Exceptional flat bands in bipartite non-Hermitian lattices

Abstract

Flat bands, in which kinetic energy is quenched and quantum states become macroscopically degenerate, host a rich variety of correlated and topological phases, from unconventional superconductors to fractional Chern insulators. In Hermitian lattices, their formation mechanisms are now well understood, but whether such states persist, and acquire new features in non-Hermitian (NH) { crystals}, relevant to open and driven systems, has remained an open question. Here we show that the Hermitian principle for flat-band formation in bipartite lattices, based on a sublattice degeneracy mismatch, extends directly to the NH regime: whenever one sublattice hosts a momentum-independent eigenvalue with degeneracy exceeding that of its partner on the other sublattice, flat bands arise regardless of gain, loss, or complex couplings. Strikingly, at exceptional points, dispersive bands coalesce to form \emph{exceptional flat bands} (EFBs) that persist beyond these singularities, exhibiting biorthogonal eigenmodes spanning both sublattices, with energies and lifetimes tunable via sublattice asymmetry and non-reciprocal couplings. This general framework unifies Hermitian and NH flat-band constructions, and reveals dispersionless states with no closed-system analogue, as is the case of a bipartite lattice with imbalanced but constant sublattice chemical potentials. The proposed construction is applicable to synthetic platforms, from classical metamaterials, where flat bands can be directly emulated, to quantum-engineered systems such as photonic crystals and ultracold atom arrays, which should host correlated and topological phases emerging from such EFBs.