A case study in topological materials from scientists, themselves
Elizabeth Pogue

The clock is counting down. Humanity is counting on the Star Trek Enterprise's science officer, Spock, to save them by inventing new physics and performing some quick calculations. Is this what scientists really do?

Real life as a scientist is not like this (although we do experience eureka moments and do make cool things). Science is a process for encountering and understanding the unknown. Think processes are boring? Science definitely isn’t! Every day, as scientists, we learn new things and see things that have never been seen before. It takes courage to peer into the unknown, try to make sense of the unexplained, and admit when you don’t understand. I interviewed three scientists from different Energy Frontier Research Centers including the Institute of Quantum Matter (IQM), the Center for the Advancement of Topological Semimetals (CATS), and Programmable Quantum Materials Center (Pro-QM), to discover how this process plays out for them, focusing on the differences between basic and applied science and how theorists who use phenomenological approaches (they describe, in general, how a phenomenon works), computational theorists, and experimentalists work together. These centers study different aspects of topological materials, a new class of materials with unusual electrical properties. This is an area where new breakthroughs are happening daily!

Basic research is the bedrock that enables applied research and, in turn technologies. Basic researchers investigate how the world works. Applied researchers then use the knowledge from basic researchers to make technologies. Some of these technologies can then be used by basic and applied researchers to discover new things, which are later used to develop new technologies. Applied research can also inspire basic research questions. Image Courtesy of Kathryn Vitarelli and Elizabeth Pogue.

Basic or applied?

The first people to grow large single crystals of materials could not have predicted the dominance of silicon-based technologies like cell phones and computers. Not all research looks the same—some researchers focus on the basics of how nature works and others use what basic researchers have discovered to make devices and learn how they work best. Professor Susanne Stemmer of UC Santa Barbara and CATS says that basic and applied science ask different questions.

“With applied research, we know what we would like to have,“ said Stemmer. “The question is, ’Can we get there?’" In fundamental, basic science, we are asking the basic question of how nature works.”

Within materials science, the discovery of new materials is basic research, as is their characterization and the development of new processing tools to make the materials. Designing, making, and testing new devices, like transistors or solar cells, made of these materials is applied research. Applied research and the resulting technological applications both build upon basic research.

The EFRCs focus on basic research, but what does this mean? Professor David Vanderbilt of Rutgers University and IQM notes that within basic research, there is ‘more basic’ and ‘less basic.’

“Instead of starting from the periodic table, suppose I first just imagine what materials can do in principle,” said Vanderbilt. “I can then explore possibilities that haven’t yet been realized in the laboratory. I can predict if it would be useful and worthy of a search for candidate materials or if it is just a pipe dream.”

Theory or experiment?

All scientists are interested in the underlying mechanisms of behavior, but generally specialize in either theory or experiment. A theorist, by definition, develops new theories. They do this by using math and existing theory to hypothesize how the world works. A theorist can either have a general focus on how a phenomenon works, regardless of the specific materials involved (asking what properties, in general, are required to make a material magnetic), or have a more specific focus on how a specific material behaves (for example, computing the magnetic moment of an iron unit cell and seeing how that compares to experimental observations or theorizing new magnetic materials).

Theory and experiment feed into each other. Topology began as theory—as a field of math that classifies geometric objects based on properties that remain unchanged when the objects are stretched and/or bent. No matter how you stretch a coffee mug, it will always have one hole for the handle. These properties are known as invariants.

Theorists predicted that the same concepts could be applied to the wave-like nature of electrons in materials. Their hypotheses introduced concepts like topological indices. Topological indices are like those invariant properties of the coffee mug.

According to Di Xiao, theorist and professor at Carnegie Mellon University and Pro-QM, “We begin with toy models to understand those fundamental concepts. We try to distill everything to a minimal model to talk about the actual physics. We also have to calculate these quantities in real materials. We also need experimentalists to determine if these materials can actually be made, their actual crystal structure, and if there are issues with defects and impurities. When theory disagrees with experiment, that’s when things become really exciting!”

