Space, matter and topology

Abstract

An old branch of mathematics, Topology, has opened the road to the discovery of new phases of matter. A hidden topology in the energy spectrum is the key for novel conducting/insulating properties of topological matter.

Invited Commentary for Nature Physics Focus issue on Topological Matter, 8 pages 1 figure

References in corpus (14)

• Topological Insulators
• Topological insulators and superconductors
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Cosmic Topology
• Dodecahedral space topology as an explanation for weak wide-angle temperature correlations in the cosmic microwave background
• Constraining the Topology of the Universe
• A road to reality with topological superconductors
• Equivalent topological invariants of topological insulators

Cited by in corpus (11)

• Giant spontaneous Hall effect in a nonmagnetic Weyl-Kondo semimetal
• Probing topology by "heating": Quantized circular dichroism in ultracold atoms
• Topological quantum critical points in the extended Bose-Hubbard model
• Quenched dynamics and spin-charge separation in an interacting topological lattice
• Interaction induced fractionalization and topological superconductivity in the polar molecules anisotropic $t-J$ model
• Topological order, mixed states and open systems
• A topological current divider
• Majorana Fermions and Orthogonal Complex Structures
• Flat connections in three-manifolds and classical Chern-Simons invariant
• Topics in Quantum Networking
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping