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FIELD Computational Sciences
DATE September 27 (Fri), 2019
TIME 16:00-18:00
PLACE 1423
SPEAKER Hee Chul Park
HOST Son, Young-Woo
TITLE Mesoscopic transport and localized interface states on the PT symmetric lattices
ABSTRACT In this presentation, I will discuss the non-trivial phenomena caused by non-Hermiticity which introduces the phase transition through exceptional points. We consider the quasi-1D lattice maintaining the combination of parity and time-reversal symmetries by controlling energy gain and loss. We demonstrate mesoscopic transport through electronic states in PT-symmetric quasi-1D lattice [1]. We investigate the phase diagram of the non-Hermitian systems where transitions take place between unbroken and broken PT-symmetric phases via exceptional points. Mesoscopic transport in the lattice is measured only in the unbroken-but not broken-phase in the energy band. The broken phase allows for spontaneous symmetry broken states where the cross-stitch lattice is separated into two identical single lattices corresponding to conditionally degenerate eigenstates. These degeneracies show a lift-up in complex energy plane, caused by the non-Hermiticity with PT-symmetry. In addition to the lattice preserving PT symmetry, there are interesting phenomena in the twofold PT-symmetric lattice preserving PT symmetries along two axes [2]. We consider the role of non-triviality resulting from a non-Hermitian lattice assembled by interconnections between a PT-symmetric lattice and its time reversal partner. Twofold PT symmetry in the lattice produces additional surface exceptional points that play the role of new critical points, along with the bulk exceptional point. We show that there are two distinct regimes possessing symmetry-protected localized states, of which localization lengths are robust against external gain and loss. The states are demonstrated by numerical calculation of a quasi-1D ladder lattice and a 2D bilayered square lattice.

[1] Jung-Wan Ryu, Nojoon Myoung, Hee Chul Park, Reconfiguration of quantum states in PT-symmetric quasi-one dimensional lattices, Scientific Reports 7, 8746 (2017).
[2] Jung-Wan Ryu, Sungjong Woo, Nojoon Myoung, Ara Go, Sang-Jun Choi, and Hee Chul Park, Emergent localized states due to the twofold PT symmetry in ladder lattice, arXiv: 1904.00444 (2019).
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