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Published byEthelbert Skinner Modified over 9 years ago
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Dirty Metals and Mott’s minimum metallic conductivity
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Temperature Dependent Resistivity and Disorder 1/tau = 1/t 1 + 1/t 2 +1/t 3 +……… Matthiessen’s rule following ρ = m/ne 2 tau ρ= ρ 1 + ρ 2 + ρ 3 +……. For electron phonon scattering
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atheissen’s Rule Scattering rates are additive Rho(T)= rho 1 (T)+rho 2 (T)+rho 3 (T)+………… Rho=m/ne 2 tau For free electron n= 4 / 3 k f 3 mv f = hk f /2 and tau= v f Mathiessen’s rule works pretty well until k f ott argued that it is difficult to imagine an extended state when the mean free path became shorter than the wavelength of the electron
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In two dimensions it becomes particularily intriguing In 2d n= k f 2 so that the resistivity at this Mott limit becomes m/ne 2 tau So when the mean free path becomes equal to the wave length of the electron the resistivity becomes h/ e 2 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!!!!!
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3 dimensional M-I transition
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Tunneling Density of States Tunneling into amorphous Nb(1-x)Si(x) With increasing x, system goes through the metal-insulator transition
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Conductivity and Density of States
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Mott’s Minimum Metallic Conductivity
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Abrahams, Anderson,Licciardello and Ramakrishnan
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Quenched Thin Films
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Exponential Temperature Dependence
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Superconductor-Insulator Transition
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Abrahams, Anderson,Licciardello and Ramakrishnan
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Quantum diffusion and interference
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N-Channel MOSFET
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Magnetoresistance Lee and Ramakrishnan
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Magnetoresistance in low and high perpendicular fields
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High Mobility:Low Field Orbital effects
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Inelastic Scattering rates
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Magnetoresistance; low-Z “metals” Magnetoresistance in 2d Mg films White and Dynes; Bergmann Weak spin-orbit scattering S.O. scattering flips spin
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A Spectroscopy for Scattering Rates
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Magnetic spin flip scattering Addition of magnetic impurities (spin-flip scattering) supresses coherence (Bergmann)
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Quantum diffusion and interference
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Magnetoresistance in low and high perpendicular fields
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