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Journal of Low Temperature Physics

, Volume 191, Issue 1–2, pp 49–60 | Cite as

Quantum Transport and Non-Hermiticity on Flat-Band Lattices

  • Hee Chul Park
  • Jung-Wan Ryu
  • Nojoon MyoungEmail author
Article

Abstract

We investigate quantum transport in a flat-band lattice induced in a twisted cross-stitch lattice with Hermitian or non-Hermitian potentials, with a combination of parity and time-reversal symmetry invariant. In the given system, the transmission probability demonstrates a resonant behavior on the real part of the energy bands. Both of the potentials break the parity symmetry, which lifts the degeneracy of the flat and dispersive bands. In addition, non-Hermiticity conserving PT-symmetry induces a transition between the unbroken and broken PT-symmetric phases through exceptional points in momentum space. Characteristics of non-Hermitian and Hermitian bandgaps are distinguishable: The non-Hermitian bandgap is induced by separation toward complex energy, while the Hermitian bandgap is caused by the expelling of available states into real energy. Deviation of the two bandgaps follows as a function of the quartic power of the induced potential. It is notable that non-Hermiticity plays an important role in the mechanism of generating a bandgap distinguishable from a Hermitian bandgap.

Keywords

Non-Hermiticity Flat bands Quantum transport 

Notes

Acknowledgements

This work was supported by Project IBS-R024-D1 and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2017076824), and research fund from Chosun University 2017.

