Wednesday, February 20, 2013

Are elemental metals quantum critical?

I doubt it.

There is an interesting paper
Similarity of Scattering Rates in Metals Showing T-Linear Resistivity
J.A.N. Bruin, H. Sakai, R.S. Perry, A.P. Mackenzie

The central result is the figure below.

The graph shows the magnitude of the estimated scattering rate per Kelvin versus the Fermi velocity for a wide range of materials.
The line alpha=1 corresponds to a value of k_B/hbar, comparable to what one gets from a simple dimensional analysis or the "minimum viscosity limit" of "quantum hydrodynamic fluids" described by some theoretical models connected to string theory.

What worries me about this graph?
It is that elemental metals [copper, silver, aluminum, paladium, ...] lie on the same curve. As far as I am aware, they are not strongly correlated. They are nowhere near a quantum critical point. The resistivity is due to electron-phonon scattering. So given that they "accidentally" lie on this "universal" curve suggests to me that the significance of other materials lying close to it may not be of much significance.

On the other hand, the authors claim this "universality" arises because the electron-phonon scattering is "highly efficient" involving "high momentum scattering". They suggest similar scattering occurs in quantum critical metals.

A couple of earlier posts discussed my skepticism/confusion about similar claims about the significance of the magnitude of the linear resistivity.

A key piece of experimental evidence is needed to rigorously justify claims of quantum criticality: measurement of a correlation length which diverges at the quantum critical point.

But, perhaps I am missing something....


  1. “What worries me about this graph?
    It is that elemental metals [copper, silver, aluminum, paladium, ...] lie on the same curve. As far as I am aware, they are not strongly correlated”.

    Yes, you are right, these elemental metals are not strongly correlated. While the strongly correlated metals exhibit the properties of elemental ones, that is they demonstrate a quasi-classical behavior at low temperatures. Please, see: Quasi-classical physics and T-linear resistivity in both strongly correlated and ordinary metals, Phys. Rev. B 88, 115103 (2013),

    With warm regards,
    Vasily Shaginyan

  2. More detailed consideration of this item can be found in "Theory of Heavy-Fermion Compounds; Theory of Strongly Correlated Fermi-Systems"

  3. The item related to the universal behavior of the scattering rate again becomes hot,
    for many authors try to explain such a behavior as the Planckian limit. We explain recent challenging experimental
    observations that the scattering rate of charge carriers collected on high temperature superconductors, graphene,
    heavy fermion and conventional metals exhibits the universal behavior generated by the quasiclassical properties of above strongly correlated materials. While the Planckian limit may occur accidentally: It
    is highly improbable that it would be realized in conventional metals, which, obviously, cannot be recognized as Planckian metals with quantum criticality at high or low temperatures. Finally, the fact that we observe the same universal behavior of the scattering rate in microscopically different strongly
    correlated compounds like HTSC, HF and conventional metals, suggests that some general theory is needed to explain the above body of materials and their behavior in the uniform manner. We may conclude that the Fermion condenstaion theory is the suitable candidate.

    [1] Fermion Condensation, T-linear Resistivity and Planckian Limit,

    [2] Flat band and Planckian metal,