Edge states manifestation in non-Hermitian topological systems

Project Director: Dr. Bogdan OSTAHIE

Project ID: PN-III-P1-1.1-PD-2019-0595

Project Director: Dr. Ostahie Bogdan

Project Type: National Project Program PD

Funded by: Romanian National Authority for Scientific Research, UEFISCDI

Contractor: National Institute of Materials Physics

Project Status: In progress

Start Date: 24.08.2020

End Date: 23.07.2022

Project Title: Edge states manifestation in non-Hermitian topological systems

Project Abstract: The proposed project investigates the spectral and transport properties in open topological systems. The open systems will consist in finite lattices to which several semi-infinite leads are attached and the resulting systems are described by an effective Hamiltonian, which is non-Hermitian. The complex energy spectrum will be analyzed at different parameters: coupling between the lattice and semi-infinite leads, impurities and lattice distortion. The aim is to show how the edge states, in the topological phase, are influence by the external environment in one and two dimensional systems. The role of disorder will be investigated using the random matrix theory. Moreover, one of the fundamental reasons is to show the correspondences between localization and spectral statistic in non-Hermitian topological systems. The quantum transport properties will be studied employing the Landauer-Büttiker formalism. In the one dimensional case the goal is to analytically calculate the transmission coefficient for the topological edge states. Additionally, the effect of the coupling with the leads of the states localized at the edge will be analyzed, emphasizing the robustness of the edge states in one dimensional systems in the topological phase with open boundaries. In two dimensional non-Hermitian topological systems it is expected that the quantum Hall phase to be richer because of the mixing between anomalous and chiral edge states. Furthermore, it is expected that the disorder will induce the appearance of a new type of topological Anderson insulator.

Dr. Ostahie Bogdan  - Project Director

Dr. Catalin Pascu Moca  - Mentor

We analyzed the topological effects and the role of perturbations (chiral disorder) in non-Hermitian systems with chiral symmetry. The system under consideration consists in a finite Su-Schrieffer-Heeger chain (the model describes the dimerization of a polyacetylene chain) to which two semi-infinite wires are attached. The system lacks parity and time reversal symmetries and is suitable for the study of quantum transport properties. The complex energy spectrum is analyzed in terms of the coupling between the system and the wires. The edge states in the center of the gap acquire a finite lifetime and are both of topological origin or are generated by the strong coupling between the system and the leads. Chiral disorder induces coalescence of topological eigenvalues, associated with exceptional points. The electron transmission coefficient is calculated with the Landauer formalism and an analytical expression for the transmission was obtained. We have shown that the chiral disorder in this non-Hermitian system induces the improvement of the unit conductance in the topological phase.

Another result is the theoretical investigation of the spectral and quantum transport properties of two-dimensional heterostructures formed by different topological materials. The surprising behavior of the edge states is due to the internal symmetries or the external magnetic field, in different constituents of the heterostructure. More precisely, we use the topological isolator of Chern type and Weyl semimetals with one or two interfaces interposed between these systems. The calculation of the quantum Hall effect may not contain negative plateaus or have asymmetric plateaus at the bottom and top of the energy spectrum. Also, the distribution of   conducting channels on the finite size system with interfaces and attached wires leads to fractional values ​​of the quantum Hall resistance. The calculations were based on a diatomic lattice model in perpendicular magnetic field, with hopping elements between the first and second order neighbors, and between the first order neighbors there is a periodic internal flux (Haldane type model).



B. Ostahie and A. Aldea "(“Interface effects on the energy spectrum and quantum transport in two-dimensional topological heterostructures”" Applied Surface Science 587 (2022) 152769

B. Ostahie and A. Aldea ”Spectral analysis, chiral disorder and topological edge states manifestation in open non-Hermitian Su-Schrieffer-Heeger chains” Physics Letters A 387 (2021) 127030


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