# Fermion condensation, $T$-linear resistivity and Planckian limit

## TL;DR

This paper explains the universal linear-temperature resistivity in strongly correlated and conventional metals as arising from phonon contributions linked to topological fermion condensation quantum phase transition, challenging the Planckian limit interpretation.

## Contribution

It demonstrates that the observed scattering rate is due to phonons from flat bands caused by FCQPT, providing a new topological perspective on resistivity behavior.

## Key findings

- Resistivity linear in temperature due to phonons from flat bands.
- Planckian limit may be coincidental, not fundamental.
- Good agreement with experimental data.

## Abstract

We explain recent challenging experimental observations of universal scattering rate related to the linear-temperature resistivity exhibited by a large corps of both strongly correlated Fermi systems and conventional metals. We show that the observed scattering rate in strongly correlated Fermi systems like heavy fermion metals and high-$T_c$ superconductors stems from phonon contribution that induce the linear temperature dependence of a resistivity. The above phonons are formed by the presence of flat band, resulting from the topological fermion condensation quantum phase transition (FCQPT). We emphasize that so - called Planckian limit, widely used to explain the above universal scattering rate, may occur accidentally as in conventional metals its experimental manifestations (e.g. scattering rate at room and higher temperatures) are indistinguishable from those generated by the well-know phonons being the classic lattice excitations. Our results are in good agreement with experimental data and show convincingly that the topological FCQPT can be viewed as the universal agent explaining the very unusual physics of strongly correlated Fermi systems.