| Summary: | Physicists are actively debating the nature of the quantum critical phase transition that determines the low-temperature properties of metals with heavy fermions. Important experimental observations of their transport properties incisively probe the nature of the quantum critical phase transition. In our short review, we consider the transport properties of strongly correlated Fermi systems like heavy fermion metals and high—<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>c</mi></msub></semantics></math></inline-formula> superconductors. Their transport properties are defined by strong inter-particle interactions, forming flat bands in these compounds. These properties do not coincide with those of conventional metals. Indeed, in contrast to the behavior of the transport properties of conventional metals, the strongly correlated compounds exhibit linear temperature resistivity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ρ</mi><mo>(</mo><mi>T</mi><mo>)</mo><mo>∝</mo><mi>T</mi></mrow></semantics></math></inline-formula>. We analyze the magnetoresistance and show that under the application of the magnetic field, it becomes negative. It is shown that near a quantum phase transition, when the density of the electronic states diverges, semiclassical physics remains applicable to describe the resistivity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula> of strongly correlated metals due to the presence of a transverse zero-sound collective mode, representing the phonon mode in solids. We demonstrate that when <i>T</i> exceeds the extremely low Debye temperature <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>T</mi><mi>D</mi></msub></semantics></math></inline-formula>, the resistivity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ρ</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> changes linearly with <i>T</i> since the mechanism of formation of the <i>T</i>-dependence <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ρ</mi><mo>(</mo><mi>T</mi><mo>)</mo></mrow></semantics></math></inline-formula> is a similar electron-phonon mechanism, which predominates at high temperatures in ordinary metals. Thus, in the region of <i>T</i>-linear resistance, electron-phonon scattering leads to a lifetime of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>τ</mi></semantics></math></inline-formula> quasiparticles practically independent of the material, which is expressed as the ratio of the Planck constant <i>ℏ</i> to the Boltzmann constant <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>k</mi><mi>B</mi></msub></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>T</mi><mi>τ</mi><mo>∼</mo><mo>ℏ</mo><mo>/</mo><msub><mi>k</mi><mi>B</mi></msub></mrow></semantics></math></inline-formula>. We explain that due to the non-Fermi-liquid behavior, the real part of the frequency-dependent optical conductivity <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>σ</mi><mrow><mi>o</mi><mi>p</mi><mi>t</mi></mrow><mi>R</mi></msubsup><mrow><mo>(</mo><mi>ω</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> exhibits a scaling behavior and demonstrates the unusual power law behavior <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>σ</mi><mrow><mi>o</mi><mi>p</mi><mi>t</mi></mrow><mi>R</mi></msubsup><mrow><mo>(</mo><mi>ω</mi><mo>)</mo></mrow><mo>∝</mo><msup><mi>ω</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow></semantics></math></inline-formula>, rather than the well-known one shown by conventional metals, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msubsup><mi>σ</mi><mrow><mi>o</mi><mi>p</mi><mi>t</mi></mrow><mi>R</mi></msubsup><mrow><mo>(</mo><mi>ω</mi><mo>)</mo></mrow><mo>∝</mo><msup><mi>ω</mi><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></semantics></math></inline-formula>. All our theoretical considerations are illustrated and compared with the corresponding experimental facts. Our results are in a good agreement with experimental observations.
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