On exotic sphere fibrations, topological phases, and edge states in physical systems

TL;DR

This paper explores the connection between exotic sphere fibrations and topological phases in condensed matter systems, revealing new insights into geometric phases, edge states, and transport phenomena in topological insulators and related heterostructures.

Contribution

It introduces a novel mapping of exotic sphere fibrations to band topologies, linking advanced geometric concepts to physical topological phases and edge states in condensed matter.

Findings

Exotic sphere fibrations correspond to specific topological band structures.

Heterostructures of topological insulators exhibit models of Weyl semimetals.

Time-reversal symmetry breaking leads to new topological phenomena.

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.