Confirmation of Old Theory Leads to Breakthrough in Understanding of Superconductors

Harvard scientists have created a bismuth-based, two-dimensional superconductor that is just one nanometer thick. By examining fluctuations in this material as it transitions into superconductivity, the scientists gained insight into the processes that induce superconductivity more generally. (See graph above of Resistivity as a function of temperature for devices of a different thickness--courtesy of Argonne National Laboratory).

The Harvard scientists experimentally confirmed a 23-year-old theory about superconductors developed by scientist Valerii Vinokur from the U.S. Department of Energy's (DOE) Argonne National Laboratory.

"Sometimes you discover something new and exotic, but sometimes you just confirm that you do, after all, understand the behavior of the every-day thing that is right in front of you." — Valerii Vinokur, Argonne Distinguished Fellow, Materials Science division.

One phenomenon of interest to researchers is the total reversal of the well-studied Hall effect when materials transition into superconductors.

When a regular, non-superconducting material carries an applied current and is exposed to a magnetic field, a voltage is induced across the material. This regular Hall effect has the voltage going in a specific direction depending on the orientation of the field and current.

When materials become superconductors, the sign of the Hall voltage reverses. So, the ​"positive" end of the material becomes the ​"negative." This is a well-known phenomenon. And the Hall effect has long been a significant tool used to study the types of electronic properties that make a material a good superconductor.

However, the cause of this reverse Hall effect has remained mysterious for decades, especially in high-temperature superconductors for which the effect is even stronger.

Optical image of Hall bar device

In 1996, theorist Vinokur, an Argonne Distinguished Fellow, and his collaborators presented a thorough description of this effect (and more) in high-temperature superconductors. The theory took into account all of the driving forces thought to be involved, and it included so many variables that testing it experimentally seemed unrealistic, until now.

"We believed we had really solved these problems," said Vinokur, ​"but the formulas felt useless at the time, because they included many parameters that were difficult to compare with experiments using the technology that existed then."

Scientists knew that the reverse Hall effect is the result of magnetic vortices that emerge when a superconducting material placed in a magnetic field.

Vortices are points of singularity in the liquid of superconducting electrons (Cooper pairs). Cooper pairs flow around these vortices, producing circulating superconducting micro-currents that yield novel features in the physics of the Hall effect in the material.

Ordinarily, the distribution of electrons in the material causes the Hall voltage.

However, in superconductors, vortices move under the applied current, which induces differences in electronic pressure that are mathematically similar to those that keep an airplane in flight.

These pressure differences change the course of the applied current in a way that is analogous to how the wings of an airplane change the course of the air passing by, uplifting the plane. The vortex motion redistributes electrons differently, reversing the direction of the Hall voltage.

The 1996 theory quantitatively details the effects of these vortices, which at the time had only been qualitatively explained. Now, with a novel material that took the Harvard scientists five years to develop, the theory was tested and confirmed.

The bismuth-based thin material is about just one atomic layer thick, making it basically two-dimensional. It is one of the only thin-film high-temperature superconductors that are known. Notably, the fabrication of the material alone is a breakthrough in superconductor science.

"By reducing the dimensions from three to two, the fluctuations of the properties in the material become much more apparent and easier to study," said Philip Kim, a lead scientist in the Harvard group. ​"We created an extreme form of the material that allowed us to quantitatively address the 1996 theory."

The theory predicts that the anomalous reverse Hall effect could exist outside of the temperatures at which the material is a superconductor. The study provided a quantitative description of the effect that entirely matched the theoretical predictions.

"Before we were sure of the role vortices play in the reverse Hall effect, we couldn't use it reliably as a measuring tool," said Vinokur. ​"Now that we know we were correct, we can use the theory to study other fluctuations in the transition phase, ultimately leading to better understanding of superconductors."

Although the material that they examined is two-dimensional, the researchers believe that the theory applies to all superconductors. They are planning future research that will include deeper study of the materials.

The behavior of the vortices is thought to even have application in mathematical research.

Vortices are objects with unique geometrical properties known as topological objects. They are currently a popular subject in mathematics because of the ways they form and deform and how they alter the a material's properties. The 1996 theories utilized topology in describing the behavior of the vortices, and these topological properties of matter could be significant in a lot of new physics.

"Sometimes you discover something new and exotic," said Vinokur about the research, ​"but sometimes you just confirm that you do, after all, understand the behavior of the every-day thing that is right in front of you."

The scientists described the results of the study in a paper titled, ​"Sign reversing Hall effect in atomically thin high-temperature superconductors," that was published on June 21 in Physical Review Letters.

The work was funded by Center for Emergent Superconductivity (an Energy Frontier Research Center), DOE's Office of Basic Energy Science, and multiple Strategic Partnership Project sponsors.