Multi-orbital topolectrical circuit for topological quantum states

Remarkable progress has been made in using electric circuits as a powerful platform to realize a plethora of exotic topological quantum states, even of higher orders and/or dimensions. So far the proposed circuits are restricted to a single-orbital tight-binding model with different lattices. Here, we introduce the concept of a multi-orbital topolectrical circuit and construct practical LC circuits to demonstrate its superiorities. As a proof of concept, we assemble two sets of inductors in one plaquette to simulate a (px, py )-orbital model within a two-dimensional hexagonal lattice. In the presence of spin-orbit coupling, as generated by mixing voltage degrees of freedom, a quantum spin Hall (QSH) state emerges with spin-resolved edge modes propagating along the boundary in the time domain. Implementation of negative impedance converters (NICs) with nonreciprocal links transforms the circuit into a quantum anomalous Hall (QAH) state. Remarkably, we demonstrate that QSH/QAH states can be reversibly switched by tuning the resistance of NIC, and an experimental observable-edge distance ratio is proposed to facilitate the phase transition detection. This work provides an exciting playground for exploring multi-orbital physics in topolectrical circuits, paving the way for future applications in nanoelectronics, telecommunications, signal processing and quantum computing.