@article{ISI:000465979400001,
 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.},
 article-number = {263001},
 author = {Ghatak, Ananya and Das, Tanmoy},
 doi = {10.1088/1361-648x/ab11b3},
 eissn = {1361-648X},
 issn = {0953-8984},
 journal = {JOURNAL OF PHYSICS-CONDENSED MATTER},
 month = {JUL 3},
 number = {26},
 times-cited = {66},
 title = {New topological invariants in non-Hermitian systems},
 unique-id = {ISI:000465979400001},
 volume = {31},
 year = {2019}
}