Linear magnetoresistance on the topological surface

A positive, nonsaturating, and dominantly linear magnetoresistance is demonstrated to occur in the surface state of a topological insulator having a wave-vector linear energy dispersion together with a finite positive Zeeman energy splitting. This linear magnetoresistance shows up within quite wide magnetic-field range in a spatially homogeneous system of high carrier density and low mobility in which the conduction electrons are in extended states and spread over many smeared Landau levels, and is robust against increasing temperature, in agreement with recent experimental findings in Bi${}_2$Se${}_3$ nanoribbons.

Figure 1

The calculated resistivity $R_{xx}$ as a function of the magnetic field $B$ having different effective $g$ factors: $g_z=0,10$, and $-10$ for a TI surface system with electron sheet density $N=1.3\times {10}^{12}{\mathrm{cm}}^{-2}$ in the cases of zero-magnetic-field mobility $\mu =0.2{\mathrm{m}}^2/\mathrm{Vs}$ (a) and $\mu =0.7{\mathrm{m}}^2/\mathrm{Vs}$ (b). Several integer-number positions of filling factor $\nu =2\pi N/\left(eB\right)$ are marked in (b).

Figure 2

The longitudinal resistivity $R_{xx}$ is shown as a function of the magnetic field $B$ for different values of zero-magnetic-field mobility: (a) $\mu =0.2$, (b) $0.35$, (c) $0.5$, (d) $0.65$, (e) $0.8$, and (f) $5{\mathrm{m}}^2/\mathrm{Vs}$. The inset of (a) illustrates the same for a larger magnetic-field range $0<B<30\mathrm{T}$. The filling factor $\nu$ is plotted versus the magnetic field in (f); and several integer-number positions of $\nu$ are also marked in (d) and (e). Here, the surface electron density $N=1.3\times {10}^{12}{\mathrm{cm}}^{-2}$ and the lattice temperature $T=0\mathrm{K}$.

Figure 3

$R_{xx}{N}^2$ is plotted as a function of the surface electron density $N$ at magnetic field $B=3\mathrm{T}$: (a) at different values of zero-field mobility $\mu$, and (b) at different values of zero-field conductivity $\sigma$.

Figure 4

The longitudinal resistivity of the surface state of a TI versus magnetic field $B$ at various lattice temperatures. Here, the zero-magnetic-field mobility at zero temperature is $\mu \left(0\right)=0.6{\mathrm{m}}^2/\mathrm{Vs}$.