Parity-violating hybridization in heavy Weyl semimetals

We introduce a simple model to describe the formation of heavy Weyl semimetals in noncentrosymmetric heavy fermion compounds under the influence of a parity-mixing, onsite hybridization. A key aspect of interaction-driven heavy Weyl semimetals is the development of surface Kondo breakdown, which is expected to give rise to a temperature-dependent reconfiguration of the Fermi arcs and the Weyl cyclotron orbits which connect them via the chiral bulk states. Our theory predicts a strong temperature-dependent transformation in the quantum oscillations at low temperatures. In addition to the effects of surface Kondo breakdown, the renormalization effects in heavy Weyl semimetals will appear in a variety of thermodynamic and transport measurements.

Figure 1

(a) Topological quantum critical point (tQCP) at the nexus between normal and topological Kondo insulators (KI/TKIs) and heavy Weyl semimetals (hWSMs). $g$ and $W$ are the band tuning and inversion symmetry breaking parameters, respectively. At the tQCP, charge neutrality pins the bulk Dirac cone to the Fermi energy (occupied bands indicated by light blue). Finite $W>0$ splits the Dirac point into four symmetry-related Weyl points, pinned to the Fermi energy. (b) Breaking of inversion symmetry leads to a finite onsite hybridization $W>0$.

Figure 2

(a) Kondo Breakdown in a heavy Weyl semimetal, contrasting the spectrum before (solid lines) and after (dashed lines) surface Kondo breakdown as a function of $k_z$ at $k_x=0$. Surface spectrum (b) before and (c) after surface Kondo breakdown: red and blue lines indicate the Fermi arcs on the top and bottom surfaces, respectively. Black dots indicate the projection of the Weyl nodes onto the surface. Parameters were taken to be $(t_x,t_y,t_z,\mu ,\alpha ,V_x,V_y,V_z,W_2,b,\lambda )=(2,1,1,-6,-0.1,0.7,0.7,1.05,0.8,0.89,0.087)$ in Eq. (5). (d) Sche-matic of the Weyl orbits, where arrows indicate the quasiparticle trajectory.

Figure 3

(a) A line-node semimetal: when $\vec{W}=0$, the line-node solution from Eq. (6) is determined by the intersections $\{r_1,r_2\}={\mathcal{S}}_I\cap {\mathcal{S}}_{II}$ indicated by blue lines. (b) A Weyl semimetal: When $\vec{W}\ne 0$, point-node solutions of Eq. (6), indicated by blue dots, develop at the intersections of plane ${\mathcal{S}}_{III}$ normal to $\vec{W}$ with the line nodes, ${\mathcal{S}}_I\cap {\mathcal{S}}_{II}\cap {\mathcal{S}}_{III}$.

Figure 4

(a) Schematic plot of the bulk nodal rings centered at $k_y$ axis. On the $\left(011\right)$ surface, the surface flat bands will emerge inside the circles which are the projection of the bulk nodal rings. The surface spectrum as a function of $(k_x,k_z^{\prime }=\frac{1}{\sqrt{2}}(k_z-k_y))$ from the Hamiltonian Eq. (5) with $(t_x,t_y,t_z,\mu ,\alpha ,W_x,W_y,W_z,W_0)=(2,1,1,-6.5,-0.1,2,2,2,1.8)$. (b) in the absence of surface Kondo breakdown and (c) in the presence of surface Kondo breakdown. The surface spectrum as a function of $k_z^{\prime }=\frac{1}{\sqrt{2}}(k_z-k_y)$ at $k_x=0$, (d) in the absence of surface Kondo breakdown, and (e) in the presence of surface Kondo breakdown.