Topological Anderson Insulator in Disordered Photonic Crystals

Recent studies have revealed the counterintuitive possibility that increasing disorder can turn a topologically trivial insulator into a nontrivial insulator, called a topological Anderson insulator (TAI). Here, we propose and experimentally demonstrate a photonic TAI in a two-dimensional disordered gyromagnetic photonic crystal in the microwave regime. We directly observe the disorder-induced topological phase transition from a trivial insulator to a TAI with robust chiral edge states. We also demonstrate topological heterostructures that host edge states at interfaces between domains with different disorder parameters.

Figure 1

Disordered gyromagnetic photonic crystal (PhC). (a) Unit cell of the disorder-free PhC (${\theta }_d=0°$), consisting of a central gyromagnetic cylinder (gray circle) surrounded by three dielectric right-triangular pillars (blue triangles). The diameter of the gyromagnetic cylinder $d=4.4\mathrm{mm}$, the hypotenuse width of each right-triangular pillar is $s=5.5\mathrm{mm}$, and the distance between the center of the unit cell and the nearest triangular vertex is $w=4.7\mathrm{mm}$. (b) Band structure of the disorder-free PhC. The Chern numbers of the lowest three bands are labeled. (c) Typical cell of a disordered PhC, with the three triangular pillars rotated by a random angle $\theta$ uniformly distributed between $-{\theta }_d/2$ and ${\theta }_d/2$. (d) Sample of a disordered PhC with ${\theta }_d=90°$. The pink stars indicate source and detector dipole antennas for measuring the bulk and edge transmission spectra. (e) Photograph showing a portion of the sample in (d). The PhC is loaded into a parallel waveguide with a height of 4 mm (the top plate is removed in this photograph). The sample size is $L_x\times L_y=10a\times 10a$, where $a=17.5\mathrm{mm}$ is the lattice constant of the initial PhC.

Figure 2

Observation of disorder-induced topological phase transition. (a) Measured bulk transmission spectra. Gray regions indicate the measured bulk band gaps (defined by $S_{\mathrm{bulk}}<-50\mathrm{dB}$), which are 8.90–9.40, 8.93–9.25, 8.95–9.28, and 9.04–9.51 GHz for ${\theta }_d=0°$, 30°, 90°, and 120°, respectively. No band gap is observed for ${\theta }_d=60°$. (b) The difference between the measured transmission spectra $S_{21}$ and $S_{12}$. Gray regions represent regions with unidirectional edge transmission ($|S_{21}-S_{12}|>20\mathrm{dB}$). No unidirectional edge transportation is observed for ${\theta }_d=0°$, 30°, and 60°. (c) Simulated localization length $L_{\mathrm{loc}}$. The band gap region ($L_{\mathrm{loc}}<5a$) is clearly distinguishable from in-band regions ($L_{\mathrm{loc}}>50a$). The pink lines with square ends show the measured gaps in (a). (d) Simulated Bott index $C_B$. With increasing disorder strength, the trivial band gap ($C_B=0$) closes and reopens as a nontrivial band gap ($C_B=-1$).

Figure 3

Robustness of chiral edge states in disordered PhC-based TAIs. The TAIs have ${\theta }_d=120°$ and measurements are performed at 9.2 GHz, near the middle of the band gap. The upper, right, and bottom boundaries of the sample have copper claddings, and the left boundary is covered with microwave absorbers. The colors show the measured distribution of $|E{|}^2$ excited by a dipole source (blue star). (a) Sample without any additional defects or obstacles. (b) Sample with a defect consisting of 9 unit cells removed in the region marked by blue dashes. (c) Sample with a large obstacle consisting of a copper bar (blue rectangle) of size $5\mathrm{mm}\times 60\mathrm{mm}\times 4\mathrm{mm}$.

Figure 4

Disorder-induced topological heterostructures. (a) Schematic of a heterostructure composed of a disorder-free PhC (${\theta }_d=0°$) and a TAI (${\theta }_d=120°$). (b)–(c) Measured field distributions ($|E{|}^2$) for the structure in (a), with source and probe antennas placed at opposite ends of the interface. (d) Schematic of a heterostructure composed of a disordered trivial PhC (${\theta }_d=20°$) and a TAI (${\theta }_d=100°$). (e)–(f) Measured field distributions ($|E{|}^2$) for the structure in (d), with source and detector antennas at opposite ends of the interface.