Open Access

Aamna Ahmed

• Flat band systems have drawn significant interest in recent times as they exhibit the twin features of compact localization and large-scale degeneracy. The localization properties and associated repressed transport have been discussed in the context of engineered lattices in one, two and three dimensions. Conventional wisdom suggests that introducing disorder in such systems would lead to the destruction of compact localization of the eigenstates and the associated degeneracy. This poster examines the interplay of dispersionless bands, compact localized eigenstates and quasiperiodic Aubry-Andr´e (AA) disorder in a one-dimensional all-band-flat (ABF) diamond chain. We show that surprisingly when the AA potential is applied in a specific symmetric manner to an ABF diamond chain, compact localization remains robust, although the degeneracy is broken. An even more exciting finding is that when the disorder is applied in an antisymmetric manner, all the eigenstates exhibit a multifractalFlat band systems have drawn significant interest in recent times as they exhibit the twin features of compact localization and large-scale degeneracy. The localization properties and associated repressed transport have been discussed in the context of engineered lattices in one, two and three dimensions. Conventional wisdom suggests that introducing disorder in such systems would lead to the destruction of compact localization of the eigenstates and the associated degeneracy. This poster examines the interplay of dispersionless bands, compact localized eigenstates and quasiperiodic Aubry-Andr´e (AA) disorder in a one-dimensional all-band-flat (ABF) diamond chain. We show that surprisingly when the AA potential is applied in a specific symmetric manner to an ABF diamond chain, compact localization remains robust, although the degeneracy is broken. An even more exciting finding is that when the disorder is applied in an antisymmetric manner, all the eigenstates exhibit a multifractal nature below a critical strength of the applied potential with the existence of a central band that remains multifractal at all strengths of the potential. A further novel aspect of our work is the finding that chiral symmetry is robust even in the presence of disorder, which we show with explicit construction of the chiral symmetry operator.…