Magnetotransport in the Weyl semimetal in the quantum limit - the role of the topological surface states

We theoretically study the magnetoconductivity of the Weyl semimetal having a surface boundary under $E$ || $B$ geometry and demonstrate that the topological surface state plays an essential role in the magnetotransport. In the long-range disorder limit where the scattering between the two Weyl nodes vanishes, the conductivity diverges in the bulk model (i.e., periodic boundary condition) as usually expected, since the direct inter-node relaxation is absent. In the presence of the surface, however, the inter-node relaxation always takes place through the mediation by the surface states, and that prevents the conductivity divergence. The magnetic-field dependence becomes also quite different between the two cases, where the conductivity linearly increases in $B$ in the surface boundary case, in contrast to $B$-independent behavior in the bulk-periodic case. This is an interesting example in which the same system exhibits completely different properties in the surface boundary condition and the periodic boundary condition even in the macroscopic size limit. In the short-range regime where the direct intervalley scattering is dominant, the surface states are irrelevant and the conductivity approaches that of the bulk periodic model.