Electrons stay put in layers of mismatched ‘quantum Legos’

Electrons can be elusive, but Cornell researchers using a new computational method can now account for where they go - or don't go - in certain layered materials.

Physics and engineering researchers have confirmed that in certain quantum materials, known as "misfits" because their crystal structures don't align perfectly - picture LEGOs where one layer has a square grid and the other a hexagonal grid - electrons mostly stay in their home layers.

This discovery, important for designing materials with quantum properties including superconductivity, overturns a long-standing assumption. For years, scientists believed that large shifts in energy bands in certain misfit materials meant electrons were physically moving from one layer to the other. But the Cornell researchers have found that chemical bonding between the mismatched layers causes electrons to rearrange in a way that increases the number of high-energy electrons, while few electrons move from one layer to the other.

"This is an important class of materials people are trying to understand," said Tomás Arias, professor of physics and Stephen H. Weiss Presidential Fellow in the College of Arts and Sciences (A&S), principal investigator of the study. "It was a perfect playground for us in terms of showcasing our new ideas about how to develop that understanding. You can't directly answer questions about these materials in any other way other than what we've developed."

Their new computational method is based on the idea that electrons mostly react to only their immediate surroundings. This foundational research could speed design of materials with desirable properties including devices with powerful electrical cooling abilities.

"Unmasking Charge Transfer in the Misfits: ARPES and Ab Initio Prediction of Electronic Structure in Layered Incommensurate Systems without Artificial Strain" was published on Nov. 14 in Physical Review Letters. The first author is doctoral student Drake Niedzielski. Also contributing from Cornell: Brendan Faeth of the Platform for the Accelerated Realization, Analysis and Discovery of Interface Materials (PARADIM) at Cornell; the late Lena Kourkoutis, M.S. '06, Ph.D. '09, associate professor in Cornell's School of Applied and Engineering Physics, Cornell Engineering; and Berit Goodge, Ph.D. '22, a former member of the Kourkoutis Electron Microscopy Group, now at the Max Planck Institute for Chemical Physics Solids. Tyrel McQueen and Mekhola Sinha of Johns Hopkins University also contributed.

Bulk incommensurate materials such as the misfits are a powerful platform for causing and studying exotic electron behavior, the researchers wrote. Their discovery builds on research from the past few decades, when material scientists started experimenting with stacked 2D materials to make electrons in them do interesting things, said Niedzielski.

Among incommensurate materials, "the most famous is magic twisted bilayer graphene, where you mismatch two layers of graphene with a twist and all of a sudden it becomes a superconductor," Niedzielski said.

In this study, the experimentalists at PARADIM analyzed misfit layered heterostructures - compounds that alternate a rare-earth metal rock salt layer, which has square symmetry, with another material with hexagonal symmetry, Niedzielski said.

Observations of the material showed an increase in the number of high-energy electrons in the hexagonal material. But when Niedzielski calculated all the electrons in one stack of incommensurate materials - one hexagonal against one that's square - he encountered a mystery.

"It looks like a lot of electrons move to the hexagonal layer, which has been seen in our collaborator's experiments and others on similar materials in the same family," he said. "It's widely interpreted in the literature that this is due to the electrons physically moving from one layer to another. It appears that a large number of electrons do that."

But according to his new method, which allows him to calculate the location and energy of the electrons precisely, he found the electron transfer was "about six times less than what they were seeing in experiments," he said. "The electrons in each layer were rearranging themselves and very few had actually moved between the layers."

Kourkoutis led the microscopy efforts to image the misfit materials, Niedzielski said. These images were important for him to locate the atoms so he could do the calculations faster.

Rather than jumping from one layer to the other, the system's electrons were staying where they were, the study found. The researchers were able to understand this because electrons mostly "care" about their local environment. At this microscopic level, electrons act like waves that spread through the material, Arias said. But in a system crowded with many electrons, such as in a misfit compound, so many of the waves cancel each other out - like waves on the surface of a pool crowded with swimmers - that only the area immediately around each electron matters.

The computational method Niedzielski developed, MINT-Sandwich, uses a new theoretical approach, enabling calculations on new materials previously thought impossible, Arias said.

"What we do is an experiment in the computer. It's not just a simulation; we're really calculating out the laws of physics. It's a third source of information about material systems" in addition to experiment and theory, he said. "These calculations give you exactly what you would get from a highly controlled experiment. That's why Drake can go in there and see where did everyone go? What actually happened to everyone? And untangle these types of mysteries."

This work received support from the National Science Foundation.

Kate Blackwood is a writer for the College of Arts and Sciences.