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This letter reports thermopower and conductivity measurements through the metal-insulator transition for 2-dimensional electron gases in high mobility Si-MOSFET's. At low temperatures both thermopower and conductivity show critical behavior as a function of electron density which is very similar to that expected for an Anderson transition. In particular, when approaching the critical density from the metallic side the diffusion thermopower appears to diverge and the conductivity vanishes. On the insulating side the thermopower shows an upturn with decreasing temperature.

We study the quantum critical behavior of the plateau-insulator (PI) transition in a low mobility In0.53Ga0.47As/InP heterostructure. By reversing the direction of the magnetic field (B) we find an averaged Hall resistance ρxy which remains quantized at the plateau value h/e 2 throughout the PI transition. We extract a critical exponent κ ′ = 0.57 ± 0.02 for the PI transition which is slightly different from (and possibly more accurate than) the established value 0.42 ± 0.04 as previously obtained from the plateau-plateau (PP) transitions.One of the fundamental issues in the field of two dimensional electron gases is the nature of the transitions between adjacent quantum Hall plateaus. By measuring the resistance tensor of low mobility In 0.53 Ga 0.47 As/InP heterostructures, Wei et al. [1,2] demonstrated that the quantum Hall steps become infinitely sharp as T → 0, indicating that the transitions between adjacent quantum Hall plateaus (PP transitions) represent a sequence of quantum phase transitions (QPT). Both the maximum slope in the Hall resistance with varying B, (∂ρ xy /∂B) max , and the inverse of the half-width of the longitudinal resistance between two adjacent quantum Hall plateaus, (∆B) −1 , have been shown to follow the power law T −κ as T approaches absolute zero, independent of Landau level index. Here, κ = p/2ν where p denotes the exponent of the phase breaking length ℓ ϕ at finite T (i.e. ℓ ϕ ∼ T −p/2 ) and ν is the critical index for the localization length ξ which is defined at zero T .In order to probe the QPT, it is essential to carry out experiments on samples where the dominant scattering mechanism is provided by short ranged random potential fluctuations [3]. Like in In 0.53 Ga 0.47 As/InP, this produces the widest range in T where quantum criticality is accessible experimentally. At the same time, little is known about the effects of macroscopic sample inhomogeneities which generally complicate experiments on the QPT. The problem of sample inhomogeneities was recently addressed by van Schaijk et al. [4] who investigated the plateau-insulator (PI) transition in the lowest Landau level. The data were taken from the same In 0.53 Ga 0.47 As/InP heterostructure which was previously used in the study of the PP transitions [2].Following the analysis by van Schaijk et al. one can extract different exponents κ and κ ′ from the transport data on the PI transition, dependent on the specific quantity one considers. For example, the longitudinal resistance ρ xx was shown to follow the exponential law [5] ρ xx (ν, T ) ∝ exp(−∆ν/ν 0 (T )). Here, ∆ν = ν − ν c represents the filling fraction ν of the lowest Landau level relative to the critical value ν c ≈ 1 2 and ν 0 (T ) ∝ T κ ′ with an experimental value κ ′ = 0.55 ± 0.05. The numerical value of the exponent κ ′ differs by more than the experimental error from the established "universal" value 0.42 ± 0.05 that was previously extracted from the resistance data on PP transitions [1,2]. In an attempt to understand the difference, van Schaijk et al. poin...

Both the temperature dependence of resistivity and thermopower of a two-dimensional hole gas in SiGe show a reentrant metal-insulator transition at filling factor 1:5, but with strikingly different behavior of the two coefficients. As the temperature is decreased in the insulating state, the resistivity diverges exponentially while the thermopower decreases rapidly, suggesting that the insulating state is due to the presence of a mobility edge rather than a gap at the Fermi energy.

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