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!!!!!

3 dimensional M-I transition

Tunneling Density of States

Tunneling into amorphous Nb(1-x)Si(x)

With increasing x, system goes through the metal-insulator transition

Conductivity and Density of States

Mott’s Minimum Metallic Conductivity

Abrahams, Anderson,Licciardello and Ramakrishnan

Quenched Thin Films

Exponential Temperature Dependence

Superconductor-Insulator Transition

Abrahams, Anderson,Licciardello and Ramakrishnan

Quantum diffusion and interference

N-Channel MOSFET

Magnetoresistance• Lee and Ramakrishnan

Magnetoresistance in low and high perpendicular fields

High Mobility:Low FieldOrbital effects

Inelastic Scattering rates

Magnetoresistance; low-Z “metals”

Magnetoresistance in 2d Mg films

White and Dynes; Bergmann

Weak spin-orbit scattering S.O. scattering flips spin

A Spectroscopy for Scattering Rates

Magnetic spin flip scattering

Addition of magnetic impurities (spin-flip scattering) supresses coherence (Bergmann)

Quantum diffusion and interference

Magnetoresistance in low and high perpendicular fields