Criterion of surface electron transport in the correlated topological insulator SmB$_6$

The galvanomagnetic characteristics of SmB$_6$ single crystals are studied within the temperature range of $1.9$–$3.6$ K at different orientations of the crystal faces. As a result, the electrical resistivities of the surfaces corresponding to the (100), (110), (111), and (211) crystallographic planes are determined. It is shown that the effective parameters of charge carriers, which determine the surface conductivity in SmB$_6$, depend both on the orientation of the surface and on the method of its processing. It is found that the etching of polished polar surfaces formed by (100) planes leads at $1.9$ K to a decrease in the density and to an increase in the mobility of surface $n$-type charge carriers from $113/a^2$ and $1.12$ cm$^2$/(V s) to $0.76/a^2$ and $18$ cm$^2$/(V s), respectively (lattice parameter $a = 4.134$ Å). For etched nonpolar surfaces corresponding to the (110) and (111) planes, the maximum density of surface charge carriers (per unit area of the surface Brillouin zone) is found to increase by factors of $2.3$ and $3.9$, respectively. It is proposed to use this parameter as a simple criterion to identify the features of electron transport due to the nontrivial topology of the band structure of SmB$_6$.