*Greg Fiete, an assistant professor of physics, was recently given a Presidential Early Career Award for Scientists and Engineers (PECASE), the highest honor bestowed by the United States government on young professionals in the early stages of their independent research careers. We sat down with him recently to discuss his research in condensed matter physics. *

**Tell me a bit about your research. **

Broadly speaking, I’m interested in the quantum mechanics of many-electron systems. What can electrons do if we change the conditions to which they are subjected? What kinds of phases, what kinds of arrangements and correlations of particles can quantum systems have? And what are the important properties of these different phases?

**What’s an example of this kind of quantum electron state you study?**

There’s an effect, called the quantum Hall effect, that occurs when you confine a large number of electrons to a two-dimensional plane and then subject them to low temperatures and apply a perpendicular magnetic field. We’ve learned that under the right conditions, the electrons form what is basically a kind of dance, a correlated state, in which all the dancers are watching each other extremely carefully. If one guy makes a certain move, everyone else follows in a certain way.

**What’s so interesting about such a state?**

This highly correlated state has properties that are fixed to an extremely high degree of precision—among the greatest precision achieved in all of physics. The only other place in quantum mechanics where we can achieve such precise measurements of the same quantity is with a single atom, which is the most pristine quantum system. It is essentially “perfect.” It’s in the atom where we first understood quantum mechanics, and that’s where we’ve had our most precise measurements. So this quantum Hall effect, which occurs in a material with huge numbers of atoms and many imperfections, is an exception. But why is it an exception? Why do we have such precision in a material that we know has a lot of disorder in it? The answer is topology.

**What do you mean by topology?**

Topology is the branch of mathematics that tells you that a donut and a coffee cup are the same type of thing. They are topologically equivalent because they each have one handle, and you can continuously distort the shape of a donut into a coffee cup without changing the number of handles. A topological property of a physical system is one that remains constant—the number of handles, for instance—even as the system is bent or distorted.

**What are the topological properties of a quantum Hall state?**

One topological property that stands out is what’s called a transport property. Electrical resistance, for instance, is a transport property, as is its inverse, conductance. They’re values that describe how electron motion occurs when one applies a voltage across some material. Ohm’s law describes a transport property: the current equals the voltage divided by the resistance. It turns out that resistance is often subtle and very difficult to calculate, and can have special properties depending on the situation.

In quantum Hall systems, we can measure the resistance and conductance values with incredible precision, and if we bend the quantum Hall system, the precision doesn’t change. It’s both precise and robust. In terms of potential practical applications, for instance, what that means is that you have a material with a great deal of precision that doesn’t care about imperfections. That’s the kind of thing that people who do state-of-the-art electronic applications are interested in.

**You’re not an engineer, though. So what is it that does it for you?**

In part, I’m just fascinated by how much we don’t know. Just a little over a century ago, people were saying that physics was all washed up. We understood Maxwell’s equations. We understood Newtonian mechanics. We understood a lot of fluid dynamics. It’s almost done. Then all of the sudden special relativity came along. Quantum mechanics came along. Here we are, more than a century later, and we still have a lot of mysteries to solve. These topological properties of condensed matter systems, for example, are a great example of how many open questions there still are in physics, how many unexplored mysteries remain. It’s a good bet that we’ve still only scratched the surface.

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