The influence of 1D topological states on the thermoelectric properties of Bi₂Te₃ from the perspective of coupled Tomonaga-Luttinger liquids (TLLs).

Bi₂Te₃, the first discovered strong 3D topological insulator is also one of the best known thermoelectric materials at ambient conditions. It has been recently discovered that in such 3D topological insulator each skew dislocation will host a pair of 1D topological states – a helical TLL. Any 1D state gives rise to huge Seebeck coefficient, a fact that is used in thermoelectricity enhancement by engineering of low dimensional nano-structures. One could then ascribe the outstanding thermoelectric properties of Bi₂Te₃ to these 1D topological states. However, in order to achieve a non-zero Seebeck coefficient, a mechanism that will induce curvature and backscattering of the 1D states is needed. One also needs a good description of 3D electronic states within a dense network of dislocations and proof that a large overlap with the 1D states is possible. In this study we show how to overcome these obstacles and then derive an exact analytic formula for Seebeck coefficient within a framework of coupled TLLs. Our study is applicable either to the regime of an extremely weakly n-doped material or to the case where the transport is activated by photo-excitations.