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 combined 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 zero magnetic field and zero gate voltage, or at large perpendicular magnetic field and nonzero gate voltage, ZT has a 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 zero perpendicular magnetic field and zero gate voltage, the height of the nth peak of S-c is kb/eIn2/(vertical bar n vertical bar + 1/2) and kb/eIn2 vertical bar n vertical bar for the longitudinal magnetic flux phi(parallel to) = 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 at strong disorder. These characteristics (that ZT has a large value, is easily regulated, and is robust against the disorder) are very beneficial for the application of thermoelectricity.