Non-Bloch Topology of Frustrated Non-Hermitian Flat Bands

Résumé :

We construct a broad class of two-dimensional frustrated non-Hermitian lattice models with exactly flat bands which can be naturally described in a non-Bloch band theory, through similarity transformation and Amoeba formulation. OBC spectra thereof are obtained by performing a constant imaginary momentum shift in one or two directions, thus forming a uniform generalized Brillouin zone. Using non-Hermitian breathing Kagome and checkerboard models as illustrations, we reveal how flat bands whose energies degenerate into a single value can acquire skin localization induced by other winding bands. A flat band becomes singular when its eigenvectors hold immovable discontinuities at band crossings. Such singularity in non-Hermitian systems is sensitive to boundary conditions and unprotected by band flatness. Non-Bloch topology underlying is uncovered in a bulk–boundary correspondence with the formation of a singular band touching in the bulk and a robust flat band skin mode on the boundary. We present a geometric approach to construct this boundary skin mode from a macroscopic sum of compact localized skin modes and trace its topological origin to two linearly independent noncontractible loop states on a non-Bloch torus. To characterize the correspondence, an invariant is proposed based on biorthogonal polarization of zero-energy corner mode. As a generalization, we further show that by breaking exact flatness, it is possible to realize nearly flat non-Bloch Chern bands.

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Contact : loic.herviou@lpmmc.cnrs.fr