New topological invariants in non-Hermitian systems

Ghatak, Ananya and Das, Tanmoy (2019) New topological invariants in non-Hermitian systems. In: JOURNAL OF PHYSICS-CONDENSED MATTER, 31 (26).

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Abstract

Both theoretical and experimental studies of topological phases in non-Hermitian systems have made a remarkable progress in the last few years of research. In this article, we review the key concepts pertaining to topological phases in non-Hermitian Hamiltonians with relevant examples and realistic model setups. Discussions are devoted to both the adaptations of topological invariants from Hermitian to non-Hermitian systems, as well as origins of new topological invariants in the latter setup. Unique properties such as exceptional points and complex energy landscapes lead to new topological invariants including winding number/ vorticity defined solely in the complex energy plane, and half-integer winding/Chem numbers. New forms of Kramers degeneracy appear here rendering distinct topological invariants. Modifications of adiabatic theory, time-evolution operator, biorthogonal bulk-boundary correspondence lead to unique features such as topological displacement of particles, `skin-effect', and edge-selective attenuated and amplified topological polarizations without chiral symmetry. Extension and realization of topological ideas in photonic systems are mentioned. We conclude with discussions on relevant future directions, and highlight potential applications of some of these unique topological features of the non-Hermitian Hamiltonians.

Item Type:	Journal Article
Publication:	JOURNAL OF PHYSICS-CONDENSED MATTER
Publisher:	IOP PUBLISHING LTD
Additional Information:	Copyright of this article belongs to IOP PUBLISHING LTD
Keywords:	topological insulator; non-Hermitian Hamiltonian; PT-symmetric system; exceptional points
Department/Centre:	Division of Physical & Mathematical Sciences > Physics
Date Deposited:	24 May 2019 09:13
Last Modified:	24 May 2019 09:13
URI:	http://eprints.iisc.ac.in/id/eprint/62707

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