Topological Anderson Phase Transition In LC Circuit

Topological state has become an important research area in condensed matter physics since it was proposed.In the study of quantum spin hall insulator,scientists discovered topological phase transition caused by disorder,which was also called topological Anderson phase transition.And this type of phase transition was then extended to many other system.In addition,the simulation of topological states in LC circuits has also attracted great attention in physics.Compared with conventional methods,the coupling in LC circuits is much easier to control,and the physical quantities are more feasible to be detected.In this paper,the topological Anderson phase transition in LC circuits system is studied theoretically.Based on the computation of non-commutative geometric topological invariants and transport simulation,we not only confirm the existence of topological Anderson phase transition in LC circuits,but also find the most proper parameter regions.At the same time,we study the realization of disorder in LC circuits by introducing imprecise grounding inductance and clarify the difference between disorder caused by imprecise grounding inductance and Anderson disorder.We find that when the error is large,the topological Anderson phase transition is suppressed due to the disorder deviation from the uniform distribution.Compared with photonic crystal and cold atom system,Green’s function and wave function in LC circuits can be directly measured.So we propose two kinds of feasible detection methods in experiment in which we can measure transmission rate and wave function distribution at the same time.Besides,the minimum size requirement for realizing topological phase is given in this paper.These results are of guiding value for realizing topological Anderson insulator in LC circuits and provide a further comprehensive understanding of its topological nature.