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Analysis of Hermitian and non-Hermitian diabolic points and exceptional rings in parity-time symmetric ZRC and RLC dimers

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Abstract

We present the analysis of diabolic points in Hermitian and non-Hermitian electronic dimers. The condition of unbreakable Parity-time symmetry is established for both PT-symmetric ZRC and RLC dimers. We show how appears non-Hermitian degeneracy points in the spectrum and how they are protected against a Hermitian perturbation. When a non- Hermitian perturbation is added in the setup, the non-Hermitian diabolic point (NHDP) turns into a ring of exceptional points as in some Dirac and Weyl semimetals. Some simulations of oscillations around these particular points in LTspice are in perfect accordance with the one predicted analytically and numerically. This work opens a gold road for investigations on topological electrical circuits for robust transport of information at room temperature.

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References

  • Alaeian, H., Dionne, J.A.: Parity-time-symmetric plasmonic metamaterials. Phys. Rev. A 89(3), 033829 (2014)

    ADS  Google Scholar 

  • Alù, A., Engheta, N.: All optical metamaterial circuit board at the nanoscale. Phys. Rev. Lett. 103(14), 143902 (2009)

    PubMed  ADS  Google Scholar 

  • Arjona, V., Chernodub, M.N., Vozmediano, M.A.: Fingerprints of the conformal anomaly in the thermoelectric transport in Dirac and Weyl semimetals. Phys. Rev. B 99(23), 235123 (2019)

    CAS  ADS  Google Scholar 

  • Armitage, N.P., Mele, E.J., Vishwanath, A.: Weyl and Dirac semimetals in three-dimensional solids. Rev. Modern Phys. 90(1), 015001 (2018)

    MathSciNet  CAS  ADS  Google Scholar 

  • Baev, A., Prasad, P.N., Ågren, H., Samoć, M., Wegener, M.: Metaphotonics: an emerging field with opportunities and challenges. Phys. Rep. 594, 1–60 (2015)

    MathSciNet  ADS  Google Scholar 

  • Belopolski, I., Yu, P., Sanchez, D.S., Ishida, Y., Chang, T.R., Zhang, S.S., Xu, S.Y., Zheng, H., Chang, G., Bian, G., Jeng, H.T.: Signatures of a time-reversal symmetric Weyl semimetal with only four Weyl points. Nat. Commun. 8(1), 942 (2017)

    PubMed  PubMed Central  ADS  Google Scholar 

  • Bender, C.M., Boettcher, S.: Real Spectra in Non-Hermitian Hamiltonians Having PT-Symmetry. Phys. Rev. Lett. 80(24), 5243–5246 (1998)

    MathSciNet  CAS  ADS  Google Scholar 

  • Bender, C.M., Boettcher, S., Meisinger, P.N.: PT-symmetric quantum mechanics. J. Math. Phys. 40(5), 2201–2229 (1999)

    MathSciNet  ADS  Google Scholar 

  • Bender, C.M., Berry, M.V., Mandilara, A.: Generalized PT symmetry and real spectra. J. Phys. a: Math. Gen. 35(31), L467–L471 (2002)

    MathSciNet  ADS  Google Scholar 

  • Cerjan, A., Xiao, M., Yuan, L., Fan, S.: Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges. Phys. Rev. B 97(7), 075128 (2018)

    CAS  ADS  Google Scholar 

  • Cerjan, A., Huang, S., Wang, M., Chen, K.P., Chong, Y., Rechtsman, M.C.: Experimental realization of a Weyl exceptional ring. Nat. Photon. 13(9), 623–628 (2019)

    CAS  ADS  Google Scholar 

  • Chen, P.-Y., Sakhdari, M., Hajizadegan, M., Cui, Q., Cheng, M.M.-C., El-Ganainy, R., Alù, A.: Generalized parity–time symmetry condition for enhanced sensor telemetry. Nat. Electron. 1(5), 297–304 (2018)

    Google Scholar 

  • El-Ganainy, R., Makris, K.G., Khajavikhan, M., Musslimani, Z.H., Rotter, S., Christodoulides, D.N.: Non-Hermitian physics and PT symmetry. Nat. Phys. 14(1), 11–19 (2018)

    CAS  Google Scholar 

  • Engheta, N., Salandrino, A., Alu, A.: Circuit Elements at optical frequencies: nanoinductors, nanocapacitors, and nanoresistors. Phys. Rev. Lett. 95(9), 095504 (2005)

