Dirty Metals and Mott’s minimum metallic conductivity.
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Transcript of Dirty Metals and Mott’s minimum metallic conductivity.
Temperature Dependent Resistivity and Disorder
1/tau = 1/t1 + 1/t2 +1/t3+………
Matthiessen’s rule following ρ = m/ne2tau
ρ= ρ1+ ρ2 + ρ3 +…….
For electron phonon scattering
atheissen’s Rule Scattering rates are additive
Rho(T)= rho1(T)+rho2(T)+rho3(T)+…………
Rho=m/ne2tau
For free electron n=4/3 kf3 mvf = hkf /2and tau=vf
Mathiessen’s rule works pretty well until kf
ott argued that it is difficult to imagine an extended state when the mean free path became shorter than the wavelength of the electron
In two dimensions it becomes particularily intriguing
In 2d n=kf2 so that the resistivity at this Mott limit becomes
m/ne2tau
So when the mean free path becomes equal to the wave length of the electron
the resistivity becomes
h/e2
This is a product of fundamental constants. Putting back all the ’s you find that Mott’s minimum metallic conductivity (maximum metallic resistivity) is 10-30 Kohms!!!!!
Tunneling Density of States
Tunneling into amorphous Nb(1-x)Si(x)
With increasing x, system goes through the metal-insulator transition
Magnetoresistance; low-Z “metals”
Magnetoresistance in 2d Mg films
White and Dynes; Bergmann
Weak spin-orbit scattering S.O. scattering flips spin
Magnetic spin flip scattering
Addition of magnetic impurities (spin-flip scattering) supresses coherence (Bergmann)