# Topological Anderson Insulator in electric circuits

## TL;DR

This paper demonstrates the realization of a topological Anderson insulator in electric circuits by constructing a disordered Haldane model with random inductance grounding, revealing a disorder-driven topological transition detectable via electrical measurements.

## Contribution

It introduces a novel circuit-based platform for studying topological Anderson insulators using disordered inductors, expanding experimental possibilities beyond cold atoms and photonic systems.

## Key findings

- Disorder induces a transition from normal to topological insulator in circuits.
- Unique disorder characteristics lead to distinguishable topological features.
- Quantized transmission and edge states confirm topological phase in 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.