There are fundamental physical laws, as well as models that describe the behavior of a limited number of systems under certain conditions. When a significant amount of experimental data accumulates that does not fit the model, it becomes necessary to revise the theory or search for hidden mechanisms that explain the discrepancies between theory and experiment.

Features of Cuprates and the Strange Metal State

High-temperature copper-based superconductors, known as cuprates, exhibit unusual properties even outside the superconducting state. In this state, called the "strange metal," the material’s electrical resistance changes linearly with temperature across the entire temperature range. This is different from the behavior of ordinary metals, where the dependence of resistance on temperature is more complex.

For cuprates, the formula for linear temperature dependence of resistance holds: ρ = ρ₀ + A·T, where A is the slope coefficient reflecting how quickly resistance changes with temperature. Resistance indicates how intensely electrons scatter as they move through the material: the higher the resistance, the more frequently charge carriers encounter obstacles.

The Effect of Doping and the Universality Problem

Experiments with cuprates have shown that the slope coefficient A strongly depends on the degree of doping of the material. Adding atoms that change the number of electrons and holes significantly affects parameters that, according to theory, should remain unchanged. This called into question the universality of the Planckian scattering limit, which defines the minimum possible electron scattering time.

Revisiting the Analysis and New Approaches

A group of physicists found that the reason for the discrepancies lay in the method of data analysis. When a more accurate model is used, the contradiction disappears. In a study published in Nature Communications, it was shown that a simplified Drude model had previously been used to describe charge carrier scattering in cuprates, treating electrons as particles with the same effective mass that includes all interactions with the material.

However, cuprates have a complex electronic structure, causing the velocities of electrons and holes to differ significantly in different directions. This can be compared to the difference between moving with or against the current in a river. In such conditions, the Drude model does not accurately reflect reality.

The Boltzmann Kinetic Equation and Plasma Frequency

To correctly describe the electronic structure of the strange metal, it is necessary to use the Boltzmann kinetic equation, which is applied to describe charge transport in classical metals. This equation takes into account the distribution of electron velocities in the material. In this case, resistance depends on the square of the optical plasma frequency—a parameter that characterizes the ability of the electronic system to respond to an electromagnetic field.

It was previously known that for some cuprates, the square of the plasma frequency increases linearly with the degree of doping, but this was not given much attention. The new study showed that if the linear relationship between doping and plasma frequency is included in the formula for the slope coefficient A, then the coefficient in the equation for the Planckian scattering limit becomes constant, restoring the universality of this limit.

The Relationship Between Plasma Frequency and Doping

Physicists also explained why the plasma frequency depends linearly on doping. Based on experimental data, it was calculated that the factor describing the degree of change in the material’s electronic structure is approximately equal to the fraction of holes in the material.

Research Conclusions

As a result of this work, the contradiction between experimental data and theory was resolved. It was shown that electron scattering in cuprates in the strange metal state does not depend on doping. The dependence of resistance on doping is due to changes in the material’s electronic structure, not the scattering mechanism. For the theory of superconductivity, it is important that the properties of the strange metal state are determined by the internal structure of the material.