Topological Anderson Insulator in electric circuits

Abstract: Although topological Anderson insulator has been predicted in 2009, the lasting investigations of this disorder established nontrivial state results in only two experimental observations in cold atoms [Science, {\bf 362 },929 (2018)] and in photonic crystals [Nature, {\bf 560}, 461 (2018)] recently. In this paper, we study the topological Anderson transition in electric circuits. By arranging capacitor and inductor network, we construct a disordered Haldane model. Specially, the disorder is introduced by the grounding inductors with random inductance. Based on non-commutative geometry method and transport calculation, we confirm that the disorder in circuits can drive a transition from normal insulator to topological Anderson insulator. We also find the random inductance induced disorder possessing unique characters rather than Anderson disorder, therefore it leads to distinguishable features of topological Anderson transition in circuits. Different from other systems, the topological Anderson insulator in circuits can be detected by measuring the corresponding quantized transmission coefficient and edge state wavefunction due to mature microelectronic technology.