Seebeck Effect And Nernst Effect In HgTe/CdTe Quantum Wells

In this paper, we investigate the Seebeck effect and Nernst effect in HgTe/CdTe quantumwells, which are topological insulators, by using the Landauer-Büttiker formalism combinedwith the nonequilibrium Green’s function method.Firstly, we research the Seebeck effect for HgTe/CdTe quantum wells in a two-terminaldevice. We calculate the Seebeck coefficient changes with Fermi energy EFunder zeromagnetic field at different temperatures for the material parameterM=10meVand M=2meV. The results indicate that the Seebeck coefficient peaks when Fermi energy EFcrosses the discrete transverse channels where quantized transmission coefficient jumps fromone step to another. For the material parameter M=10meV, the magnitude of the Seebeckcoefficient increases gradually when the temperature increases under no magnetic field. Theheight of nth peak is [ln2/1] for E2+N F>0in the two-terminal system. For the materialparameter M=2meV，the height of nth peak is [ln2/2] when transmission coefficient5+N at zero temperature is not zero value. In addition, with the rises of temperature, the Seebeckcoefficient increases gradually when the transmission coefficient is not zero. Whentransmission coefficient at zero temperature is near zero value, the value of the Seebeckcoefficient is very large. Moreover, the Seebeck coefficient decreases gradually withincreasing temperature. Next, we study the perpendicular magnetic field effect on the Seebeckeffect for the material parameter M=10meV. For a perpendicular magnetic field, bycomparing the energy band, the Seebeck coefficient shows peaks when Fermi energy EFpasses the Landau levels, and the Seebeck coefficient shows valleys between adjacent Landaulevels. The Landau levels formed valence band make the Seebeck coefficient appear negativepeak values, and the Landau levels formed in the conduction band make Seebeck coefficientappear positive peak values.Finally, we investigate the Nernst effect for HgTe/CdTe quantum wells in a four-terminalsystem. Since Nernst effect will be generated when the magnetic field is applied, we use themethod of applying a perpendicular magnetic field in this paper. We investigate the perpendicular magnetic field effect on the Nernst effect for the materialparameter M=10meV. The results indicate that the Nernst coefficient shows peaks whenthe Fermi energy EFpasses the Landau levels, and the Nernst coefficient shows valleysbetween adjacent Landau levels. At E F=0, due to no Landau levels, there is no peak. Withincreasing temperature, the Nernst coefficient increases gradually. In addition, some peaksand valleys vanish.