Topological current for transverse electrical and thermal conductivity in thermoelectric effect

Thermoelectric efficiency of the traditional thermoelectric material is low, which restricts the large scale applications. Recently, the developing of the topological insulator provides a new opportunity to get high thermoelectric efficiency material. There are two effects in topological insulator: anomalous Hall and Nernst effect, which have contribution to the transport properties. Because of anomalous Hall and Nernst effect the electrical thermal conductivity have transverse parts, which affect the Seebeck coefficient. However, the transverse parts can be expressed by Berry curvature. By using of -mapping topological theory, the Berry curvature is studied and we find there is topological vortex in the momentum space. The Bloch wave function is zero at the topological vortex. Finally, the relationships between the topological vortex and the transverse electrical and thermal conductivity is given and how the topology affects the Seebeck coefficient is researched in detail.