Emergent localized states at the interface of a twofold PT -symmetric lattice

Jung-Wan Ryu,Ara Go,Hee Chul Park,Nojoon Myoung,Sang-Jun Choi,Sungjong Woo

doi:10.1103/physrevresearch.2.033149

Jung-Wan Ryu, Ara Go + Show 4 more

Open Access

https://doi.org/10.1103/physrevresearch.2.033149

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Abstract

We consider the role of non-triviality resulting from a non-Hermitian Hamiltonian that conserves twofold PT-symmetry 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.

Highlights

A non-Hermitian system (H† = H) with parity-time (PT ) symmetry exhibits a phase transition through spontaneous symmetry breaking from an unbroken PT -symmetric phase with real eigenenergies to a broken phase with pairs of conjugate complex eigenenergies [1]
Phase transitions in these systems occur via exceptional points (EPs), which are degenerate points of eigenenergies in non-Hermitian systems that generate a Möbius strip structure of eigenenergies in parametric space [15,16]
If an interface state with a PT -symmetric phase distinct from that of bulk states lies within the bulkenergy gap, the imaginary momentum becomes independent of non-Hermiticity with varying real momentum

Summary

INTRODUCTION

A wide range of PT -symmetric systems have been explored over several fields, including optics [4,5,7,8,9,10,11], electronic circuits [12], atomic physics [13], and magnetic metamaterials [14] Phase transitions in these systems occur via exceptional points (EPs), which are degenerate points of eigenenergies in non-Hermitian systems that generate a Möbius strip structure of eigenenergies in parametric space [15,16]. Modes with the real part of complex eigenenergies zero [21,22], analogous to Majorana zero modes in condensedmatter physics Such non-Hermitian zero modes (NHZMs) are protected by non-Hermitian particle-hole (NHPH) symmetry, which is called charge-conjugate symmetry; i. Using these robust localized states, we design a lossless one-dimensional (1D) waveguide whose output power to the external environment vanishes from various geometrical deformations

SINGLE PT SYMMETRIC LADDER

TWOFOLD PT -SYMMETRIC LADDER

DISCUSSION

Crossconnected two PT-symmetric ladder lattices

Robustness to disorder and spatial defect