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We propose a scheme to realize parity-time (PT) symmetric photonic Lieblattices of ribbon shape and complex couplings, thereby demonstrating thehigher-order exceptional point (EP) and Landau-Zener Bloch (LZB) oscillationsin presence of a refractive index gradient. Quite different from non-Hermitianflatband lattices with on-site gain/loss, which undergo thresholdless PTsymmetry breaking, the spectrum for such quasi-one-dimensional Lieb latticeshas completely real values when the index gradient is applied perpendicular tothe ribbon, and a triply degenerated (third-order) EP with coalescedeigenvalues and eigenvectors emerges only when the amplitude of gain/loss ratioreaches a certain threshold value. When the index gradient is applied parallelto the ribbon, the LZB oscillations exhibit intriguing characteristicsincluding asymmetric energy transition and pseudo-Hermitian propagation as theflatband is excited. Meanwhile, a secondary emission occurs each time when theoscillatory motion passes through the EP, leading to distinct energydistribution in the flatband when a dispersive band is excited. Such novelphenomena may appear in other non-Hermitian flatband systems. Our work may alsobring insight and suggest a photonic platform to study the symmetry andtopological characterization of higher-order EPs that may find uniqueapplications in for example enhancing sensitivity.

Higher-order exceptional point and Landau-Zener Bloch oscillations in driven non-Hermitian photonic Lieb lattices