Quantum magnetotransport properties of topological insulators under strain

We present a detailed theoretical investigation of the quantum magnetotransport properties of topological insulators under strain. We consider an external magnetic field perpendicular to the surface of the topological insulator in the presence of strain induced by the substrate. The strain effects mix the lower and upper surface states of neighboring Landau levels into two unequally spaced energy branches. Analytical expressions are derived for the collisional conductivity for elastic impurity scattering in the first Born approximation. We also calculate the Hall conductivity using the Kubo formalism. Evidence for the beating of Shubnikov–de Haas oscillations is found from the temperature and magnetic field dependence of the collisional and Hall conductivities. In the regime of a strong magnetic field, the beating pattern is replaced by a splitting of the magnetoresistance peaks due to finite strain energy. These results are in excellent agreement with recent HgTe transport experiments.

Figure 1

Collisional conductivity as a function of Fermi energy for zero (black lines) and finite (red lines) strain energy. The velocity is taken to be $4\times {10}^5$ m/s, $B=2$ T, $T=5$ K, and $\Delta =4.2$ meV.

Figure 2

Collisional (black lines) and Hall (red lines) resistivities as a function of magnetic field for a fixed value of the strain energy. The velocity is taken to be $4\times {10}^5$ m/s, the Fermi energy to be 54 meV, $T=1$ K, and $\Delta =4.2$ meV.

Figure 3

Collisional resistivity as a function of magnetic field, using the same parameters as in Fig. 2.