Gate voltage controlled thermoelectric figure of merit in three-dimensional topological insulator nanowires

The thermoelectric properties of the surface states in three-dimensional topological insulator nanowires are studied. The Seebeck coefficients $S_c$ and the dimensionless thermoelectrical figure of merit $ZT$ are obtained by using the tight-binding Hamiltonian combining with the nonequilibrium Green's function method. They are strongly dependent on the gate voltage and the longitudinal and perpendicular magnetic fields. By changing the gate voltage or magnetic fields, the values of $S_c$ and $ZT$ can be easily controlled. At the zero magnetic fields and zero gate voltage, or at the large perpendicular magnetic field and nonzero gate voltage, $ZT$ has the large value. Owing to the electron-hole symmetry, $S_c$ is an odd function of the Fermi energy while $ZT$ is an even function regardless of the magnetic fields. $S_c$ and $ZT$ show peaks when the quantized transmission coefficient jumps from one plateau to another. The highest peak appears while the Fermi energy is near the Dirac point. At the zero perpendicular magnetic field and zero gate voltage, the height of $n$th peak of $S_C$ is $\frac{k_B}{e}\texttt{ln}2/(|n|+1/2)$ and $\frac{k_B}{e}\texttt{ln}2/|n|$ for the longitudinal magnetic flux $\phi_{\parallel} = 0 $ and $\pi$, respectively. Finally, we also study the effect of disorder and find that $S_c$ and $ZT$ are robust against disorder. In particular, the large value of $ZT$ can survive even if at the strong disorder. These characteristics (that $ZT$ has the large value, is easily regulated, and is robust against the disorder) are very beneficial for the application of the thermoelectricity.