Topological states and anomalous localization in non-Hermitian systems*

Recently, the search for topological states has reached to non-Hermitian lattices (see [1] and references therein), systems where non Hermiticity models gains and losses (as in photonic crystals) or the effect of interactions (electron-electron, electron-phonon). Capital to this endeavor is the ability to build a proper bulk-boundary correspondence, a task that has gained much attention during the last year.

Here we focus on recent results challenging the usual viewpoint, the occurrence of higher-order exceptional points where a macroscopic fraction of the states coalesce at a single point with a geometrical multiplicity of one [2] and where the the system becomes devoid of extended states [2].

A scheme to generate such higher-order exceptional points in lattices will be presented together with an argument [3] regarding the separation of the spectrum into topological states and localized states originated by higher-order exceptional points.

[1] V. M. Martinez Alvarez et al., Eur. Phys. J. Spec. Top. (2018), https://doi.org/10.1140/epjst/e2018-800091-5
[2] V. M. Martinez Alvarez, J. E. Barrios Vargas, and L. E. F. Foa Torres, Phys. Rev. B 97, 121401(R) (2018).
[3] V. M. Martinez Alvarez, E. Rodríguez-Mena, L. E. F. Foa Torres, to be published.