IISc research finds graphene electrons violate a fundamental law of Physics

Not only did electrons in ultrapure graphene flow in a fluid state, they violated the Wiedemann-Franz law. As per the law, when electrical conductivity increases, thermal conductivity should also increase, and when one reduces the other should also reduce. But in ultrapure graphene, electrical and thermal conductivities shared an inverse relationship — as electrical conductivity increased, thermal conductivity decreased and vice versa

For the first time, IISc researchers observed a new state of material where electrons in a single sheet of graphene flow like a perfect fluid with minimal resistance. The electrons that flow in a fluid state were found violating the traditional Wiedemann-Franz law which states that both electrical and thermal conductivities are directly proportional. As per the Wiedemann-Franz law, when electrical conductivity increases, thermal conductivity also increases, and when one reduces the other also automatically reduces. Instead, IISc researchers found that in their study of ultrapure graphene, electrical and thermal conductivities shared an inverse relationship — as electrical conductivity increased, thermal conductivity decreased and vice versa.

“We combined measurements of both electrical and thermal conductivities to demonstrate the quantum critical conductivity scale in monolayer graphene — an effect that was theoretically predicted nearly two decades ago but without an experimental verification so far,” says Dr. Arindam Ghosh, Professor at the Department of Physics at IISc Bangalore and one of the corresponding authors of a paper published in the journal Nature Physics. The work was done in collaboration with the National Institute for Materials Science, Japan.

Exotic behaviour of electrons

The exotic behaviour of electrons and violation of the Wiedemann-Franz law were seen close to the “Dirac point” where graphene behaves neither like a conductor nor like an insulator. “At the Dirac point, the electrons do not behave like individual particles but flow like a fluid,” says Aniket Majumdar, a PhD student at the Department of Physics at IISc Bangalore, and the first author of the paper. “The number of electrons and holes in the Dirac fluid is exactly the same but they have opposite charge. As a result, the total charge in the fluid is zero. But the thermal conduction of the Dirac fluid is not affected.”

When an electric field is applied from outside, electrical density decreases but remains finite. “Electrical conductivity decreases but remains finite, while thermal conductivity increases to very large values, thereby breaking the Wiedemann-Franz law,” says Dr. Ghosh. “The thermal conductivity is 200 times more than what is expected under the Wiedemann-Franz law.”  

How particles interact

While in metals, particles move independently and interparticle interaction is suppressed, in the case of graphene, electrons do not move independently but interact with each other when the electron density is high. As the electron density is reduced by removing some electrons, electrons start interacting with the holes, says Majumdar.  

However, when graphene has plenty of impurities, electrons start interacting with the impurities than with each other, thus suppressing and weakening the electron-electron interaction. For the study, the researchers engineered exceptionally clean samples of graphene and tracked how these materials conduct electricity and heat simultaneously. “Near the Dirac Point, electrical and thermal conductivities decoupled, in violation of the Wiedemann-Franz law,” says Majumdar.

“While previous experimental probes for quantum criticality in graphene suffered due to the low quality of devices, we fabricated multiple “ultra-clean” graphene devices by a careful combination of well-known fabrication protocols. These are among the very best quality of graphene available in the world today. In such graphene, electrons flow like a liquid, because electron-electron scattering dominates over electron-impurity scattering, and thus obey hydrodynamic equations,” says Dr. Ghosh.

Existence of a universal parameter

“We found the existence of a parameter, which controls the thermal and electrical conductivities. This parameter is the quantum critical conductivity, which does not depend on external variables,” Majumdar says. “Though thermal and electrical conductivities are decoupled, they are governed by a single universal parameter — quantum critical conductivity, which is seen close to the Dirac point.”

Significance of the work

Explaining the significance of the work, Dr. Ghosh says: “We have also, for the first time, performed simultaneous measurements of the shear viscosity and the entropy density in our devices, and found their ratio to be as close as four times the holographic lower bound (which is approximately the ratio of the Planck’s constant and the Boltzmann constant). This means that the electron fluid near the Dirac point of clean graphene behaves like a near-ideal (minimally dissipative) quantum fluid — a phase that was predicted to exist at the event horizon of charged black holes in cosmology, or quark-gluon plasma in nuclear physics.”

He adds: “The impact of the observation of quantum critical conductivity scale is immense because it now quantitatively establishes the mapping of the electronic properties of pristine graphene to some of the most important areas of solid-state physics, e.g. high temperature superconductivity, to even those in high-energy nuclear physics or cosmology.”