Physicists have discovered the upper limit of electrical resistance in metals, offering a rare clean look at a problem that is usually tangled up in real materials by vibrations, disorder, and structural changes. The study, published in Physical Review Letters, uses ultracold atoms to measure time without a clock, providing a new perspective on the behavior of electrons in metals. The team, led by Professor Joseph Thywissen of the University of Toronto, found that stronger and stronger collisions eventually stop adding more resistivity, leading to a phenomenon known as collisional resistivity saturation. This discovery has significant implications for our understanding of resistivity in low-density metals and could help researchers interpret puzzling transport measurements in quantum materials.
The experiment centered on fermionic potassium-40 atoms placed in a three-dimensional cubic lattice with a period of 0.53 micrometers. The researchers used atoms as stand-ins for electrons and observed how their motion slowed when interactions were tuned upward. This tuning was achieved through a magnetic Feshbach resonance, which allows physicists to adjust the strength of the short-range interaction between atoms. In ordinary solids, changing interactions so cleanly is impossible, but in the lattice, it allowed the team to isolate atom-atom scattering as the main brake on transport.
The measurements were carried out in a low-filling regime, with the average occupation staying well below one atom per site. This choice mattered because it kept the system strongly interacting but only weakly correlated. This made it possible to compare the data directly with a nonperturbative solution of the two-body problem rather than relying only on broad many-body approximations.
To probe conductivity, the team applied a sinusoidal force by displacing the optical dipole trap. They then imaged the cloud in situ and tracked its center-of-mass motion. From that response, they extracted the real and imaginary parts of the conductivity and, from there, the complex resistivity.
The key finding was that at modest interaction strengths, more interaction led to faster current dissipation and higher resistivity. However, this trend broke down in the strongly interacting regime. The conductivity spectra broadened sharply as the interaction strength rose, signaling a reduced current lifetime due to scattering. Yet pushing the interaction to about U/t = 6 produced almost no further broadening, and the increase in resistivity flattened.
This flattening was identified as the main result of the work: collisional resistivity saturation. The researchers observed that the atoms, which are only a few nanometers in size, bump into each other as if they were much larger due to a quantum enhancement of the effective atom size. This makes collisions on a given lattice site much more likely, increasing the resistivity of the system.
However, this quantum enhancement did not produce unlimited resistance. The key insight was that the scattering amplitude itself becomes bounded in the lattice. Even in the limit of very large on-site interaction U, the transition matrix that sets the scattering strength cannot grow without limit. In the strong-collision regime, the system crosses over from interaction-limited dissipation to tunneling-limited dissipation.
The paper frames this upper limit as "lattice unitarity." The authors found that even at infinite U, a thermal ensemble cannot fully reach the upper bound on the scattering cross section because the transition matrix depends on momentum. At the highest interaction strengths in the experiment, the inferred dissipation rate reached only about one-third of the lattice-unitary bound.
The researchers built a dissipation model based on kinetic theory and the full two-body transition matrix, then compared it with the measurements. The agreement was strong and did not rely on free parameters in the transport calculation. This is unusual for resistivity work, where experiments often outpace first-principles explanations.
The model also helped separate the role of current dissipation from changes in static susceptibility or effective mass. The saturation, the team argues, is dynamical and comes from the scattering rate itself, not from a trivial saturation of another quantity hiding inside the transport signal.
Temperature added another layer. At fixed strong interaction, resistivity rose steadily with temperature across the accessible range, by roughly a factor of ten. The analysis showed that in this regime, resistivity is dominated by umklapp events, which transfer momentum from the moving particles to the lattice.
"Our results provide a clear microscopic understanding of how resistivity works in low-density metals and open the door to new studies of strongly correlated atomic systems and quantum materials," said Thywissen. "This work does not promise a new wire or a near-term device. Its value is more basic, and in some ways more durable. By showing that collision-driven resistivity can saturate, the study sharpens one of the central questions in condensed-matter physics: what really sets the limit on how much interactions alone can impede transport?"
The findings suggest that in low-density, strongly interacting systems, rising collision strength does not automatically mean ever-rising resistance. This could help researchers interpret puzzling transport measurements in quantum materials, especially where strong interactions are present but conventional explanations fall short. It also establishes ultracold atoms as a more precise test bed for transport theory, including questions about hydrodynamics, dilute Fermi liquids, and the boundary between weakly and strongly correlated behavior.
