Edge supercurrent reveals competing electron-pairing mechanisms in a topological superconductor

Written by
Tom Garlinghouse for the Department of Physics
Jan. 16, 2024

Since its discovery, superconductivity — a quantum state in which electrons flow without generating heat — has revealed a wealth of novel quantum phenomena. But physicists still have much to learn about the subject. A currently active area of research is the search for edge supercurrents in a class of materials called topological superconductors. The edge supercurrents, which are confined to the boundaries of a crystal, are protected against hybridizing with the bulk supercurrents in the interior of the crystal.

“The boundary states are special,” said N. Phuan Ong, the Eugene Higgins Professor of Physics at Princeton University and the senior author of the paper. “As in the well-explored topological insulators, the electronic edge states are distinct from the states in the bulk. Research on edge supercurrents in topological superconductors is still in its infancy.” 

The study of edge supercurrents could potentially add a new dimension to the study of superconductivity that may benefit future superconducting and quantum technologies. For a long time, though, evidence for edge supercurrents eluded scientists. It remained unobserved despite numerous searches. 

In 2020, the Princeton team published evidence for edge supercurrents in molybdenum telluride (MoTe2), a topological semimetal that becomes a superconductor when cooled to temperatures below 100 milliKelvin, which is a tenth of a Kelvin above absolute zero. This material is a Weyl semimetal, named after physicist Herman Weyl who investigated theoretically the properties of electrons in high-energy physics in the limit when their mass is set to zero. Recent research in quantum materials has turned up “Weyl semimetals” in which the electrons mimic the behavior of Weyl electrons.

The Princeton team observed edge supercurrents by first cooling MoTe2 to 20 milliKelvin. When they varied the applied magnetic field, they observed rapid oscillations of the critical current. The critical current is “the maximum electrical current that can be injected into the crystal without killing the superconductivity,” said Ong. This finding, which established the existence of edge supercurrents in MoTe2, was published in Science in May, 2020. 

Since that time, Ong and his colleagues have continued to investigate the edge supercurrent in MoTe2. The new experiment, led by Stephan Kim, a graduate student in the Department of Electrical and Computer Engineering, began when the researchers sought to enhance the intrinsic pair potential of molybdenum telluride so that they could track the edge supercurrent oscillations to much higher magnetic fields. The hallmark of superconductivity is the binding of two electrons to form Cooper pairs. The pair potential refers to the “glue” that bonds the two electrons in the superconducting state. However, not all pair potentials are the same. The pair potential intrinsic to molybdenum telluride is very weak. The superconducting state is destroyed in a relatively weak magnetic field; it also dies above 100 mK. The glue that bonds these Cooper pairs together will not hold. 

“To enhance its strength, we evaporated niobium contacts on top of the molybdenum telluride crystal,” said Stephan Kim who performed the measurements on high-quality crystals grown by Professor Leslie M. Schoop and Professor Robert J. Cava with postdoc Shiming Lei in the Department of Chemistry.

Niobium was chosen because it is a well-understood superconductor. Alloys of niobium are crucial for producing intense magnetic fields in diverse applications ranging from MRI (magnetic resonance imaging) to magnetically levitated trains, and from plasma fusion reactors to particle accelerators. In the present experiment, niobium provides a pair potential roughly 80 times stronger than that in molybdenum telluride. 

Kim evaporated strips of niobium over the molybdenum telluride crystal. Using the niobium strips as current electrodes, he injected supercurrent from niobium into molybdenum telluride.

“The niobium Cooper pairs invade the molybdenum telluride and, as they diffuse, they carry the ‘memory’ of this very strong glue into the new material,” said Ong. As the word memory suggests, the Cooper pairs behave as if they are still diffusing inside niobium rather than in molybdenum telluride, so they carry the memory of this strong glue into the new material. The net effect is that electrons in the molybdenum telluride crystal also experience this strong pair potential. This is known as the “proximity effect,” a concept that describes the leakage of the pair potential into the new environment. However, sooner or later the injected Cooper pairs collide with lattice vibrations in the new environment, and the memory dies. 

