Effect of impurity resonant states on optical and thermoelectric properties on the surface of a topological insulator

Abstract

We investigate the thermoelectric effect on a topological insulator surface with particular interest in impurity-induced resonant states. To clarify the role of the resonant states, we calculate the dc and ac conductivities and the thermoelectric coefficients along the longitudinal direction within the full Born approximation. It is found that at low temperatures, the impurity resonant state with strong energy de-pendence can lead to a zero-energy peak in the dc conductivity, whose height is sensitively dependent on the strength of scattering potential, and even can reverse the sign of the thermopower, implying the switching from n- to p-type carriers. Also, we exhibit the thermoelectric signatures for the filling process of a magnetic band gap by the resonant state. We further study the impurity effect on the dynamic optical conductivity, and find that the resonant state also generates an optical conductivity peak at the absorption edge for the interband transition. These results provide new perspectives for understanding the doping effect on topological insulator materials.

Figure 1

Evolution of (a) real and imaginary parties of impurity self-energies ∑₀(ω) and of (b) DOS with impurity potential U, where a resonant state is developed remarkably. (c) The position of DOS resonant peak as a function of U. (d) The electron spectrum function A(k, ω) as functions of k and ω for U = 0 (left side) and U = 1 (right side). The other parameters are $\Lambda =300,T=0.01,M=0,\hslash v_F=1$, and n _i = 0.01.

Figure 2

(a–c) Dependence on chemical potential μ of the electric conductivity σ, the thermopower S, and the figure of merit ZT for different scalar potential U = 0, 1, 2, 4. The other parameters are the same as in Fig. 1.

Figure 3

(a–c) The electric conductivity σ, the thermopower S, and the figure of merit ZT, respectively, at the Fermi level μ = 0 as a function of temperature T for various impurity potential U as indicated. The other parameters are the same as in Fig. 1.

Figure 4

(a–d) Evolution of energy dispersion with impurity potential U = 0, 1, 2, 4 for gapped surface states. Dependence of (e) ∑_z(ω) and (f) ∑₀(ω) on U. The magnetic potential is chosen as M = 0.8 and the other parameters are the same as in Fig. 1.

Figure 5

(a–c) The electric conductivity σ, the thermopower S, and the figure of merit ZT as a function of μ for U = 0, 1, 2, 4. We chose M = 0.8 and the other parameters are the same as in Fig. 1.

Figure 6

The optical conductivity σ(Ω) as a function of photon frequency Ω for gapless case M = 0 (a) and gapped case M = 0.8 (b). Insets are the blowup in the vicinity of Ω = 0 for corresponding main frame. The other parameters are the same as in Fig. 1.