From the zero-field metal-insulator transition in two dimensions to the quantum Hall transition: A percolation-effective-medium theory

Abstract

Effective-medium theory is applied to the percolation description of the metal-insulator transition in two dimensions with emphasis on the continuous connection between the zero-magnetic-field transition and the quantum Hall transition. In this model the system consists of puddles connected via saddle points, and there is loss of quantum coherence inside the puddles. The effective conductance of the network is calculated using appropriate integration over the distribution of conductances, leading to a determination of the magnetic field dependence of the critical density. Excellent quantitative agreement is obtained with the experimental data, which allows an estimate of the puddle physical parameters.PACS numbers: 71.30.+h,73.40.Hm,72.15.Rn, Extensive experimental and theoretical effort has been invested in the attempt to understand and characterize the observation of metallic-like behavior in two dimensions [1]. One of the intriguing experimental findings [2] is that this zero-magnetic-field "transition" is continuously connected with the integer quantum Hall transition. In previous publications [3] I presented a simple non-interacting electron model, combining local quantum transport and global classical percolation, which treated the zero field transition and the quantum Hall transition on the same footing. Numerical calculations showed behavior qualitatively similar to that observed experimentally. In the present paper I present an analytic approach, based on the effective-medium theory of percolation [4], that allows quantitative comparison with the experiment. This comparison also allows determination of physical properties of the underlying electronic state. The implications on transport in the quantum Hall regime due to this continuous connection to the zero-field transition are discussed and shown to be in agreement with experimental observations in the quantum Hall regime.The model is based on two assumptions: (a) the potential fluctuations due to the disorder define density puddles, connected via saddle points, or quantum pointcontacts (QPCs), and (b) The electron wavefunction totally dephases in the puddles, i.e. the time the particle spends in the puddle is larger that the dephasing time. Each saddle point is characterized by its critical energy ǫ c , such that the transmission through it is given by T (ǫ) = Θ(ǫ − ǫ c ), where quantum tunneling has been neglected. Thus the conductance through each QPC is given by the Landauer formula,

Resistance noise scaling in a dilute two-dimensional hole system in GaAs

“…The fact that our experimental points in Fig. 6 scale together whatever the temperature suggests that x is a function of both p s and T. The simplest relationship x ∝ p s is obtained in a percolation model where the disordered potential landscape is progressively filled by the Fermi liquid when the density increases [39][40][41] . In such a description, the transport occurs by percolation through a network of Fermi liquid puddles connected by quantum point contacts.…”

“…Concerning a percolation transition, two kinds of models must be considered. The first one is that of Fermi liquid puddles connected by quantum point contacts [39][40][41] . In the second one, the system is a mixture of two phases (conducting and insulating) as suggested by theories of interacting electrons 3,[43][44][45][46][47][48] .…”

“…In such theories, the transport and other physical properties could be due to the percolation of one of the phases through the other, each of them being conducting or insulating. Another (different) percolation description of the system consists in Fermi liquid puddles connected by quantum point contacts [39][40][41] . In the present study, we use 1/f noise as a tool to investigate the physical properties of a 2DHS in p-GaAs.…”

Transport in Two-Dimensional Disordered Semimetals

“…(c) The long-ranged fluctuations in the potential create regions where only electrons (red) or only holes (blue) are occupied, and regions where both carriers coexist (purple) [top view].ing inhomogeneous, two-component conductance problem using an effective medium approximation (EMA) [9][10][11][12][13][14]. EMA has already been used successfully to characterize transport in GaAs quantum wells, where smooth disorder has been identified as the main mechanism for the transition from metallic to insulating behavior as a function of electron density [15][16][17][18][19][20][21][22]. We investigate dependences of the transport on band-overlap, temperature, gate voltage, electron-hole recombination rate, and arXiv:1405.0277v3 [cond-mat.mes-hall]…”

“…We solve the result- ing inhomogeneous, two-component conductance problem using an effective medium approximation (EMA) [9][10][11][12][13][14]. EMA has already been used successfully to characterize transport in GaAs quantum wells, where smooth disorder has been identified as the main mechanism for the transition from metallic to insulating behavior as a function of electron density [15][16][17][18][19][20][21][22]. We investigate dependences of the transport on band-overlap, temperature, gate voltage, electron-hole recombination rate, and magnetic-field, using parameters we believe appropriate to the HgTe quantum wells in Ref.…”