Topology classifies objects based on properties that don’t change if they are stretched or bent. The same concept can be applied to electron wave functions. When such invariants change from one region to another, one can observe unusual electronic and magnetic properties, such as forced electron band crossings that make electrons behave like photons of light. Image courtesy of Elizabeth Pogue.

Topological insulators are, overall, electrically insulating, but have very conductive surfaces due to invariant electron “knots” required by topology. Does this sound scifi yet? “The motion of electrons in topological materials is different from normal materials…Bismuth selenide (Bi2Se3) is a topological insulator but bismuth oxide (Bi2O3) is not,” noted Xiao. “Why? For these [questions], state-of-the-art computational techniques must be applied.”

These theories led experimentalists to try to make these unusual materials—and they were successful! Both theorists and experimentalists always ask, “What can be measured?,” “How?,” and “Am I seeing what I think I am seeing or is it a product of my experimental setup?” The discovery of topological materials could have happened in reverse order, with experimental observations of unusual electrical conduction predating theory describing it like the discovery of fire (our ancestors saw and interacted with fire before they understood it). Prior unusual experimental observations gave theorists some guidance into which real materials may have topological properties, illustrating how theorists and experimentalists work together.

“Topological materials have interesting features in their electronic structures, but it is often less clear which experiments will reveal them,” said Stemmer. “We have to think of the experiments, themselves, [guided by theory] to tease out the properties.” For example, defects, insufficient mixing, or poor crystallinity can hide useful and unusual properties.

An experimentalist figures out how to test these theories, performs experiments, and analyzes what happens. According to experimentalist Stemmer, “The fun of experimentation is that you can directly probe what happens in all its complexity, which is often difficult to predict using theory. With experiments, you can just see what happens! You sometimes get unexpected outcomes and the answers are not always known. We look where no one has looked before.”

Experimenting takes time and equipment. For example, Stemmer began growing high-quality thin films of cadmium arsenide (Cd3As2) once she determined that it was compatible with her equipment and promising for the investment, where molecular beam epitaxy, a difficult but extremely precise thin-film growth technique, could reveal interesting physics. Cd3As2 is interesting because of its unusually large electron mobilities that result from the topology of its electrons—it’s electrically like a 3-D version of graphene! Interpreting the results of experiments is often difficult, according to Stemmer.

“The correct interpretation of an experiment is something that people sometimes fight about for years on end,” she said. “It’s part of the process of science. Results are published and it starts a big debate in the literature, sometimes about alternative explanations of the experiment.”

Theorists also ‘experiment,’ constantly evaluating whether their computations reasonably describe reality. For example, professor Vanderbilt’s group has recently been modeling some europium-manganese-phosphorus compounds. At this point, their current results don’t agree with the experiments at all. It takes a lot of time and expertise to identify the incorrect assumptions behind a calculation that disagrees with experiment and apply a successful fix.

“This emphasizes why the feedback between theory and experiment is important,” explains Vanderbilt. “Experimentation tells you what’s happening in the real world. We theorists try to understand the important ingredients to the theory that gives the desired behavior, feeding these back to the experimentalists.”

Does the scientific process ever end?

In short, no, but a scientific theory means much more than the way “theory” is used in everyday conversation—hypotheses derived from theories like quantum theory have been tested, refined, and proven useful since the early 1900s and, most likely, will continue to be useful hundreds of years from now, like Newton’s laws. This scientific process is our continuing mission—to explore strange new materials. To seek new properties and behaviors, and to boldly go where no one has gone before!

About the author(s):

Elizabeth “Lisa” Pogue is a materials scientist and postdoctoral researcher at Johns Hopkins University working with Tyrel McQueen. She is a member of the Institute of Quantum Matter Energy Frontier Research Center and is synthesizing new quantum materials. She is working to make new and better topological insulators and line nodal semimetals. For her doctoral work at University of Illinois in the Rockett and Shoemaker laboratories, Lisa investigated phase stability, defects, and structures of materials in the Copper-Zinc-Tin-Sulfur system. These materials are of interest as Earth-abundant, nontoxic, and inexpensive thin film solar cells.