Presentation is loading. Please wait.

Presentation is loading. Please wait.

Dirty Metals and Mott’s minimum metallic conductivity.

Similar presentations


Presentation on theme: "Dirty Metals and Mott’s minimum metallic conductivity."— Presentation transcript:

1 Dirty Metals and Mott’s minimum metallic conductivity

2 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

3

4  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

5

6 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!!!!!

7 3 dimensional M-I transition

8 Tunneling Density of States Tunneling into amorphous Nb(1-x)Si(x) With increasing x, system goes through the metal-insulator transition

9 Conductivity and Density of States

10 Mott’s Minimum Metallic Conductivity

11 Abrahams, Anderson,Licciardello and Ramakrishnan

12 Quenched Thin Films

13 Exponential Temperature Dependence

14 Superconductor-Insulator Transition

15

16

17 Abrahams, Anderson,Licciardello and Ramakrishnan

18 Quantum diffusion and interference

19 N-Channel MOSFET

20

21 Magnetoresistance Lee and Ramakrishnan

22 Magnetoresistance in low and high perpendicular fields

23 High Mobility:Low Field Orbital effects

24 Inelastic Scattering rates

25 Magnetoresistance; low-Z “metals” Magnetoresistance in 2d Mg films White and Dynes; Bergmann Weak spin-orbit scattering S.O. scattering flips spin

26 A Spectroscopy for Scattering Rates

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

28 Quantum diffusion and interference

29 Magnetoresistance in low and high perpendicular fields

30

31


Download ppt "Dirty Metals and Mott’s minimum metallic conductivity."

Similar presentations


Ads by Google