On exotic sphere fibrations, topological phases, and edge states in physical systems
Abstract
We suggest that exotic sphere fibrations can be mapped to band topologies in condensed matter systems. These fibrations can correspond to geometric phases of two double bands or state vector bases with second Chern numbers m+n and -n respectively. They can be related to topological insulators, magneto-electric effects, and photonic crystals with special edge states. We also consider time-reversal symmetry breaking perturbations of topological insulator, and heterostructures of topological insulators with normal insulators and with superconductors. We consider periodic TI/NI/TI/NI' heterostuctures, and periodic TI/SC/TI/SC' heterostuctures. They also give rise to models of Weyl semimetals which have thermal and electrical transports.
Keywords
Cite
@article{arxiv.1304.0046,
title = {On exotic sphere fibrations, topological phases, and edge states in physical systems},
author = {Hai Lin and Shing-Tung Yau},
journal= {arXiv preprint arXiv:1304.0046},
year = {2013}
}
Comments
23 pages; journal version