A state of electrons in a material where they behave collectively as a viscous fluid rather than as independent particles.An electron liquid is a collective state of electrons in a material where they behave not as independent particles but as a viscous, fluid-like medium. This behavior emerges in extremely clean, low-temperature systems where electron-electron interactions dominate over scattering from impurities or lattice vibrations. In such a state, electrons can flow around obstacles in a manner analogous to a classical fluid, exhibiting phenomena like vortices and laminar flow.
The concept of electron hydrodynamics was first proposed in the 1960s by Russian physicist Yuri Pines, but experimental evidence remained elusive for decades. Direct observations of electron vortices were reported in 2019 in graphene devices.
In ordinary metals, electrons scatter frequently off impurities and phonons, making their motion diffusive. In an electron liquid, the mean free path for electron-electron collisions becomes shorter than the system's dimensions, so the electrons thermalize among themselves and behave as a hydrodynamic fluid. This is described by the Navier-Stokes equations with a viscosity that depends on the electron-electron interaction strength.
Understanding electron liquids is crucial for designing next-generation electronic devices, particularly those based on graphene and other 2D materials, where hydrodynamic effects can improve conductivity and reduce heat dissipation.
In an electron liquid, the viscosity can be so low that it approaches a fundamental quantum limit set by the Heisenberg uncertainty principle.










