Valley-dependent bilayer circuit networks

Recent investigations have shown that the valley degree of freedom existing in bilayer graphene with different stacking patterns can lead to novel topological phases. In this work, we propose a bilayer circuit network, which is composed of two layers of coupled hexagonal circuit lattices, to engineer exotic valley physics and design valley-selected electronic devices. By tuning the interlayer coupling pattern and the distribution of node grounding, the valley-dependent chiral edge states located at two kinds of domain walls, AB-AB- and AB-BA-type interfaces, are fulfilled in the designed bilayer circuit. The existence of these novel valley edge states is evidently confirmed by eigenspectrum calculations and impedance simulations. Assisted by the designed valley-dependent bilayer circuit networks, we further prove that the valley-enabled voltage splitter could be fulfilled by integrating the bilayer circuits with several nontrivial domain walls. Because the existence of more tuning degrees of freedom for the bilayer circuit networks compared to the single layer circuit, we expect that they could be used to control electronic signal in much more novel ways. Our findings suggest a flexible platform to study valley physics beyond natural materials and other classical wave systems and may have potential applications in the field of integrated circuit design.