    PubMed  ADS  Google Scholar 

  • Feng, S.: Loss-induced super scattering and gain-induced absorption. Opt. Express 24(2), 1291 (2016)

    PubMed  ADS  Google Scholar 

  • Fotsa-Ngaffo, F., Tabeu, S.B., Tagouegni, S., Kenfack-Jiotsa, A.: Thresholdless characterization in space and time reflection symmetry electronic dimers. J. Opt. Soc. Am. B 34(3), 658 (2017)

    CAS  ADS  Google Scholar 

  • He, W.Y., Chan, C.T.: The emergence of Dirac points in photonic crystals with mirror symmetry. Sci. Rep. 5(1), 8186 (2015)

    PubMed  PubMed Central  Google Scholar 

  • Imhof, S., Berger, C., Bayer, F., Brehm, J., Molenkamp, L.W., Kiessling, T., Schindler, F., Lee, C.H., Greiter, M., Neupert, T., Thomale, R.: Topolectrical-circuit realization of topological corner modes. Nat. Phys. 14(9), 925–929 (2018)

    CAS  Google Scholar 

  • Kartashov, Y.V., Malomed, B.A., Torner, L.: Unbreakable PT symmetry of solitons supported by inhomogeneous defocusing nonlinearity. Opt. Lett. 39(19), 5641 (2014)

    PubMed  ADS  Google Scholar 

  • Klauck, F., Teuber, L., Ornigotti, M., Heinrich, M., Scheel, S., Szameit, A.: Observation of PT-symmetric quantum interference. Nat. Photon. 13(12), 883–887 (2019)

    CAS  ADS  Google Scholar 

  • Lim, L.K., Fuchs, J.N., Piéchon, F., Montambaux, G.: Dirac points emerging from flat bands in Lieb-kagome lattices. Phys. Rev. B 101(4), 045131 (2020)

    CAS  ADS  Google Scholar 

  • Lin, Z., Pick, A., Lončar, M., Rodriguez, A.W.: Enhanced spontaneous emission at third-order Dirac exceptional points in inverse-designed photonic crystals. Phys. Rev. Lett. 117(10), 107402 (2016a)

    PubMed  ADS  Google Scholar 

  • Lin, Q., Xiao, M., Yuan, L., Fan, S.: Photonic Weyl point in a two-dimensional resonator lattice with a synthetic frequency dimension. Nat. Commun. 7(1), 13731 (2016b)

    CAS  PubMed  PubMed Central  ADS  Google Scholar 

  • Lin, C.-L., Arafune, R., Liu, R.-Y., Yoshimura, M., Feng, B., Kawahara, K., Ni, Z., Minamitani, E., Watanabe, S., Shi, Y., Kawai, M., Chiang, T.-C., Matsuda, I., Takagi, N.: Visualizing type-II Weyl points in tungsten ditelluride by quasiparticle interference. ACS Nano 11(11), 11459–11465 (2017)

    CAS  PubMed  Google Scholar 

  • Lu, L., Fu, L., Joannopoulos, J.D., Soljačić, M.: Weyl points and line nodes in gyroid photonic crystals. Nat. Photon. 7(4), 294–299 (2013)

    CAS  ADS  Google Scholar 

  • Lu, Y., Jia, N., Su, L., Owens, C., Juzeliūnas, G., Schuster, D.I., Simon, J.: Probing the Berry curvature and Fermi arcs of a Weyl circuit. Phys. Rev. B 99(2), 020302 (2019)

    CAS  ADS  Google Scholar 

  • Lutsky, V., Luz, E., Granot, E.E., Malomed, B.A.: Making the PT symmetry unbreakable. In parity-time symmetry and its applications, pp. 443–464. Springer Singapore, Singapore (2018)

    Google Scholar 

  • Mann, C.R., Sturges, T.J., Weick, G., Barnes, W.L., Mariani, E.: Manipulating type-I and type-II Dirac polaritons in cavity-embedded honeycomb metasurfaces. Nat. Commun. 9(1), 2194 (2018)

    PubMed  PubMed Central  ADS  Google Scholar 

  • Milićević, M., Montambaux, G., Ozawa, T., Jamadi, O., Real, B., Sagnes, I., Lemaître, A., Le Gratiet, L., Harouri, A., Bloch, J., Amo, A.: Type-III and tilted Dirac cones emerging from flat bands in photonic orbital graphene. Phys. Rev. X 9(3), 031010 (2019)

