Soft topological objects in topological media

TL;DR

This paper explores how topological invariants derived from Green's functions characterize smooth textures in topological media, linking them to physical properties like fermion number and quantized Hall conductivity.

Contribution

It introduces a framework connecting topological invariants in Green's functions to physical properties of textures in different dimensions within topological media.

Findings

In 1D, the invariant N_3 determines fermion number of solitons.

In 3D, the invariant N_5 relates to quantized Hall conductivity.

The approach unifies topological characterization across dimensions.

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.