Anomalous mobility edges in one-dimensional quasiperiodic models

Mobility edges, separating localized from extended states, are known to arise in the
single-particle energy spectrum of disordered systems in dimension strictly higher than
two and certain quasiperiodic models in one dimension. Here we unveil a different
class of mobility edges, dubbed anomalous mobility edges, that separate energy intervals
where all states are localized from energy intervals where all states are critical in
diagonal and off-diagonal quasiperiodic models. We first introduce an exactly solvable
quasi-periodic diagonal model and analytically demonstrate the existence of anomalous
mobility edges. Moreover, numerical multifractal analysis of the corresponding wave
functions confirms the emergence of a finite energy interval where all states are critical.
We then extend the sudy to a quasiperiodic off-diagonal Su-Schrieffer-Heeger model and
show numerical evidence of anomalous mobility edges. We finally discuss possible experimental
realizations of quasi-periodic models hosting anomalous mobility edges. These
results shed new light on the localization and critical properties of low-dimensional systems
with aperiodic order