Universität zu Köln

Kunst, Flore K. and Dwivedi, Vatsal (2019). Non-Hermitian systems and topology: A transfer-matrix perspective. Phys. Rev. B, 99 (24). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2469-9969

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Abstract

Topological phases of Hermitian systems are known to exhibit intriguing properties such as the presence of robust boundary states and the famed bulk-boundary correspondence. These features can change drastically for their non-Hermitian generalizations, as exemplified by a general breakdown of bulk-boundary correspondence and a localization of all states at the boundary, termed the non-Hermitian skin effect. In this paper, we present a completely analytical unifying framework for studying these systems using generalized transfer matrices, a real-space approach suitable for systems with periodic as well as open boundary conditions. We show that various qualitative properties of these systems can be easily deduced from the transfer matrix. For instance, the connection between the breakdown of the conventional bulk-boundary correspondence and the existence of a non-Hermitian skin effect, previously observed numerically, is traced back to the transfer matrix having a determinant not equal to unity. The vanishing of this determinant signals real-space exceptional points, whose order scales with the system size. We also derive previously proposed topological invariants such as the biorthogonal polarization and the Chern number computed on a complexified Brillouin zone. Finally, we define an invariant for and thereby clarify the meaning of topologically protected boundary modes for non-Hermitian systems.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kunst, Flore K. UNSPECIFIED UNSPECIFIED UNSPECIFIED Dwivedi, Vatsal UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-137937
DOI:	10.1103/PhysRevB.99.245116
Journal or Publication Title:	Phys. Rev. B
Volume:	99
Number:	24
Date:	2019
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	2469-9969
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language PARITY-TIME SYMMETRY; EXCEPTIONAL POINTS; PHASE-TRANSITION; BOUND-STATES; QUANTUM; SURFACE; INSULATOR Multiple languages Materials Science, Multidisciplinary; Physics, Applied; Physics, Condensed Matter Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/13793