The behaviour of electrons in materials like graphene often defies traditional descriptions, prompting scientists to investigate whether a fluid-like approach, known as electron hydrodynamics, better explains their movement. Subhalaxmi Nayak, Cho Win Aung, and Thandar Zaw Win, all from the Indian Institute of Technology Bhilai, alongside colleagues, comprehensively review the current understanding of this phenomenon in graphene, examining both experimental evidence and theoretical models. Their work highlights key observations, including unusual resistance patterns and deviations from established physical laws, that suggest electrons behave as a flowing fluid rather than individual particles. This research is significant because it challenges conventional solid-state physics and could pave the way for designing new, more efficient electronic devices that exploit these fluid-like properties.
Carrier transport in solid state systems depends on various microscopic interactions, such as scattering with electrons, phonons, impurities, boundaries, and disorder. The scattering length, or mean free path, of charge carriers significantly influences this transport. Recent research focuses on velocity resistance, fluid-like flow, and deviations from the Wiedemann-Franz law, with particular attention to measurements of the Lorenz ratio. Current theoretical efforts aim to develop hydrodynamic frameworks for calculating the thermodynamic and transport coefficients of electrons in graphene.
Visualizing Hydrodynamic Electron Flow in Graphene
A major theme in recent research concerns the behaviour of electrons in graphene, suggesting they can behave not as individual particles, but as a fluid exhibiting properties like viscosity and potentially laminar flow in confined spaces. Sulpizio and colleagues demonstrated direct visualization of fluid-like flow in graphene, providing key evidence for this hydrodynamic behaviour. Earlier theoretical work by Müller, Schmalian, and Fritz proposed that graphene could exhibit nearly ideal fluid behaviour, while Narozhny’s work provides a broader theoretical treatment of hydrodynamic behaviour in two-dimensional systems, including graphene. Graphene often deviates from this law, indicating unusual transport mechanisms. Wei and colleagues discovered anomalous thermoelectric transport of Dirac particles in graphene, and Zuev and colleagues conducted thermoelectric and magnetothermoelectric transport measurements. Ghahari and colleagues highlighted the role of inelastic scattering in violating the Wiedemann-Franz law, while Dwibedi and colleagues investigated the violation in graphene and quark-gluon plasma systems. Some research explores the connection between graphene’s transport properties and quantum criticality, the behaviour of systems near a quantum phase transition. Majumdar and colleagues suggest graphene exhibits universal behaviour related to quantum criticality. Hartnoll and colleagues connected concepts from condensed matter physics to black hole physics, relevant to understanding emergent phenomena, and Kovtun and colleagues provided important theoretical work on the relationship between viscosity and strongly interacting systems.
De Groot’s work provides the theoretical framework for understanding transport phenomena, and Jaiswal’s work explores spin-hydrodynamics of electrons in graphene and magnetization due to thermal vorticity. Jaiswal and Roy’s work provides an overview of relativistic hydrodynamics in heavy-ion collisions, and Crossno and colleagues observed transport in inhomogeneous quantum critical fluids and in the Dirac fluid in graphene. Hartnoll and colleagues developed a theory of the Nernst effect near quantum phase transitions, and Novoselov’s Nobel lecture provided a foundational overview of graphene’s properties and potential.
Graphene Hydrodynamics, Pressure and Carrier Density Relationship
This work details a comprehensive investigation into electron hydrodynamics in graphene, presenting both experimental observations and theoretical developments. Researchers meticulously calculated thermodynamic and transport coefficients, focusing on the ratio of shear viscosity to entropy density and the Lorenz ratio, key indicators of electron behaviour. The team developed mathematical structures for shear viscosity and its ratio to entropy density within an electron-hole plasma in graphene, revealing how these values are influenced by Fermi integral functions and carrier density. Results demonstrate a clear relationship between pressure and carrier concentration, with increasing pressure observed for both electrons and holes around the charge neutrality point at a fixed temperature of 60 Kelvin, and energy density follows a similar trend.
Analysis of carrier density reveals that electron transport dominates at high chemical potentials, while hole transport prevails at negative chemical potentials, with both contributing significantly in the intermediate range. Further investigation into enthalpy density per particle, scaled by chemical potential, shows a crucial role in the hydrodynamic regime. At 60 Kelvin, this value approaches one for chemical potentials exceeding 3. 5, diverging near the Dirac point. Comparative studies of the Lorenz ratio reveal significant violations of the Wiedemann-Franz law, with enhancements reaching up to 22times the baseline value in ultra-pure graphene samples.
The team’s calculations, based on enthalpy per particle, demonstrate a substantial violation of this law near the Dirac point. The normalized ratio of shear viscosity to entropy density exhibits a valley-shaped pattern, reaching a minimum at the charge neutrality point. The electronic contribution to this ratio becomes negligible for negative chemical potentials, while the hole contribution diminishes for positive values. This research confirms that graphene, near the charge neutrality point, behaves as a quantum critical fluid and a quasi-relativistic plasma, exhibiting hydrodynamic motion rather than simple diffusion, supported by experimental observations of fluid-like flow, negative vicinity resistance, and violations of the Wiedemann-Franz law.
Graphene Hydrodynamics, Viscosity and Carrier Density Relations
This work presents a comprehensive investigation into electron hydrodynamics in graphene, detailing both experimental observations and theoretical developments. Researchers have successfully established clear distinctions in the mathematical descriptions of transport coefficients, such as electrical and thermal conductivity, when comparing non-fluid and fluid-based frameworks for graphene. Specifically, the team derived novel mathematical expressions for shear viscosity and the ratio of shear viscosity to entropy density, considering the behaviour of electron-hole plasmas within the material. The results demonstrate how pressure and carrier density vary with chemical potential, revealing that electron transport dominates at higher positive potentials, while hole transport prevails at lower negative potentials, contributing to a more nuanced understanding of charge carrier behaviour in graphene and providing a foundation for exploring novel electronic devices.