Resistivity in a three-dimensional elemental metal has been shown to vary with sample size and temperature as predicted by physicist Radii Gurzhi more than 60 years ago, physics.aps.org reported on November 9, 2026.
Ordinary metals typically see conductivity decrease as they warm up because electron-phonon collisions impede flow. The Gurzhi effect describes how thermal energy can instead reduce internal resistance to flow, or viscosity, causing conductivity to rise with temperature.
A research team led by Kamran Behnia of ESPCI Paris and Zengwei Zhu of Huazhong University of Science and Technology in China tested high-purity crystals of hexagonal close-packed cadmium. They used focused-ion-beam etching to create samples ranging from about 2 to 114 micrometers.
The largest cadmium sample behaved like an ordinary metal. Its resistivity decreased quadratically in temperature toward a constant residual value as researchers cooled it.
However, samples measuring about 65 micrometers and smaller exhibited the Gurzhi effect. Their resistivity reached a minimum near 5 Kelvin before rising upon further cooling.
By subtracting boundary scattering resistance obtained at 5 Kelvin, researchers found that the hydrodynamic contribution to conductivity grew as the square of both temperature and sample size. Below about 2.5 Kelvin, smaller samples deviated from this scaling as the momentum-conserving mean free path became comparable to the sample size, marking the ballistic regime.
Cadmium’s primary charge carriers reside in three main pockets of its Fermi surface with Fermi energies on the order of 1 electron-volt. Behnia, Zhu, and colleagues used ab initio calculations of the band structure to find additional small pockets with Fermi energies as low as 0.5 milli-electron-volts.
The research team proposes that these tiny pockets determine the momentum-conserving collision rate at low temperatures. This setup allows momentum-conserving collisions to remain dominant despite the metal’s relatively large primary Fermi energy.
Complications remain because the smallest pockets lie close to much larger hole-like pockets. Inter-pocket electron scattering may play as large a role as small Fermi energies in setting the momentum-conserving lifetime.
Researchers used a technique to prepare a series of high-purity cadmium crystals of varying sizes without introducing new defects to study the Gurzhi effect.
In samples measuring about 65 micrometers and smaller, the electrical resistivity reached a minimum near 5 Kelvin before increasing as the material cooled further.
The experiment confirmed predictions made by Radii Gurzhi over 60 years ago regarding how viscosity and conductivity behave in specific hydrodynamic metal regimes.
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