Topological Amorphous Metals

TL;DR

This paper introduces a new class of topological amorphous metals in three dimensions, characterized by unique topological invariants and observable surface states, expanding the understanding of topological phases beyond crystalline materials.

Contribution

The study demonstrates the existence of topological amorphous metals in 3D, characterized by the Bott index and Hall conductivity, and proposes an experimental realization using electric circuits.

Findings

Topological amorphous metals exhibit diffusive metallic behavior.

Surface states and topological invariants are observable despite lack of translational symmetry.

Experimental proposal using electric circuits to detect the phenomena.

Abstract

We study amorphous systems with completely random sites and find that, through constructing and exploring a concrete model Hamiltonian, such a system can host an exotic phase of topological amorphous metal in three dimensions. In contrast to the traditional Weyl semimetals, topological amorphous metals break translational symmetry, and thus cannot be characterized by the first Chern number defined based on the momentum space band structures. Instead, their topological properties will manifest in the Bott index and the Hall conductivity as well as the surface states. By studying the energy band and quantum transport properties, we find that topological amorphous metals exhibit a diffusive metal behavior. We further introduce a practical experimental proposal with electric circuits where the predicted phenomena can be observed using state-of-the-art technologies. Our results open a door for exploring topological gapless phenomena in amorphous systems.