References

  1. 1.
    S. Murakami, N. Nagaosa, S.-C. Zhang, Dissipationless quantum spin current at room temperature. Science 301, 1348 (2003)ADSCrossRefGoogle Scholar
  2. 2.
    C.L. Kane, E.J. Mele, \(Z_2\) topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005)ADSCrossRefGoogle Scholar
  3. 3.
    B.A. Bernevig, T.L. Hughes, S.-C. Zhang, Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757 (2006)ADSCrossRefGoogle Scholar
  4. 4.
    M.Z. Hasan, C.L. Kane, Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045 (2010)ADSCrossRefGoogle Scholar
  5. 5.
    S. Flach, D. Leykam, J.D. Bodyfelt, P. Matthies, A.S. Desyatnikov, Detangling flat bands into Fano lattices. Europhys. Lett. 105, 30001 (2014)ADSCrossRefGoogle Scholar
  6. 6.
    W. Maimaiti, A. Andreanov, H.C. Park, O. Gendelman, S. Flach, Compact localized states and flat-band generators in one dimension. Phys. Rev. B 95, 115135 (2017)ADSCrossRefGoogle Scholar
  7. 7.
    S. Flach, R. Khomeriki, Fractional lattice charge transport. Sci. Rep. 7, 40860 (2017)ADSCrossRefGoogle Scholar
  8. 8.
    D. Leykam, J.D. Bodyfelt, A.S. Desyatnikov, S. Flach, Localization of weakly disordered flat band states. Eur. Phys. J. B 90, 1 (2017)ADSCrossRefGoogle Scholar
  9. 9.
    C.M. Bender, S. Boettcher, Real spectra in non-Hermitian Hamiltonians having PT symmetry. Phys. Rev. Lett. 80, 5243 (1998)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    R. El-Ganainy, K.G. Makris, D.N. Christodoulides, Z.H. Musslimani, Theory of coupled optical PT-symmetric structures. Opt. Lett. 32, 2632 (2007)ADSCrossRefzbMATHGoogle Scholar
  11. 11.
    A. Guo et al., Observation of PT-symmetry breaking in complex optical potentials. Phys. Rev. Lett. 103, 093902 (2009)ADSCrossRefGoogle Scholar
  12. 12.
    C.E. Rüter et al., Observation of parity-time symmetry in optics. Nat. Phys. 6, 192 (2010)CrossRefGoogle Scholar
  13. 13.
    A. Regensburger et al., Parity-time synthetic photonic lattices. Nature (London) 488, 167 (2012)ADSCrossRefGoogle Scholar
  14. 14.
    A. Cerjan, A. Raman, S. Fan, Exceptional contours and band structure design in parity-time symmetric photonic crystals. Phys. Rev. Lett. 116, 203902 (2016)ADSCrossRefGoogle Scholar
  15. 15.
    D.R. Nelson, V.M. Vinokur, Boson localization and correlated pinning of superconducting vortex arrays. Phys. Rev. B 48, 13060 (1993)ADSCrossRefGoogle Scholar
  16. 16.
    N. Hatano, D.R. Nelson, Localization transitions in non-Hermitian quantum mechanics. Phys. Rev. Lett. 77, 570 (1996)ADSCrossRefGoogle Scholar
  17. 17.
    P.W. Brouwer, P.G. Silvestrov, C.W.J. Beenakker, Theory of directed localization in one dimension. Phys. Rev. B 56, R4333 (1997)ADSCrossRefGoogle Scholar
  18. 18.
    P.G. Silvestrov, Localization in an imaginary vector potential. Phys. Rev. B 58, R10111 (1998)ADSCrossRefGoogle Scholar
  19. 19.
    N. Hatano, D.R. Nelson, Non-Hermitian delocalization and eigenfunctions. Phys. Rev. B 58, 8384 (1998)ADSCrossRefGoogle Scholar
  20. 20.
    J.-W. Ryu, N. Myoung, H.C. Prak, Reconfiguration of quantum states in PT-symmetric quasi-one dimensional lattices. Sci. Rep. 7, 8746 (2017). (and references in this paper) ADSCrossRefGoogle Scholar
  21. 21.
    C. Dembowski et al., Experimental observation of the topological structure of exceptional points. Phys. Rev. Lett. 86, 787 (2001)ADSCrossRefGoogle Scholar
  22. 22.
    C. Dembowski et al., Observation of a chiral state in a microwave cavity. Phys. Rev. Lett. 90, 034101 (2003)ADSCrossRefGoogle Scholar
  23. 23.
    W.D. Heiss, Exceptional points of non-Hermitian operators. J. Phys. A 37, 2455 (2004)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    C.M. Bender, Making sense of non-Hermitian Hamiltonians. Rep. Prog. Phys. 70, 947 (2007)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    S.-Y. Lee et al., Divergent Petermann factor of interacting resonances in a stadium-shaped microcavity. Phys. Rev. A 78, 015805 (2008)ADSCrossRefGoogle Scholar
  26. 26.
    S.-B. Lee et al., Observation of an exceptional point in a chaotic optical microcavity. Phys. Rev. Lett. 103, 134101 (2009)ADSCrossRefGoogle Scholar
  27. 27.
    N. Moiseyev, Non-Hermitian Quantum Mechanics (Cambridge University Press, New York, 2011)CrossRefzbMATHGoogle Scholar
  28. 28.
    W.D. Heiss, The physics of exceptional points. J. Phys. A 45, 444016 (2012)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    J.-W. Ryu, W.-S. Son, D.-U. Hwang, S.-Y. Lee, S.W. Kim, Exceptional points in coupled dissipative dynamical systems. Phys. Rev. E 91, 052910 (2015)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    L. Ge, Parity-time symmetry in a flat band system. Phys. Rev. A 92, 052103 (2015)ADSCrossRefGoogle Scholar
  31. 31.
    N. Zhang et al., Single nanoparticle detection using far-field emission of photonic molecule around the exceptional point. Sci. Rep. 5, 11912 (2015)ADSCrossRefGoogle Scholar
  32. 32.
    H. Hodaei, Enhanced sensitivity at higher-order exceptional points. Nature 548, 187 (2017)ADSCrossRefGoogle Scholar
  33. 33.
    K.-H. Ahn, H.C. Park, B. Wu, Dynamic localization and Fano resonance in double-dot molecules with microwave radiation. Physica E 34, 468 (2006)ADSCrossRefGoogle Scholar
  34. 34.
    H.C. Park, K.-H. Ahn, Mesoscopic noise and admittance of an electrically driven nano-structure. Physica E 40, 1510 (2008)ADSCrossRefGoogle Scholar
  35. 35.
    J.-W. Ryu, N. Myoung, H.C. Park, Antiresonance induced by symmetry-broken contacts in quasi-one-dimensional lattices. Phys. Rev. B 96, 125421 (2017)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Theoretical Physics of Complex SystemsInstitute for Basic Science (IBS)DaejeonRepublic of Korea
  2. 2.Department of Physics EducationChosun UniversityGwangjuRepublic of Korea

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