    Google Scholar 

  • Miri, M.A., Alu, A.: Exceptional points in optics and photonics. Science 363(6422), eaar7709 (2019)

    MathSciNet  CAS  PubMed  Google Scholar 

  • Mock, A.: Comprehensive understanding of parity-time transitions in PT-symmetric photonic crystals with an antiunitary group theory. Phys. Rev. A 95(4), 043803 (2017)

    ADS  Google Scholar 

  • Mostafazadeh, A.: Pseudo-Hermiticity versus PT symmetry: the necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian. J. Math. Phys. 43(1), 205–214 (2002)

    MathSciNet  ADS  Google Scholar 

  • Nixon, S., Yang, J.: All-real spectra in optical systems with arbitrary gain-and-loss distributions. Phys. Rev. A 93(3), 031802 (2016)

    ADS  Google Scholar 

  • Noh, J., Huang, S., Leykam, D., Chong, Y.D., Chen, K.P., Rechtsman, M.C.: Experimental observation of optical Weyl points and Fermi arc-like surface states. Nat. Phys. 13(6), 611–617 (2017)

    CAS  Google Scholar 

  • Ozawa, T., Price, H.M., Amo, A., Goldman, N., Hafezi, M., Lu, L., Rechtsman, M.C., Schuster, D., Simon, J., Zilberberg, O., Carusotto, I.: Topological photonics. Rev. Modern Phys. 91(1), 015006 (2019)

    MathSciNet  CAS  ADS  Google Scholar 

  • Özdemir, ŞK., Rotter, S., Nori, F., Yang, L.: Parity–time symmetry and exceptional points in photonics. Nat. Mater. 18(8), 783–798 (2019)

    PubMed  ADS  Google Scholar 

  • Parkavi, J.R., Chandrasekar, V.K.: Unbreakable-symmetry and its consequence in a-symmetric dimer. J. Phys. a: Math. Theor. 53(19), 195701 (2020)

    MathSciNet  ADS  Google Scholar 

  • Rui, W.B., Hirschmann, M.M., Schnyder, A.P.: PT-symmetric non-Hermitian Dirac semimetals. Phys. Rev. B 100(24), 245116 (2019)

    CAS  ADS  Google Scholar 

  • Schindler, J., Lin, Z., Lee, J.M., Ramezani, H., Ellis, F.M., Kottos, T.: PT-symmetric electronics”. J. Phys. a: Math. Theor. 45(44), 444029 (2012)

    ADS  Google Scholar 

  • Soluyanov, A.A., Gresch, D., Wang, Z., Wu, Q., Troyer, M., Dai, X., Bernevig, B.A.: Type-II Weyl semimetals. Nature 527(7579), 495–498 (2015)

    CAS  PubMed  ADS  Google Scholar 

  • Suchkov, S.V., Fotsa-Ngaffo, F., Kenfack-Jiotsa, A., Tikeng, A.D., Kofane, T.C., Kivshar, Y.S., Sukhorukov, A.A.: Non-Hermitian trimers: PT-symmetry versus pseudo-Hermiticity. New J. Phys. 18(6), 065005 (2016)

    ADS  Google Scholar 

  • Tabeu, S.B., Fotsa-Ngaffo, F., Kenfack-Jiotsa, A.: Imaginary resistor based parity-time symmetry electronics dimers. Opt. Quant. Electron. 51(10), 335 (2019a)

  • Tabeu, S.B., Fotsa-Ngaffo, F., Kenfack-Jiotsa, A.: Non-Hermitian Hamiltonian of two-level systems in complex quaternionic space: an introduction in electronics. EPL (europhys. Lett.) 125(2), 24002 (2019b)

    ADS  Google Scholar 

  • Tabeu, S.B, F. Fotsa-Ngaffo, A. Kenfack-Jiotsa and Kazuhiro Shouno “Classification of positive, negative and imaginary components in non-hermitian systems and applications”, unpublished (2019c)

  • Tassin, P., Zhang, L., Koschny, T., Economou, E.N., Soukoulis, C.M.: Low-loss metamaterials based on classical electromagnetically induced transparency. Phys. Rev. Lett. 102(5), 053901 (2009)

    CAS  PubMed  ADS  Google Scholar 

  • Wang, H.X., Chen, Y., Hang, Z.H., Kee, H.Y., Jiang, J.H.: Type-ii Dirac photons. Npj Quantum Mater. 2(1), 54 (2017)

