Spawning rings of exceptional points out of Dirac cones
By B. Zhen, Chia Wei Hsu, Y. Igarashi, Ling Lu, Ido Kaminer, A. Pick, Song Liang Chua, John D. Joannopoulos, Marin Soljačić. Nature, 2015
819 citations recorded by the source corpus.
The Dirac cone underlies many unique electronic properties of graphene and topological insulators, and its band structure—two conical bands touching at a single point—has also been realized for photons in waveguide arrays, atoms in optical lattices, and through accidental degeneracy. Deformation of the Dirac cone often reveals intriguing properties; an example is the quantum Hall effect, where a constant magnetic field breaks the Dirac cone into isolated Landau levels. A seemingly unrelated phenomenon is the exceptional point, also known as the parity–time symmetry breaking point, where two resonances coincide in both their positions and widths. Exceptional points lead to counter-intuitive phenomena such as loss-induced transparency, unidirectional transmission or reflection, and lasers with reversed pump dependence or single-mode operation. Dirac cones and exceptional points are connected: it was theoretically suggested that certain non-Hermitian perturbations can deform a Dirac cone and spawn a ring of exceptional points. Here we experimentally demonstrate such an ‘exceptional ring’ in a photonic crystal slab. Angle-resolved reflection measurements of the photonic crystal slab reveal that the peaks of reflectivity follow the conical band structure of a Dirac cone resulting from accidental degeneracy, whereas the complex eigenvalues of the system are deformed into a two-dimensional flat band enclosed by an exceptional ring. This deformation arises from the dissimilar radiation rates of dipole and quadrupole resonances, which play a role analogous to the loss and gain in parity–time symmetric systems. Our results indicate that the radiation existing in any open system can fundamentally alter its physical properties in ways previously expected only in the presence of material loss and gain.
Subfields: Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/06a6dbc9dddb3ce774af35f78096d094f30bff45
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Citations in the corpus
- PT symmetry in a fractional Schrödinger equation (2016, background): “It is also known that in topological photonics [16–19], Dirac cones in the energy zones can be deformed by the PT symmetry, which results in the complex eigenvalues [20, 21] becoming distributed in a circular fashion.”
- Non-Hermitian systems and topology: A transfer-matrix perspective (2018, background): “[15] Bo Zhen, Chia Wei Hsu, Yuichi Igarashi, Ling Lu, Ido Kaminer, Adi Pick, Song-Liang Chua, John D Joannopoulos, and Marin Soljačić, “Spawning rings of exceptional points out of Dirac cones,” Nature 525, 354 (2015).”
- Exceptional points in optics and photonics (2019, background): “In addition, exceptional points have been demonstrated in photonic crystal slabs (60), in which out-of-plane radiation losses due to the finite thickness of the dielectric slab result in the merging of two eigenfrequency bands, inducing a ring of exceptional points in the wave number space.”
- Topological photonics (2018, background): “One example is photonic “tachyonlike” dispersion (Szameit et al., 2011) that was demonstrated in the form of exceptional rings in photonic crystals (Zhen et al., 2015) as well as “Fermi arc”-type states that connect between exceptional points in two-dimensional systems (Kozii and Fu, 2017; Malzard…”
- Edge States and Topological Invariants of Non-Hermitian Systems. (2018, neutral): “[11] Bo Zhen, Chia Wei Hsu, Yuichi Igarashi, Ling Lu, Ido Kaminer, Adi Pick, Song-Liang Chua, John D Joannopoulos, and Marin Soljačić, “Spawning rings of exceptional points out of dirac cones,” Nature 525, 354 (2015).”
- Experimental observation of optical Weyl points and Fermi arc-like surface states (2016, background): “The observation of Weyl points in optics can lead to a range of novel phenomena arising from the interplay of the Weyl dispersion and nonlinear [45], non-Hermitian [46], and quantum optics [47, 48].”