Amorphous topological matter: Predicting new phases with enhanced properties in a vast pool of amorphous materials

Discovering new phases of matter in materials with superior properties is a central goal of condensed matter physics. Topological phases are a remarkable example: their robust and universal properties are key to groundbreaking technologies, notably robust quantum computation based on topological superconductors. However, our methodology to discover and classify topological materials relies heavily on crystal symmetry, thereby overlooking the largest, most affordable and scalable pool of materials - amorphous materials. Amorphous matter can outperform crystals, and is ubiquitous in technology: e.g. amorphous bismuth superconducts below 6K, a temperature 10,000 times larger than crystal bismuth, and amorphous silicon makes large-area solar cells affordable. This raises the fundamental question of whether we have overlooked new topological phases intrinsic to amorphous matter in materials with properties unparalleled by crystals. It is also unknown if any amorphous superconductor is topological. The core objective of this project is to harvest the superior properties of the vast pool of amorphous solids to find fundamentally distinct topological phases with high technological potential, via three specific goals: 1. Establish a predictive methodology to unlock the vast pool of amorphous matter to discover new topological materials. 2. Use this methodology to define unaccounted for amorphous topological phases with superior capabilities and no crystal analogues. 3. Use the above to predict the first amorphous topological superconductors. These goals will establish amorphous topological matter as a radically new direction to solve the challenge of finding novel platforms for topological superconductivity, where robust quantum computers can be based. This project will establish the necessary and currently absent theoretical background, guaranteeing a long-term impact on how we understand and discover new phases of matter with superior properties.