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A long-standing problem in the study of topological phases of matter has been to understand the types of fractional topological insulator (FTI) phases possible in 3+1 dimensions. Unlike ordinary topological insulators of free fermions, FTI phases are characterized by fractional 𝜃-angles,long-range entanglement, and fractionalization. Starting from a simple family of ℤ_N lattice gauge theories due to Cardy and Rabinovici, we develop a class of FTI phases based on the physical mechanism of oblique confinement and the modern language of generalized global symmetries. We dub these phases oblique topological insulators. Oblique TIs arise when dyons—bound states of electric charges and monopoles—condense, leading to FTI phases characterized by topological order, emergent one-forms symmetries, and gapped boundary states not realizable in 2+1-D alone.Based on the lattice gauge theory, we present continuum topological quantum field theories (TQFTs) for oblique TI phases involving fluctuating one-form and two-form gauge fields. We show explicitly that these TQFTs capture both the generalized global symmetries and topological orders seen in the lattice gauge theory. We also demonstrate that these theories exhibit a universal “generalized magneto-electric effect” in the presence of two-form background gauge fields. Moreover,we characterize the possible boundary topological orders of oblique TIs,finding a new set of boundary states not studied previously for these kinds of TQFTs.
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Reconfigurable Floquet elastodynamic topological insulator based on synthetic angular momentum bias
Originating with the discovery of the quantum Hall effect (QHE) in condensed matter physics, topological order has been receiving increased attention also for classical wave phenomena. Topological protection enables efficient and robust signal transport; mechanical topological insulators (TIs), in particular, are easy to fabricate and exhibit interfacial wave transport with minimal dissipation, even in the presence of sharp edges, defects, or disorder. Here, we report the experimental demonstration of a phononic crystal Floquet TI (FTI). Hexagonal arrays of circular piezoelectric disks bonded to a PLA substrate, shunted through negative electrical capacitance, and manipulated by external integrated circuits, provide the required spatiotemporal modulation scheme to break time-reversal symmetry and impart a synthetic angular momentum bias that can induce strong topological protection on the lattice edges. Our proposed reconfigurable FTI may find applications for robust acoustic emitters and mechanical logic circuits, with distinct advantages over electronic equivalents in harsh operating conditions.
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- Award ID(s):
- 1929849
- PAR ID:
- 10176490
- Date Published:
- Journal Name:
- Science Advances
- Volume:
- 6
- Issue:
- 29
- ISSN:
- 2375-2548
- Page Range / eLocation ID:
- eaba8656
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1126/sciadv.aba8656
