Dislocation defect as a bulk probe of monopole charge of multi-Weyl semimetals

Multi-Weyl semimetals feature band crossings with the dispersion that is, in general, linear in only one direction, and as a consequence their band structure is characterized by the monopole charge $n$ which can be greater than one. We show that a single screw dislocation defect oriented in the direction connecting the nodal points, which acts as an effective pseudomagnetic flux tube, can serve as a direct probe of the monopole charge $n\ge 1$ characterizing the bulk band structure of a multi-Weyl semimetal. To this end, as a proof of principle, we propose a rather simple mesoscopic setup in which the monopole charge leaves a direct imprint on the conductance measured in the plane perpendicular to the dislocation. In particular, the ratio of the positions of the neighboring maxima in the conductance as a function of the gate voltage can serve to deduce the monopole charge, while the value of the effective pseudomagnetic flux can be extracted from the position of a conductance maximum. We expect that these findings will prompt further studies on the role of multiple dislocations, as well as other topological lattice defects, such as grain boundaries and disclinations, in topological nodal materials.

Figure 1

Illustration of the setup for the transport experiment probing the monopole charge in a multi-Weyl semimetal. The screw dislocation is characterized by a Burgers vector along the $z$ axis generating an effective pseudomagnetic field $B_D={\mathrm{\Phi }}_D/\pi a^2$ pointing in the same direction as the Burgers vector. The radius of the dislocation core is $a$. The leads are placed in the $x\text{−}z$ plane and are biased at a voltage $V$. The monopole charge and the effective flux are directly imprinted in the measured dependence of the conductance on the gate voltage (see Fig. 2).

Figure 2

Conductance (dimensionless) calculated from the analytical Eq. (13), as a function of applied bias $V$ [in units of ${\alpha }_n{(\hslash /a)}^n]$ at a finite temperature $T$. The solid blue (dotted red) line corresponds to a pseudomagnetic flux $N_{\varphi }=1\left(N_{\varphi }=1.8\right)$. (a)–(c) correspond to the values of the monopole charge $n=1,n=2$, and $n=3$, respectively.