Probing hydrodynamics in graphene and quark matter via Seebeck coefficient

In the vast landscape of physics, there is a quiet revolution happening in how we understand the movement of particles. For decades, scientists have treated the flow of electricity and heat in materials like metals as a chaotic, individualistic process. In this traditional view, electrons zip through a solid like cars in heavy traffic, constantly bumping into impurities or vibrating atoms, losing their momentum with every collision. This behavior is well understood and predictable, governed by rules that have served engineers and physicists for generations. However, under specific conditions, nature changes the rules entirely. When interactions between particles become strong enough, they stop acting like independent individuals and begin to move as a unified, collective fluid. This phenomenon, known as hydrodynamics, is familiar in the macroscopic world of water flowing in a river or air swirling around a wing, but its emergence in the microscopic quantum world is a profound and relatively recent discovery. It suggests that in certain materials, electrons can forget their individual collisions and flow together with a viscosity and coherence that defies standard expectations.

A team of researchers has now turned their attention to a specific property called the Seebeck coefficient to probe this hidden fluid behavior. The Seebeck coefficient is a measure of how well a material converts a temperature difference into an electric voltage. In everyday terms, if you heat one end of a wire and cool the other, a voltage builds up; the size of that voltage relative to the temperature difference is the Seebeck coefficient. For ordinary metals, this value follows a strict, well-established formula known as the Mott relation, which acts as a reliable fingerprint for standard, diffusive electron transport. The researchers asked a simple but deep question: does this familiar rule still hold when electrons begin to behave like a fluid? To find out, they looked at two vastly different systems: graphene, a single layer of carbon atoms that is a wonder material in modern electronics, and quark-gluon plasma, a state of matter so hot and dense that it existed only microseconds after the Big Bang, where protons and neutrons melt into a soup of their constituent quarks.

The team used a mathematical framework based on kinetic theory to simulate how these systems respond to heat and electric fields. They focused on graphene first, where they could tune the number of charge carriers by adjusting the chemical potential, effectively dialing the material from a state where electrons act like a standard gas to a state where they form a "Dirac fluid." In the high-density regime, where electrons are plentiful, their calculations confirmed what was already known: the Seebeck coefficient followed the traditional Mott relation, behaving exactly like a standard metal. However, as they lowered the density of charge carriers, moving toward the charge neutrality point where the material is neither positively nor negatively charged, the behavior shifted dramatically. In this low-density domain, the electrons began to interact so strongly that they started to flow collectively. The researchers found that the Seebeck coefficient in this regime deviated significantly from the Mott prediction. Instead of following the old rule, the value was driven by a different physical quantity: the enthalpy per particle, which represents the total energy content of the fluid flow. This deviation was not a minor error; it was a clear signature that the electrons had entered a hydrodynamic state, moving as a coordinated fluid rather than a scattered crowd.

The findings were strikingly consistent with experimental data already available for graphene. When the researchers compared their theoretical curves with real-world measurements taken at various temperatures, from room temperature down to just 19 Kelvin, the match was excellent. The experimental data showed a sharp rise in the Seebeck coefficient near the charge neutrality point, a feature that the traditional Mott relation could not explain but which their fluid-based model predicted perfectly. This agreement suggests that the violation of the Mott relation is not just a theoretical curiosity but a real, observable phenomenon that marks the transition from ordinary transport to collective hydrodynamic flow. The study highlights that the enthalpy per particle is the key driver in this fluid regime, a factor that is largely irrelevant in the standard, diffusive picture of electron transport.

To test whether this behavior was unique to carbon or a more universal feature of strongly interacting quantum systems, the researchers extended their formalism to quark-gluon plasma. Despite the immense difference in scale and the nature of the particles involved, the results were remarkably similar. In the low-density regime of the quark matter, the Seebeck coefficient again showed a substantial deviation from the Mott relation, mirroring the behavior seen in graphene. The magnitude of the Seebeck coefficient in this quark fluid was found to be orders of magnitude larger than what would be expected if the quarks were behaving as independent particles. This parallel suggests that the emergence of hydrodynamic transport is a fundamental property of strongly correlated quantum matter, appearing whether the system is a thin sheet of carbon on a lab bench or the primordial soup of the early universe.

The study does not claim to have solved every mystery of quantum transport, nor does it suggest that the Mott relation is wrong in all contexts. Rather, it delineates the boundaries where the old rules apply and where new, fluid-like physics takes over. The researchers emphasize that their work relies on specific theoretical assumptions, such as a constant relaxation time for the particles, yet the resulting predictions align so well with experimental observations that the core conclusion appears robust. The violation of the Mott relation serves as a clear, measurable indicator of hydrodynamic behavior, offering a new way to identify when particles have begun to flow as a collective. By linking the behavior of graphene and quark matter through the lens of the Seebeck coefficient, the work provides a unified perspective on how strongly interacting systems organize themselves, revealing that the same fluid dynamics governing the flow of water may also dictate the flow of charge in the most extreme environments of the universe.