New PNAS Study Reveals Hidden Topological Structure in Polarons

A new study published in the Proceedings of the National Academy of Sciences (PNAS), “Symmetry-protected topological polarons,” uncovers an unexpected layer of structure in one of the most common quasiparticles in solid-state physics: the polaron. The research shows that the atomic distortions surrounding an electron can form stable, symmetry-driven patterns, revealing an internal organization that had not been recognized before.

In everyday terms, this work reshapes how scientists understand the microscopic behavior of materials used in technologies like solar cells, LEDs, and electronic devices. Instead of behaving as simple, featureless objects, polarons can carry structured patterns that influence how energy and charge move through a material.

This discovery builds on earlier computational work from physics professor Feliciano Giustino’s research center. The previous research revealed vortex-like polarons in halide perovskites, a class of materials widely studied for solar cells and LED lighting. While that earlier research focused on a specific family of materials, the new PNAS study demonstrates that such symmetry-driven patterns are a general phenomenon, appearing across a broad range of crystalline solids.

The research team was led by Giustino, who directs the Center for Quantum Materials Engineering at the Oden Institute for Computational Engineering and Sciences at The University of Texas at Austin. Additional Oden-affiliated co-authors on the paper include Kaifa Luo, Oden Institute graduate student, and Jon Lafuente-Bartolome, previously at the Oden Institute and who is now an assistant professor at the University of the Basque Country in Bilbao, Spain.

Polarons form when electrons moving through crystalline solids—ordered materials such as semiconductors and insulators—interact strongly with vibrations of the atomic lattice, known as phonons. In many materials, this interaction traps the electron in a localized wave packet surrounded by a distortion of nearby atoms. Until now, polarons were thought to be relatively simple, characterized mainly by how tightly an electron is bound and how far its wavefunction spreads through the material. The new PNAS study shows that this picture is incomplete.

“Our work shows that the structure of a polaron is much more complex than previously thought,” Luo explained. Rather than forming a uniform bulge or dip in the lattice, the surrounding atoms can reorganize into swirling, vortex-like patterns dictated by the symmetry of the crystal itself.

These swirling distortions are not random. By analyzing the symmetry of a crystal, the team derived general rules that predict which type of atomic pattern will form around a trapped electron. This means that, in many cases, researchers can anticipate the shape of a polaron’s distortion before performing large-scale simulations.

What makes these polarons especially intriguing is that their swirling patterns come with built-in “ID tags.” These tags do not describe the electron itself so much as the way the surrounding atoms twist and bend. Like fingerprints, they encode what makes each distortion pattern unique, giving every polaron texture a distinct and mathematically well-defined identity.

This additional structure is protected by symmetry, meaning it is remarkably stable. Small defects or modest changes in conditions tend to deform the pattern without destroying it. Rather than disappearing, the polaron keeps its identity, which is an important feature if such effects are to be observed experimentally or used in future technologies.

At an intuitive level, a topological polaron can be imagined as a tiny, persistent twist in a material’s atomic lattice that is bound to an electric charge. As the electron moves through the crystal, it carries this twist along with it.

Capturing these effects required simulations at a scale that was out of reach until recently. Large polarons can extend over regions involving hundreds of thousands to millions of atoms. To observe these subtle rearrangements, the team relied on leadership-class supercomputing resources.

The simulations were carried out using advanced computational tools developed by Giustino’s group, using high-performance computing systems at the National Energy Research Scientific Computing Center (NERSC) and at the Texas Advanced Computing Center (TACC). A collaboration with TACC’s team provided technical expertise to optimize performance at scale.

Access to these large-scale computing systems made it possible for researchers to move beyond isolated example materials and conduct a systematic survey across many systems. Rather than focusing on a few showcase cases, the team was able to map an entire landscape of possible polaron patterns and connected symmetry-based predictions to realistic, experimentally relevant materials.

“This research would not have been possible without the support of the Department of Energy (DOE), which enabled the ground-breaking discovery reported in this work through a Computational Materials Science award within the DOE Basic Energy Sciences Directorate. DOE support was also crucial for refactoring and preparing the EPW code for GPU-enabled supercomputers such as Perlmutter at NERSC and Aurora at Argonne Leadership Computing Facility,” said Giustino. “The project also benefited from collaborations with TACC, which provided us with the opportunity to stress-test our code on systems such as Frontera and Vista. These resources are absolutely essential for producing cutting-edge quantum simulations of advanced materials, and are even more critical today as we transition toward AI-supported materials discovery,” he added.

In addition to computing power, visualization played a key role in interpreting the results. Three-dimensional renderings of atomic displacements made the swirling patterns immediately visible, helping researchers distinguish genuine physical effects from numerical artifacts: spurious features that can arise from limited resolution or approximations in simulations.

Beyond the specific systems studied, the discovery opens new directions for research in quantum materials. The results suggest that topology, long known to shape the behavior of electrons in exotic materials, can also emerge in more conventional semiconductors due to electron-lattice interactions.

By introducing a symmetry-protected identity for polarons, the work raises new questions about how these quasiparticles respond to electric, magnetic, or optical fields, and whether their robust structure could be harnessed for next-generation quantum and information technologies.

Next steps include collaborating with experimental researchers who have the tools to look for predicted signatures in real materials using feasible measurement probes. “Physics ultimately relies on experimental validation, and as researchers, we are interested in working with experimentalists to test whether our predictions are borne out in the lab, or, if not, to understand what assumptions need to be refined,” said Luo.

The study highlights the role of the Oden Institute in advancing foundational computational science and shows how the combination of theory, large-scale computer simulation, visualization, and interdisciplinary collaboration can reveal new physics hidden within familiar materials.

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This work was supported by the Computational Materials Science program of the U.S. Department of Energy, Office of Science, Basic Energy Sciences under Award DE-SC0020129. This research used resources of the National Energy Research Scientific Computing Center (NERSC), a Department of Energy User Facility using NERSC award BES-ERCAP003496. An award of computer time was provided by the ASCR Leadership Computing Challenge (ALCC) program. This research used resources of the Argonne Leadership Computing Facility, a DOE Office of Science User Facility. The collaboration with TACC to prepare the EPW code for the Horizon supercomputer was supported by NSF awards 2513830 and 2323116.