Wigner-Mott Scaling of Transport Near Two-Dimensional Metal-Insulator Transitions
Phys. Rev. B 85, 085133 (2012)


This paper was also described in the "Conensed Concepts" Blog by Ross McKenzie.

 INTRODUCTION
“Metal-insulator transition in 2DEG.”



Pudalov data

Development of the experimental techniques has made two dimensional electron gases (2DEG) one of the most interesting fields of study in condensed matter physics. 

Early experiments and theories predicted insulating behavior at the lowest temperatures. In the nineties, first experiments appeared reporting the existence of metallic phase in high-quality MOSFETs and 2D metal-insulator transition (MIT) tuned by the change of concentration of charge carriers. All later experiments have confirmed these observations to the lowest accessible temperatures (~4mK). 

Here we provide evidence that the electron-electron scattering dominates the transport in a broad concentration and temperature range on the metallic side of the metal-insulator transition in Si MOSFETS and GaAs/AlGaAs heterostructures.






Figure 1:
Resistivity as a function of temperature from the experiments on Si MOSFET by Pudalov et al. Physica E



Strong correlations in 2DEGs

“Are 2DEGs strongly correlated systems?”

There are several convincing signatures of strong electron correlations in diluted Si-MOSFETs and GaAs heterostructures:

scaling
  • Strong temperature dependence and nonmonotonic behavior of metallic resistivity curves
  • Large enhancement of the effective mass near the critical density nc as observed from several complementay probes. These included Shubnikov-de Haas oscillations,  and both spin susceptibility and magneto-capacitance measurements. All these results were found to be suprisingly insensitive to the level of disorder.
  • Recent experiments have reported very large enhancement of the thermoelectric power, consistent with the previous works that documented effective mass enhancements.

    

      
Figure 2:
Scaled resistivity as a function of scaled temperature for  different electron concentrations, for Si MOSFET. The experimental  data are taken from Fig. 1. The solid red line is obtained from the DMFT solution of the half-filled Hubbard model.



Scaling analysis of the resistivity curves

“Which scattering mechanism dominates transport properties? Interaction or Disorder?”


tmaxIn this work we show that all resistivity curves can be collapsed to a single curve when the temperature is scaled by the coherence temperature T*.  This represents a characteristic energy scale (renormalized Fermi temperature) which determines the transport properties in the incoherent regime. We use the scaling ansatz

δρ (T )=δρmax (n ) f [T /Tmax ( n)]

which follows from the premise (confirmed for strongly correlated materials with week and moderate disorder) that the resistivity assumes additive form

ρ (T )=ρ0 + δρ(T ).

   
Figure 3:
The scaling parameter Tmax in Si-MOSFETs is inversely proportional to the effective mass m*.


Here ρ0 is a temperature-independent term which originates from the elastic scattering of electrons on impurities and defects. The second part of the resistivity δρ(T ) is strongly temperature dependent and it is due to the inelastic (electron-electron) scattering which is responsible for the destruction of Landau quasi-particles. We find that our scaling ansatz works very well for the data from different experiments on Si-MOSFETs and GaAs hetero-structures. Examination of the critical behavior of the scaling parameter Tmax reveals power-law dependence on reduced concentration (n−nc )/nc. For Si-MOSFETs, using complementary experiments which determined the electron effective mass m* , we find that  Tmax ∼ 1/m* . Exactly the same trends are found from our DMFT theory.




Our phenomenological scaling theory strongly supports the
Wigner-Mott 
picture of the 2D MIT.