Topological edge states appear at the interface of topologically distinct two Hermitian insulators. We study the extension of this idea to non-Hermitian systems. We consider PT symmetric and topologically distinct non-Hermitian insulators with real spectra and study topological edge states at the interface of them. We show that PT symmetry is spontaneously broken at the interface during the topological phase transition. Therefore topological edge states with complex energy eigenvalues appear at the interface. We apply our idea to a complex extension of the Su-Schrieffer-Heeger (SSH) model.
The free particle Schrodinger equation admits a non-trivial self-accelerating Airy wave packet solution. Recently, the Airy beams that freely accelerate in space was experimentally realized in photonics community. Here we present self-accelerating waves for the Bose-Einstein condensate in a time dependent harmonic oscillator potential. We show that parity and time reversal symmetries for self accelerating waves are spontaneously broken. * Electronic address: cyuce@anadolu.edu.tr
We consider a non-Hermitian generalization of the Kitaev model and study the existence of stable Majorana zero energy modes. We show that they exist in the limit of zero chemical potential even if balanced gain and loss are randomly distributed along the lattice. We show that Majorana zero modes also appear if the chemical potential is different from zero provided that not the full Hamiltonian but the non-Hermitian part of the Hamiltonian is PT symmetric.
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