Localization properties of an amorphous photonics-inspired system

Anderson showed that disorder from impurities localizes electronic eigenstates in 2D mesoscopic quantum systems [2]. In topological quantum systems, such as integer quantum Hall systems, this disorder localizes almost all states except for the chiral edge state [5] and is an important stabilizing mechanism for topological phases. Recent work [1, 3, 6] has suggested that topological phases also arise in amorphous systems: those where impurities are absent and the disorder is purely geometric. However, the possibility of localization purely from geometric disorder has been largely unexplored. We present evidence for a metal-insulator transition in an amorphous version of a Chern insulator, inspired by simulations of an experimental topological photonics system [4]. We present results from finite size scaling and level-spacing distributions to corroborate this, and compare with localization from impurity disorder.

[1] A. Agarwala and V. Shenoy. Topological insulators in random lattices. Phys. Rev. Lett., 118:1–6, 2017.

[2] P. W. Anderson. Absence of diffusion in certain random lattices. Phys. Rev., 109:1492, 1958.

[3] P. Corbae, S. Ciocys, D. Varjas, E. Kennedy, S. Zeltmann, M. Molina-Ruiz, S. Griffin, C. Jozwiak, Z. Chen, L. Wang, M. Scott, A. Grushin, A. Lanzara, and F. Hellman.

Evidence for topological surface states in amorphous Bi2Se3. arXiv:1910.13412

[4] Z. Jia, M. Secli, A. Avdoshkin, W. Redjem, E. J. Dresselhaus, J. E. Moore, and B. Kante. Disordered topological graphs enhancing nonlinear phenomena. Under review.

[5] A. W. W. Ludwig, M. P. A. Fisher, R. Shankar, and G. Grinstein. Integer quantum Hall transition: An alternative approach and exact results. Phys. Rev. B, 50:7526, 1994.

[6] Q. Marsal, D. Varjas, and A. Grushin. Topological Weaire–Thorpe models of amorphous matter. Proc. National Academy of Science, 117, 2020.