    ADS  Google Scholar 

  • Xu, Y., Zhang, C.: Dirac and Weyl rings in three-dimensional cold-atom optical lattices. Phys. Rev. A 93(6), 063606 (2016)

    ADS  Google Scholar 

  • Xu, Y., Wang, S.T., Duan, L.M.: Weyl exceptional rings in a three-dimensional dissipative cold atomic gas. Phys. Rev. Lett. 118(4), 045701 (2017)

    PubMed  ADS  Google Scholar 

  • Yan, Z., Wang, Z.: Tunable Weyl points in periodically driven nodal line semimetals. Phys. Rev. Lett. 117(8), 087402 (2016)

    PubMed  ADS  Google Scholar 

  • Yang, B., Guo, Q., Tremain, B., Liu, R., Barr, L.E., Yan, Q., Gao, W., Liu, H., Xiang, Y., Chen, J., Fang, C.: Ideal Weyl points and helicoid surface states in artificial photonic crystal structures. Science 359(6379), 1013–1016 (2018)

    MathSciNet  CAS  PubMed  ADS  Google Scholar 

  • Zhang, Y., Sun, Y., Yan, B.: Berry curvature dipole in Weyl semimetal materials: an ab initio study. Phys. Rev. B 97(4), 041101 (2018)

    CAS  ADS  Google Scholar 

  • Zhang, X., Ding, K., Zhou, X., Xu, J., Jin, D.: Experimental observation of an exceptional surface in synthetic dimensions with magnon polaritons. Phys. Rev. Lett. 123(23), 237202 (2019)

    CAS  PubMed  ADS  Google Scholar 

  • Zhao, H., Feng, L.: Parity–time symmetric photonics. Natl. Sci. Rev. 5(2), 183–199 (2018)

    CAS  Google Scholar 

  • Zhen, B., Hsu, C.W., Igarashi, Y., Lu, L., Kaminer, I., Pick, A., Chua, S.L., Joannopoulos, J.D., Soljačić, M.: Spawning rings of exceptional points out of Dirac cones. Nature 525(7569), 354–358 (2015)

    CAS  PubMed  ADS  Google Scholar 

  • Zheng, C.: Duality quantum simulation of a general parity-time-symmetric two-level system. EPL (europhys. Lett.) 123(4), 40002 (2018)

    ADS  Google Scholar 

  • Zyuzin, A.A., Simon, P.: Disorder-induced exceptional points and nodal lines in Dirac superconductors. Phys. Rev. B 99(16), 165145 (2019)

    CAS  ADS  Google Scholar 

  • Zyuzin, A.A., Zyuzin, A.Y.: Flat band in disorder-driven non-Hermitian Weyl semimetals. Phys. Rev. B 97(4), 041203 (2018)

    MathSciNet  CAS  ADS  Google Scholar 

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Authors and Affiliations

  1. Laboratory of Electronics and Signal Processing, Department of Electrical and Telecommunication Engineering, National Advanced School of Engineering, University of Yaoundé I, P.O. Box 8390, Yaoundé, Cameroon

    Stéphane Boris Tabeu

  2. Laboratory of Mechanics, Materials and Structures, Department of Physics, University of Yaoundé I, P.O. Box 812, Yaoundé, Cameroon

    Stéphane Boris Tabeu

  3. Nonlinear Physics and Complex Systems Group, Department of Physics, The Higher Teacher’s Training College, University of Yaoundé I, P.O. Box 47, Yaoundé, Cameroon

    Stéphane Boris Tabeu & Aurélien Kenfack-Jiotsa

  4. Institute of Wood Technologies, University of Yaoundé I, P.O. Box 306, Mbalmayo, Cameroon

    Fernande Fotsa-Ngaffo

  5. High-Tech and Slow Technology (HITASTEC), P.O. Box 105, Yaoundé, Cameroon

    Aurélien Kenfack-Jiotsa

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  1. Stéphane Boris Tabeu
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SBT, FFN and AKJ worked on the idea for the project. SBT made the developments and everyone participated in the discussions, the interpretations and the writing of the article.

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Tabeu, S.B., Fotsa-Ngaffo, F. & Kenfack-Jiotsa, A. Analysis of Hermitian and non-Hermitian diabolic points and exceptional rings in parity-time symmetric ZRC and RLC dimers. Opt Quant Electron 56, 218 (2024). https://doi.org/10.1007/s11082-023-05755-z

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