Toward Realistic Amorphous Topological Insulators

Abstract

The topological properties of materials are, until now, associated with the features of their crystalline structure, although translational symmetry is not an explicit requirement of the topological phases. Recent studies of hopping models on random lattices have demonstrated that amorphous model systems show a non-trivial topology. Using ab initio calculations we show that two-dimensional amorphous materials can also display topological insulator properties. More specifically, we present a realistic state-of-the-art study of the electronic and transport properties of amorphous bismuthene systems, showing that these materials are topological insulators. These systems are characterized by the topological index Z 2 = 1 and bulk-edge duality, and their linear conductance is quantized, G = 2e 2 /h, for Fermi energies within the topological gap. Our study opens the path to the experimental and theoretical investigation of amorphous topological insulator materials.

Disentangling Orbital and Valley Hall Effects in Bilayers of Transition Metal Dichalcogenides

“…, where, for the SH conductivity, X η ¼ ŝη and for the OH conductivity (OHC), X η ¼ lη ; ŝη and l η represent the η components of the spin and of the atomic angular momentum operators, respectively. This is implemented in the PAOFLOW code [41] that has been successfully used to study topological materials [42,43] and time dependent spin dynamics [44] among other topics. For our conductivity calculations, we have increased the sampling to 200 × 200 × 1 k points in the 2D BZ.…”

Robustness of topological insulating phase against vacancy, vacancy cluster, and grain boundary bulk defects

“…These results agree well with those obtained above from the generic TB model. Here, we did not consider the structural relaxation of the defected systems since the surface-supported film can largely hold the bulk geometry in the presence of defects, and a recent study has shown that the TI phase can persist even in amorphous state with local atomic displacements without "bulk" defects [51].…”

Topological Weaire–Thorpe models of amorphous matter

“…This well-developed understanding dates back at least to studies of integer quantum Hall transitions (8)(9)(10). More recently, several classes of amorphous models have been shown to host integer quantum Hall (or Chern insulator) phases, as well as other topological states (7,(11)(12)(13)(14)(15)(16)(17)(18)(19), including numerical work that suggests differences compared to known quantum Hall transitions (19,20). Although the corresponding topological phase diagrams can be computed numerically, by simulating responses to external fields (18) or through real space topological markers (7,11), these methods are not generalizable to every discrete symmetry in every dimensionality.…”