Chiral magnetic effect in the absence of Weyl node

The nodal points in a Weyl semimetal are generally considered as the causes of the chiral anomaly and the chiral magnetic effect (CME). Employing a linear-response analysis of a two-band lattice model, we show that the Weyl nodes and thus the chirality are not required for the CME, while they remain crucial for the chiral anomaly. Similar to the anomalous Hall effect, the CME results directly from the Berry curvature of energy bands, even when there is no monopole source from the Weyl nodes. Therefore, the phenomenon of the CME could be observed in a wider class of materials. Motivated by this result, we suggest that the nodeless CME may appear in three-dimensional quantum anomalous Hall insulators, but after they become metallic due to the band deformation caused by inversion symmetry breaking.

Figure 1

Various types of semimetals. (a) Two conical bands that touch at a nodal point. The Fermi surface is a point. (b) Tilted cones (or type-II Weyl semimetal [23]). The Fermi surfaces enclose an electron pocket and a hole pocket. (c) Overlapped bands that do not touch with each other. Dashed lines denote the location of the chemical potential.

Figure 2

Phase diagram of the Hamiltonian in Eq. (2) for $a\ge 0$. Here, a circled number (in blue) shows the number of Weyl nodes in a particular phase. Doubly circled numbers indicate that they are double-Weyl nodes (see the Appendix for more details). This occurs when $a=0$ and $1<\left|m\right|<3$ (two red line segments). Outside the colored regions, the system is a trivial phase without node. The vertical dashed line indicates the path calculated in the right panels of Fig. 4.

Figure 3

Band energies as functions of $k_z\left(k_x=k_y\right)$. The parameters are (a) $m=1$ (a single merged node with zero topological charge) and (b) $m=0.8$ (nontouching energy bands). Here $a=0$ and $t_1=1$.

Figure 4

Hall conductivity ${\sigma }_H$ (in units of $e^2/h$) and CME coefficient $\alpha$ (in units of $e^2/h^2$). Left panels: $a=0$ and $m\in [0,3]$ (along the positive $a$ axis in Fig. 2). Right panels: $m=0.5$ and $a\in [0,2]$ (along the vertical dashed line in Fig. 2). The parameter $t_1$ varies from 0 to 1 with step 0.25. Temperature $T={10}^{-2}$ and the chemical potential $\mu =0$. Phase boundaries at $t_1=0$ are denoted by the vertical dotted lines. The calculations are done with ${600}^3$ lattice sites.