Soft topological objects in topological media

Abstract

Topological invariants in terms of the Green's function in momentum and real space determine properties of smooth textures within topological media. In space dimension D=1 the topological invariant N_3 in terms of the Green's function G(\omega,k_x,x) determines the fermion number of the 1D soliton, while in space dimension D=3 the topological invariant N_5 in terms of the Green's function G(\omega,k_x,k_y,k_z,z) determines quantization of Hall conductivity in the soliton plane within the topological insulators.