# Barry Bradlyn

Assistant Professor

## Primary Research Area

- Condensed Matter Physics

## Biography

Professor Bradlyn received his bachelor's degree in Physics from the Massachusetts Institute of Technology in 2009. He went on to receive his Ph.D. from Yale University in 2015, under the supervision of Nicholas Read. His thesis research focused on linear response and Berry phases in the fractional quantum Hall effect. His primary contributions was the development of a formalism for computing the viscoelastic and thermal response functions for two dimensional Topological phases.

From 2015 to 2018, Professor Bradlyn held a postdoctoral research position at the Princeton Center for Theoretical Science, where he studied the role of crystal symmetries in topological insulators and semimetals. He predicted the existence of topologically charged, multiply degenerate fermions in weakly interacting crystals with no known analogue in high energy physics. Additionally, he developed a real-space formulation of topological band theory, allowing for the prediction of many new topological insulators and semimetals.

Professor Bradlyn joined the physics department at the University of Illinois in 2018.

## Research Interests

- symmetry protected topological semimetals
- geometric response in condensed matter
- the quantum Hall effect
- topological insulators

## Research Statement

One of the most exciting developments in condensed matter physics over the last thirty years has been the discovery of topological phases of matter. Under the broadest possible definition, a system is in a topological phase if there is a gap in its bulk spectrum. Of course, such a definition describes any ordinary thermal or electrical insulator. The key theoretical breakthrough was the realization that not all insulators are created equal. In fact, given a model for an insulating system, there exist certain numerical invariants - topological quantum numbers - that we can compute in order to distinguish between different possible topological phases. These invariants vanish for most ordinary insulators (strictly speaking, they take the same values as in the vacuum) - they are "topologically trivial"Â. The distinguishing feature of such topological invariants is that they depend on the global structure of the system under consideration; topological phases are not locally ordered like magnets or solids. Consequently, systems in nontrivial topological phases are host to a wide range of exotic phenomena, from quantized transport coefficients to fractional bulk excitations that harbor the potential to allow for fault tolerant quantum computation.

Since this initial discovery, the influence of topology has spread across all areas of condensed matter physics. It is this--in addition to individual realizations of topological phases--that is in my opinion the biggest boon of this new paradigm. Topology now stands alongside abstract algebra (as it pertains, for instance, to symmetry groups) as one of our main tools for exploring quantum phenomena in solids and liquids. Broadly speaking, the goal of my research is to marry ideas from these two areas in order to study new phenomena in condensed matter. Currently, I am focusing on the following main topics:

1. Viscous and optical response of topological insulators and semimetals

2. Magnetic topological materials

3. Crystal symmetry protected topological phenomena

## Selected Articles in Journals

- B. Offertaler and B. Bradlyn, "Viscoelastic response of quantum Hall fluids in a tilted field," Phys. Rev. B 99, 035427 (2019).
- B. J. Wieder, B. Bradlyn, Z. Wang, J. Cano, Y. Kim, H.-S. D. Kim, A. M. Rappe, C. L. Kane, and B. A. Bernevig, "Wallpaper fermions and the nonsymmorphic Dirac insulator," Science 361, 246--251 (2018).
- J. Cano, B. Bradlyn, Z. Wang, L. Elcoro, M. G. Vergniory, C. Felser, M. I. Aroyo, and B. A. Bernevig, "Topology of Disconnected Elementary Band Representations," Phys. Rev. Lett. 120, 266401 (2018).
- J. Cano, B. Bradlyn, Z. Wang, L. Elcoro, M. G. Vergniory, C. Felser, M. I. Aroyo, and B. A. Bernevig, "Building Blocks of Topological Quantum Chemistry: Elementary Band Representations," Phys Rev. B 97, 035139 (2018).
- L. Elcoro, B. Bradlyn, Z. Wang, M. G. Vergniory, J. Cano, C. Felser, B. A. Bernevig, D. Orobengoa, G. de la Flor, and M. I. Aroyo, "Double crystallographic groups and their representations on the Bilbao Crystallographic Server," J. Appl. Cryst. 50, 1457--1477 (2017).
- M. G. Vergniory, L. Elcoro, Z. Wang, J. Cano, C. Felser, M. I. Aroyo, B. A. Bernevig, and B. Bradlyn, "Graph Theory Data for Topological Quantum Chemistry," Phys. Rev. E 96, 023310 (2017).
- B. Bradlyn, L. Elcoro, J. Cano, M. G. Vergniory, Z. Wang, C. Felser, M. I. Aroyo, and B. A. Bernevig, "Topological quantum chemistry," Nature 547, 298--305 (2017).
- A. Gromov, S. D. Geraedts, and B. Bradlyn, "Investigating anisotropic quantum Hall states with bi-metric geometry," Phys. Rev. Lett. 119, 146602 (2017).
- B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, "Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals," Science 353, aaf5037 (2016).
- V. V. Albert, B. Bradlyn, M. Fraas, and L. Jiang, "Geometry and response of Lindbladians," Phys. Rev. X 6, 041031 (2016).
- B. Bradlyn and N. Read, "Kubo formulas for viscosity: Hall viscosity, Ward identities, and the relation with conductivity," Phys. Rev. B 86, 245309 (2012).