Non-Hermitian topological states in 2D line-graph lattices: evolving triple exceptional points on reciprocal line graphs

Journal Article · Wed Dec 22 00:00:00 EST 2021 · New Journal of Physics

DOI:https://doi.org/10.1088/1367-2630/ac40cb· OSTI ID:1979329

Liu, Hang ^[1]; Meng, Sheng ^[2]; Liu, Feng ^[3]

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1. University of Utah, Salt Lake City, UT (United States); Songshan Lake Materials Laboratory, Guangdong (China); Chinese Academy of Sciences (CAS), Beijing (China); OSTI
2. Songshan Lake Materials Laboratory, Guangdong (China); Chinese Academy of Sciences (CAS), Beijing (China)
3. University of Utah, Salt Lake City, UT (United States)

Non-Hermitian (NH) topological states, such as the doubly-degenerate nodes dubbed as exceptional points (EPs) in Bloch band structure of 2D lattices driven by gain and loss, have attracted much recent interest. We demonstrate theoretically that in the three-site edge-centered lattices, i.e. the so-called line-graph lattices, such as kagome lattice which is a line graph of hexagonal lattice, there exist three types of triply-degenerate EPs evolving intriguingly on another set of line graphs in the reciprocal space. A single TEP (STEP) with ±1/3 topological charge moves faithfully along the edges of reciprocal line graphs with varying gain and loss, while two STEPs merge distinctively into one unconventional orthogonal double TEP (DTEP) with ±2/3 charge at the vertices, which is characterized with two ordinary self-orthogonal eigenfunctions but one surprising 'orthogonal' eigenfunction. Differently, in a modified line-graph lattice with an off-edge-center site, the ordinary coalesced state of DTEPs emerges with three identical self-orthogonal eigenfunctions. Such NH states and their evolution can be generally realized in various artificial systems, such as photonic and sonic crystals, where light and sonic vortex beams with different fractional twisting can be found. Our findings shed new light on fundamental understanding of gapless topological states in NH systems in terms of creation and evolution of high-order EPs, and open up new research directions to further link line graph and flow network theory coupled with topological physics, especially under non-equilibrium gain/loss conditions.

• Research Organization: University of Utah, Salt Lake City, UT (United States)
• Sponsoring Organization: China Postdoctoral Science Foundation; National Natural Science Foundation of China; USDOE Office of Science (SC), Basic Energy Sciences (BES)
• Grant/Contract Number: FG02-04ER46148
• OSTI ID: 1979329
• Journal Information: New Journal of Physics, Journal Name: New Journal of Physics Journal Issue: 12 Vol. 23; ISSN 1367-2630
• Publisher: IOP Publishing
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Physics
exceptional point
line graph
non-Hermitian systems
topological states