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


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.


Non-Hermiticity Flat bands Quantum transport 



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.


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© 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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