sigma }_1\left(\omega \right)={\sigma }_1\left(\omega \right)-{\sigma }_1^{\text{Drude}}\left(\omega \right)$ at 5 K for (a) LaAlGe and (b) CeAlGe, obtained by subtracting the calculated Drude intraband $\left[{\sigma }_1^{\text{Drude}}\left(\omega \right)\right]$ component from the total ${\sigma }_1\left(\omega \right)$ (see insets). The thick dashed lines emphasize the linear frequency dependencies of $\mathrm{\Delta }{\sigma }_1\left(\omega \right)$, encountered in selected energy intervals (colored shaded areas). The vertical dashed and dotted lines mark the characteristic frequencies ${\mathrm{\Omega }}_1$ and ${\mathrm{\Omega }}_2$, respectively, which define the onset of linearities in $\mathrm{\Delta }{\sigma }_1\left(\omega \right)$ [32, 50]. The insets highlight ${\sigma }_1\left(\omega \right)$ at FIR energies together with the contribution ${\sigma }_1^{\text{Drude}}\left(\omega \right)$ obtained within the two-Drude approach (i.e., sum of the narrow (D1) and broad (D2) Drude terms, insets of Fig. S5 in SM [32]). A similar procedure was applied at all $T$.

Figure 3

$T$ dependence of the Fermi velocity $v_F$, extracted from $\mathrm{\Delta }{\sigma }_1\left(\omega \right)$ (Fig. 2). The dash-dot line for CeAlGe is a guide to the eyes, while the dashed one for LaAlGe corresponds to the functional $v_F\sim A+Bln(1/T)$ (see text) [55]. The tilting parameter (i.e., $\widehat{\mathit{w}}$ in Eq. (S3) and in Table I in SM [32]) is shown for CeAlGe as well [50]. Inset: $T$ dependence of the total Drude $SW$ (i.e., ${\omega }_p^2={\omega }_{p,D1}^2+{\omega }_{p,D2}^2$, ${\omega }_{p,Di}$ being the plasma frequencies of D1 and D2 Drude terms [32]), which follows a $T^2$ behavior (thick dashed line) below 200 K for both compounds [56, 57].