  We propose a scheme to realize parity-time (PT) symmetric photonic Lieb
lattices of ribbon shape and complex couplings, thereby demonstrating the
higher-order exceptional point (EP) and Landau-Zener Bloch (LZB) oscillations
in presence of a refractive index gradient. Quite different from non-Hermitian
flatband lattices with on-site gain/loss, which undergo thresholdless PT
symmetry breaking, the spectrum for such quasi-one-dimensional Lieb lattices
has completely real values when the index gradient is applied perpendicular to
the ribbon, and a triply degenerated (third-order) EP with coalesced
eigenvalues and eigenvectors emerges only when the amplitude of gain/loss ratio
reaches a certain threshold value. When the index gradient is applied parallel
to the ribbon, the LZB oscillations exhibit intriguing characteristics
including asymmetric energy transition and pseudo-Hermitian propagation as the
flatband is excited. Meanwhile, a secondary emission occurs each time when the
oscillatory motion passes through the EP, leading to distinct energy
distribution in the flatband when a dispersive band is excited. Such novel
phenomena may appear in other non-Hermitian flatband systems. Our work may also
bring insight and suggest a photonic platform to study the symmetry and
topological characterization of higher-order EPs that may find unique
applications in for example enhancing sensitivity.