To explain this scenario, Ong offered a rough analogy. Picture two dancers in a ballroom, he said. They slip into an adjoining ballroom that doesn’t have any music, but the dancers still react—continue to dance for a time—as if they were listening to the music. Eventually they become cognizant of their new surroundings and, waking up to the new reality, cease their dancing. 

As the researchers had hoped, injection of Cooper pairs from niobium succeeded in prolonging the oscillations so that they persisted to much higher magnetic fields (by a factor of 30). But Ong and Kim soon discovered several things that they had not anticipated.

“This was where the experiment got interesting,” said Ong. 

The first thing they noticed was that the glue carried from the niobium into the molybdenum telluride was incompatible with the intrinsic glue. 

“It’s as if we had introduced an invasive species into a pristine environment and the invasive species was much more powerful than the native species,” said Ong.

The competition to pair the available electrons pits a strong invasive pair potential of short range against a weak intrinsic pair potential that pervades over the entire volume. The first sign of the incompatibility emerged in measurements of the critical current.

“Normally, as you increase the current, you eventually hit the critical value at which superconductivity is destroyed. This happens at a very reproducible value,” said Ong. “But, in the face of this competition, the destruction of superconductivity is purely stochastic.”

They termed this phenomenon “stochastic switching.” Although the superconductivity is suppressed as usual, its suppression is unpredictable, occurring stochastically with a broad probability distribution. 

The second unexpected phenomenon appeared when the researchers scrutinized the oscillations of the edge supercurrent, now extending to 100 periods thanks to the stronger injected pair potential. Kim tracked the oscillations as the magnetic field is slowly scanned. However, he soon recognized a striking difference between in-bound field scans and out-bound scans. Here, “in-bound” refers to scans in which the magnitude of the magnetic field decreases to zero with time (irrespective of whether the field points up or down), while out-bound refers to scans in which the magnitude increases with time.

“We fully expected that, given the stochasticity of the switching, the oscillations would always be random, or ‘noisy,’” said Ong. But what happened was this: the oscillations on the out-bound branch of the field scan were invariably regular and periodic, whereas the in-bound branch was “noisy.”  

“Why should the sample care whether the field scan is in-bound or out-bound?” Ong said. “But it does.” 

From these results, Ong and Kim inferred that noise appears whenever Cooper pairs at the edge adopt a pairing symmetry different from that within the bulk of molybdenum telluride; conversely when the symmetries are the same the oscillations occur without noise.

Finally, the third phenomenon observed is a property they call “anti-hysteresis.” It is the opposite of the well-understood concept of hysteresis, which is used to explain a lag that occurs in magnetic materials between an input and an output. For example, in all superconductors, the internal magnetic field is very different from the magnetic field produced by an external coil. This comes about because, according to a concept known as Ampere’s law, the changing external field induces large supercurrents to flow in the superconductor. Changes in the internal field always lag behind changes in the coils. 

In the experiment, however, the researchers found that, as they varied the magnetic field, the opposite occurred. These changes led, rather than lagged, the changes in the external field. This is the exact opposite to what is found in conventional superconductors. 

“This was rather freaky, actually,” said Ong. “It’s as if the material knows what’s about to happen and it jumps the gun.” 

The research took Ong and his team two and a half years and the findings no doubt will provide physicists with ample fodder with which to understand how electrons behave in an environment with incompatible pair potentials. 

“It was an exciting two and a half years,” said Ong. “Although progress was slow and incremental, the progress was largely positive. We believe we have shown that an edge supercurrent exists and it can be harnessed to eavesdrop on the behavior of superconducting electrons.” 

The study, “Edge supercurrent reveals competition between condensates in a Weyl superconductor,” by Stephan Kim, Shiming Lei, Leslie M. Schoop, R.J. Cava, and N. P. Ong, was published January 11, 2024 in the journal Nature Physics DOI: 10.1038/s41567-023-02316-9. 

This work was supported by the U.S. Department of Energy (DE-SC0017863). The crystal growth effort was supported by a MRSEC grant from the U.S. National Science Foundation (NSF DMR2011750).  The Gordon and Betty Moore Foundation’s EPiQS initiative provided additional generous support via grants GBMF9466 (N.P.O.) and GBMF9064 (L.M.S.).