Topological Insulators in Amorphous Systems

Titus Neupert, Frank Schindler

Archisman Panigrahi, Bitan Roy

We introduce projected amorphous topological insulators (PATIs) that despite containing only a fraction ($x$) of otherwise randomly selected {\it disconnected} sites of a parent crystal, feature a quantized global topological invariant ({\it strong} PATIs) when its effective Hamiltonian is constructed by integrating out the residual sites of the original lattice. Within the topological regime of the parent model, additionally, there exists a critical $x$ below which such systems foster a {\it fragile} PATI that only supports quantized local topological marker on a small fraction of sites therein. Both strong and fragile PATIs accommodate in-gap modes near the boundary. The system also hosts a normal insulator in the entire trivial parameter regime of the lattice-based model for any $x$, devoid of gapless boundary modes, for which both global topological invariant and local topological marker vanish. We demonstrate these {\it possibly} generic outcomes by starting with a parent square lattice-based model for time-reversal symmetry breaking insulators. Then the strong-to-fragile PATI quantum phase transition, tunable via $x$, is characterized by the {\it mean} correlation length exponent $ν\in (1.00,1.46)$.

Stephan Rachel, Karyn Le Hur

Kai Li, Jiong-Hao Wang, Yan-Bin Yang +1 more

Recent theoretical studies predict that structural disorder, serving as a bridge connecting a crystalline material to an amorphous material, can induce a topological insulator from a trivial phase. However, to experimentally observe such a topological phase transition is very challenging due to the difficulty in controlling structural disorder in a quantum material. Given experimental realization of randomly positioned Rydberg atoms, such a system is naturally suited to studying structural disorder induced topological phase transitions and topological amorphous phases. Motivated by the development, we study topological phases in an experimentally accessible one-dimensional amorphous Rydberg atom chain with random atom configurations. In the single-particle level, we find symmetry-protected topological amorphous insulators and a structural disorder induced topological phase transition, indicating that Rydberg atoms provide an ideal platform to experimentally observe the phenomenon using state-of-the-art technologies. Furthermore, we predict the existence of a gapless symmetry-protected topological phase of interacting bosons in the experimentally accessible system. The resultant many-body topological amorphous phase is characterized by a Z_{2} invariant.

Hiroki Isobe

Sunghoon Kim, Adhip Agarwala, Debanjan Chowdhury

Band topology is traditionally analyzed in terms of gauge-invariant observables associated with crystalline Bloch wave functions. Recent work has demonstrated that many of the free fermion topological characteristics survive even in an amorphous setting. In this Letter, we extend these studies to incorporate the effect of strong repulsive interactions on the fate of topology and other correlation induced phenomena. Using a parton-based mean-field approach, we obtain the interacting phase diagram for an electronic two-orbital model with tunable topology in a two-dimensional amorphous network. In addition to the (non-)topological phases that are adiabatically connected to the free fermion limit, we find a number of strongly interacting amorphous analogs of crystalline Mott insulating phases with nontrivial chiral neutral edge modes, and a fractionalized Anderson insulating phase. The amorphous networks thus provide a new playground for studying a plethora of exotic states of matter, and their glassy dynamics, due to the combined effects of nontrivial topology, disorder, and strong interactions.