New insights into the plateau–insulator transition in the quantum Hall regime

Abstract

We have measured the quantum critical behavior of the plateau-insulator (PI) transition in a low-mobility InGaAs/GaAs quantum well. The longitudinal resistivity measured for two different values of the electron density follows an exponential law, from which we extract critical exponents κ = 0.54 and 0.58, in good agreement with the value (κ = 0.57) previously obtained for an InGaAs/InP heterostructure. This provides evidence for a non-Fermi liquid critical exponent. By reversing the direction of the magnetic field we find that the averaged Hall resistance remains quantized at the plateau value h/e 2 through the PI transition. From the deviations of the Hall resistance from the quantized value, we obtain the corrections to scaling.

Quantum criticality at the Chern-to-normal insulator transition

“…We compare these results with the known facts for the PIT in IQHE. 17,[19][20][21][22]24,[82][83][84][85] We find that, like at PIT in IQHE, the graphs of ρ xx as function of electron density, recorded at different temperatures, intersect at one single critical point, and they collapse into a single curve after a single-parameter rescaling. The scaling exponent κ is in good agreement with what one would predict by using the universally accepted value of the finite-size scaling exponent ν = 2.58 ± 0.03, 54,[86][87][88][89][90][91] and with p fixed like in our simulations (p = 1).…”

Quantum critical behaviour of the plateau-insulator transition in the quantum Hall regime

“…At the high temperature side this is due to thermal broadening by the Fermi-Dirac distribution. When fitting the data below 2 K, we obtain a critical exponent = 0.58 and T 0 = 230 K. In order to investigate the universality of our scaling results for the PI transition we have also conducted experiments on a quite different semiconductor structure, namely a low-mobility InGaAs/GaAs QW (well width 12 nm) [10,11]. The sample is insulating in the dark state, but could be tuned to different carrier densities by the persistent photoconductivity effect.…”

“…In this paper, we briefly address the principles of scaling and delineate our methodology to disentangle the quantum critical aspects of the two-dimensional electron gas from the sample dependent effects. Next we review the results of recent high-field magnetotransport studies carried out on different InGaAs/InP heterostructures (HS) [1,6,8,10] and an InGaAs/GaAs quantum well (QW) [10,11] .…”

Magneto-transport of graphene and quantum phase transitions in the quantum Hall regime

“…In such transition there exists a T-independent crossing point corresponding to a critical magnetic field B c where all the isotherms collapse. The value obtained for the critical exponent of this transition in semiconductor samples (InGaAs/InP and InGaAs/GaAs) [18][19][20][21][22][23] was κ = 0.58, but there still exist some controversy whether this transition belongs to the same universality class of the PP one.…”