Topological orders of monopoles and hedgehogs: From electronic and magnetic spin-orbit coupling to quarks

Journal Article · Mon Mar 30 00:00:00 EDT 2020 · Physical Review B

DOI:https://doi.org/10.1103/PhysRevB.101.115144· OSTI ID:1767746

Nikolić, Predrag ^[1]

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1. George Mason Univ., Fairfax, VA (United States); Johns Hopkins Univ., Baltimore, MD (United States); OSTI

Topological states of matter are, generally, quantum liquids of conserved topological defects. We establish this by constructing and analyzing topological field theories which introduce gauge fields to describe the dynamics of singularities in the original field configurations. In this work, homotopy groups are utilized to identify topologically protected singularities, and the conservation of their protected number is captured by a topological action term that unambiguously obtains from the given set of symmetries. Stable phases of these theories include quantum liquids with emergent massless Abelian and non-Abelian gauge fields, as well as topological orders with long-range quantum entanglement, fractional excitations, boundary modes, and unconventional responses to external perturbations. This paper focuses on the derivation of topological field theories and basic phenomenological characterization of topological orders associated with homotopy groups π_n(Sⁿ), n ≥ 1 . These homotopies govern monopole and hedgehog topological defects in d = n + 1 dimensions, and enable the generalization of both weakly interacting and fractional quantum Hall liquids of vortices to d > 2 . Hedgehogs have not been in the spotlight so far, but they are particularly important defects of magnetic moments because they can be stimulated in realistic systems with spin-orbit coupling, such as chiral magnets and d = 3 topological materials. We predict topological orders in systems with U(1) × Spin(d) symmetry in which fractional electric charge attaches to hedgehogs. Monopoles, the analogous defects of charge or generic U(1) currents, may bind to hedgehogs via Zeeman effect, or effectively emerge in purely magnetic systems. The latter can lead to spin liquids with different topological orders than that of the resonant valence bond spin liquid. Charge fractionalization of quarks in atomic nuclei is also seen as possibly arising from the charge-hedgehog attachment.

• Research Organization: Energy Frontier Research Centers (EFRC) (United States). Institute for Quantum Matter (IQM); Johns Hopkins Univ., Baltimore, MD (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
• Grant/Contract Number: SC0019331
• OSTI ID: 1767746
• Alternate ID(s): OSTI ID: 1607797
• Journal Information: Physical Review B, Journal Name: Physical Review B Journal Issue: 11 Vol. 101; ISSN 2469-9950; ISSN PRBMDO
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
charge transport
defects
magnetism and spin physics
materials and chemistry by design
optics
quantum information science
superconductivity
synthesis (novel materials)
thermal conductivity