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VOLUME 93 | ISSUE 6 | PAGE 378
Soft topological objects in topological media
J. I. Väyrynen*, G. E. Volovik*+

*Low Temperature Laboratory, Aalto University School of Science, FI-00076 AALTO, Finland
+Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia

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 N3 in terms of the Green's function {\cal G}(\omega,k_x,x) determines the fermion number of the kink, while in space dimension d=3 the topological invariant N5 in terms of the Green's function {\cal G}(\omega,k_x,k_y,k_z,z) determines quantization of Hall conductivity in the soliton plane within the topological insulators.

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