Quantum mechanics is notoriously counterintuitive, its properties usually manifesting  at the smallest of scales, beyond our everyday experiences. But Ali Yazdani, a physicist at Princeton University and Emergent Phenomena in Quantum Systems Initiative investigator, is now bringing that world into view.

Armed with a scanning tunneling microscope, Yazdani and his collaborators have captured images of how electrons in a solid material behave and interact. In doing so, they've discovered and measured phenomena that further unveil the secrets of quantum mechanics — and can potentially lead to new kinds of technology.

“The thing that has been most exciting is imaging actual quantum behaviors of electrons."

That's difficult, and not just because electrons are too small for light to detect. According to quantum mechanics, the position of a particle like an electron is inherently probabilistic — it does not occupy a defined spot, but fills a sort of cloud, smeared across a region in space. What Yazdani’s team has seen are electron clouds shaped as rings, which look like an orbit around a mini solar system.

These orbiting electrons are in what’s called a quantum Hall phase, akin to a phase of matter like solid, liquid or gas. In particular, it’s an example of a topological phase, whose theoretical foundations won the 2016 Nobel Prize (two other Nobel Prizes were previously awarded for the quantum Hall effect and related phenomena). To create a quantum Hall phase, you can start with a two-dimensional electron gas, in which electrons confined to a plane are free to move. The presence of a strong magnetic field forces the electrons to loop around in circles. Other than these orbits, the electrons are now stationary — and thus cannot generate any electric current. The material, then, is an insulator.

But this is different at the material’s edge. Because the electrons are all orbiting in the same direction, the electrons along the edge have a net motion, which enables electric current to flow. So, unlike the rest of the material, the boundaries can conduct electricity.

Quantum Hall phases were discovered nearly 40 years ago, and physicists have long tried to capture an image of the electrons in this phase.

Yazdani’s team was the first to succeed, publishing their results in Science in 2016. The trick, he said, is to use nearly pure crystal — a piece of bismuth produced using techniques pioneered by his Princeton colleague and fellow EPiQS investigator Robert Cava. But the crystal can’t be perfect. Rare defects in the material are needed to snag the electrons, allowing the microscope to capture them — similar to how an exposed rock in a pond induces ripples to form around it.

Not only did the researchers see electron clouds in the shape of loops, but the rings were also elongated. This, they realized, was because the electrons occupied additional quantum states related to so-called valley degrees of freedom. There are six valleys in bismuth, and they are minimum energy states that correspond to different directions of the electron’s momentum. A ring elongated in one particular direction corresponds to an electron in one of these valley states. And because of how the electrons interact with one another, the elongated rings tend to align.

In a paper published in Nature Physics in May 2018, the researchers discovered that by adjusting the strength of the magnetic field, they could coax all the electrons in a bismuth crystal to occupy the same valley state. The elongated rings align and generate an electric field within the crystal. They created a type of material called a ferroelectric, where one side is positively charged and the other is negatively charged — analogous to the north and south poles of your refrigerator magnet (which is a ferromagnetic material).

But they showed these phases of bismuth can be even more complex. In a new paper published in Nature, the researchers again toggled the magnetic field to control electron behavior in bismuth. This time, they were able to put half the electrons in one valley state, elongated in one direction, and the other half in another, oriented in another direction. That means two halves of the same bismuth crystal were in two different phases—almost like water that’s half liquid and half ice. As with the original quantum Hall phase, electrons can flow along the edge of the phase, forming a quantum wire. In this two-phase scenario, an electrically conducting boundary forms not just at the edge of the material, but also through the middle, separating the two phases. Electrons can move through this boundary, forming a one-dimensional channel.

By adjusting the magnetic field further, researchers can put the electrons in multiple valley states at the same time. They can tune the number of channels and manipulate even more complex behaviors and properties of these channels. The quantum interactions between the electrons determine whether the channels are insulating or conducting, and researchers found surprising new rules that dictate these interactions — revealing new insight into the quantum physics of electrons in these one-dimensional, multi-channel quantum wires.

These types of images and measurements enable researchers to better understand these valley states and potentially develop a new class of electronic devices dubbed “valleytronics.” While conventional electronics uses electric charge to store and process the 0s and 1s of information, valleytronics would be based on the different valley states. In particular, Yazdani says, the experiments may lead to new types of quantum wires that don't dissipate energy.

For physicists like Yazdani, simply teasing out the weird quantum behavior of electrons is thrilling. “They can have collective behavior that’s very exotic. But by being able to look inside and take these images and compare them with theoretical calculations, you can verify a lot of ideas that you can't do with simpler measurements,” he said. “They provide a new way to look at quantum states that was just not available a few years ago.”


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