Hybrid-Order Skin Effect from Loss-Induced Nonreciprocity

Skin effects, the phenomena of the bulk states collapsing toward open boundaries, have mostly been revealed in non-Hermitian systems hosting nonreciprocity. Either the first-order or the higher-order of skin effects have been observed. Here, we report our first discovery of a hybrid-order of skin effects, of which the utilized two-dimensional system exhibits not only the first-order skin modes, but also the second-order skin modes respectively on the edges and the corners, the different type of open boundaries. We propose a universal approach to achieving nonreciprocal couplings by virtue of the loss and bilayer degree of freedom, as the critical role it plays. Our models are implemented in square- and diamond-shaped phononic crystals, and the hybrid order of acoustic skin modes is evidenced in experiment. Our Letter may foster the development of non-Hermitian physics.