TITLE : PT symmetry and the non-Hermitian skin effect

ABSTRACT :

In recent years, there has been a growing fascination with unique attributes of non-Hermitian (NH) systems due to their diverse characteristics and relevance to open quantum systems. Building on the foundational contributions of Bender and Boettcher [1], it has been shown that NH systems, characterized by parity and time-reversal (PT ) symmetry, may possess real eigenvalues despite their inherent non-Hermitian nature. The phenomenon of imbalanced accumulation of majority of the eigenstates at either of the edges in an open boundary condition, known as the non-Hermitian skin effect (NHSE), has also garnered significant attention. In this seminar, we explore the interplay between PT symmetry and topology using simple tight-binding chains, namely, the NH Su-Schrieffer-Heeger (SSH) model [2] and an NH half Bernevig-Hughes-Zhang (BHZ) model [3]. Both variants of non-Hermiticity, namely, the PT -symmetric and PT -broken are introduced through staggered imaginary potentials and the nonreciprocal hopping parameters in the models. We comprehensively study the criteria for observation of NHSE, topology and bi-orthogonal bulk-boundary correspondence, analysis of spectral gaps, exceptional points, topological invariants, phase diagrams, and localization properties. Finally, we construct electronic circuits, a study commonly referred to as 'topo-electronics', corresponding to our models to illustrate the localization of edge modes etc via computing measurable quantities, such as a two-port impedance.
References:
[1] Bender, Carl M. & Boettcher, Stefan Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry Phys. Rev. Lett. 80, 5243-5246 (1998).
[2] Dipendu Halder, Sudin Ganguly and Saurabh Basu, Properties of the non-Hermitian SSH model: role of PT symmetry, 2023 J. Phys.: Condens. Matter 35 105901, DOI: 10.1088/1361-648X/acadc5
[3] Dipendu Halder and Saurabh Basu, Topological properties of a non-Hermitian two-orbital model, arXiv:2304.12723

MEETING DETAILS :

Joining Link: events.php

Speaker: Prof. Saurabh Basu

Venue: SC-NKN (South Campus)

Date and Time: Tuesday, October 10, 2023; 4 pm