# Topological Materials Beyond Symmetry Indicators

> **NSF 01002526DB NSF RESEARCH & RELATED ACTIVIT** · University of Illinois at Urbana-Champaign (IL) · $423,000

## Abstract

NONTECHNICAL SUMMARY
 
This award supports theoretical research and educational activities aimed at understanding topological materials. These materials are distinguished in having properties that remain unchanged when the material is reshaped or disturbed. Topological materials have robust, i.e. impervious to material imperfections or shape, metallic conduction on their surfaces and interfaces that hold promise for device applications. Recent theoretical work has revealed that topological materials are ubiquitous in nature. However, the analytic tools for efficiently identifying and classifying topological materials are applicable to only about half of the crystal arrangements of constituent atoms that occur in nature, and only in materials where electrons do not interact strongly. A unifying framework for understanding how these analytical tools relate to measurable properties of materials is also lacking.

This project will focus on addressing this issue by exploiting mathematical connections between topology and symmetry as they apply in materials. The PI will develop new mathematical frameworks for describing the connection between symmetry in topology in solids and apply these to the discovery of new topological materials. Additionally, the PI will use symmetry to study how electron flow and crystal imperfections can reflect universal properties of topological materials.

In addition to the research, this project supports the training and mentorship of graduate st

## Key facts

- **NSF award ID:** 2510219
- **Awardee organization:** University of Illinois at Urbana-Champaign (IL)
- **SAM.gov UEI:** Y8CWNJRCNN91
- **PI:** Barry Bradlyn
- **Primary program:** 01002526DB NSF RESEARCH & RELATED ACTIVIT
- **All programs:** QUANTUM INFORMATION SCIENCE
- **Estimated total:** $423,000
- **Funds obligated:** $282,000
- **Transaction type:** Continuing Grant
- **Period:** 07/01/2025 → 06/30/2028

## Primary source

NSF Award Search: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2510219

## Citation

> US National Science Foundation, Award 2510219, Topological Materials Beyond Symmetry Indicators. Retrieved via AI Analytics 2026-06-07 from https://api.ai-analytics.org/grant/nsf/2510219. Licensed CC0.

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