Friday, January 14, 2022

Why the resistance of strange metals is linear in temperature?

The so-called strange metals are a real troublemaker for condensed matter theorists. This posting was inspired by the most recent findings about strange metals (see this).

Could one understand the somewhat mysterious looking linear high T dependence of the resistivity of strange metals in TGD the framework?

In the TGD based model of high T superconductivity (see this) charge carriers are dark electrons, or rather Cooper pairs of them, at magnetic flux tubes which are effectively 1-D systems. Magnetic flux tubes are much more general aspect of TGD based model of condensed matter (see this).

Could magnetic flux tubes carrying dark matter with heff=nh0> h also explain the resistance of strange metals. I have actually asked this question earlier.

More precisely: Could the effective 1-dimensionality of flux tubes, darkness of charge carriers, and isolation from the rest of condensed matter together explain the finding?

Isolation would mean that only the collisions of dark electrons with each other cause resistance.

One can make a dimensional estimate.

  1. Assume that the resistance ρ can be written in the form

    ρ= (4π/ω2)/τ= (me/ne e2)/τ .

    Here ω is the plasma frequency

    ω2= 4πne e2/me.

    ne is 3-D electron density.

    What happens for 3-D ne in the case of 1-D flux tube? It would seem that ne must be replaced with linear density divided by the transversal area S of the flux tube: ne= (dne/dl)×(1/S).

  2. τ is the time spent by the charge carrier in free motion between collisions. Charge carrier is in thermal motion with thermal velocity vth= kT/m . The length Lf of the free path is determined non-thermally. Hence one has

    τ= Lf/vth= mLf/kT .

    This gives 1/τ= kT/mLf.

  3. For the resistivity ρ one obtains

    ρ= (me/nee2)kT/mLf,

    which indeed depends linearly on T as it does for strange metals.

    For m=me, one would have

    ρ= kT/(nee2Lf) .

For the TGD based view of condensed matter, see for instance this.

For a summary of earlier postings see Latest progress in TGD.

Articles and other material related to TGD.

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