Session K44: Transport in Disordered Electronic Systems

Metals and insulators at infinite temperature

Numerical exact diagonalization results for spectral correlations and finite temperature transport of strongly disordered and interacting lattice fermions are presented. We study the finite temperature metal-insulator transition recently proposed by Basko and collaborators (condmat/0506617) focussing in particular on establishing the existence of the insulating phase.   

Magnetism near the percolation transition in two-dimensional electron systems

Recent thermodynamic measurements on two-dimensional (2D) electron systems have found divergence in the magnetic susceptibility and appearance of ferromagnetism as the electron density is lowered. The critical density for these phenomena coincides with the metal-insulator transition (MIT) recorded in transport measurements. Based on density functional calculations within the local spin-density approximation, we have investigated the compressibility and magnetic susceptibility of a 2D electron gas in the presence of remote impurities. A correlation between the minimum in the inverse capacitance, which is identified with the percolation transition, and the maximum of magnetization and magnetic susceptibility was found. This is also coincident with the MIT point based on values we obtain for the inverse participation ratio.   

Melting of the electron Wigner Crystal: Theory of the metal-insulator transition in two dimensions (2DMIT)

Past theoretical work in explaining the 2D metal-to-insulator transition at $T = 0$ has focused on perturbative approaches around the Fermi Liquid state, and has met with limited success [1]. Starting from the opposite limit we propose a charge transfer model with vacancy-interstitial pair formation as the mechanism for the phase transition. A new picture of the phase diagram has emerged [2], which our theory explains. At low carrier density we find an insulating phase with short-range order, at high density a metallic phase with no order, and a persistent intermediate density metallic phase with short range order. Our theory also explains the experimentally observed strong effective mass enhancements, as the metal-insulator transition is approached from the metallic side. \newline 1. Abrahams, E., Kravchenko, S. V., and Sarachik, M. P., Rev. Mod. Phys. 73, 251-266 (2001). 2. Falakshahi, H. \& Waintal, X., Phys. Rev. Lett. 94, 046801 (2005).   

Transport of GaAs two-dimensional holes in strong Coulomb interaction regime

We report experimental findings on the 2D holes in a GaAs/AlGaAs heterojunction insulated-gate field-effect transistor in the strong interaction regime ($E_{ee}>>E_ {F},kT$) with the carrier densities (p) varying from $7\times10^ {9}$ $cm^{-2} $ to $7\times10^{8}$ $cm^{-2}$. Though the temperature dependence of the resistivity ($\rho$) resembles that observed in typical 2D Metal-to-Insulator Transition (MIT), there are two things strikingly different. First, for each density, a kink/dip appears in the $T$-dependence of the conductivity ($\sigma$) around a characteristic temperature which we call $T_{c}$. In the $T_{c}$-$p$ relation, there is a sudden change at a characteristic density which is the same as the critical density $p_{c}$ where the apparent MIT is observed. The linear $T_{c}$-$p$ at high densities suggests that $T_{c}$s for $p>p_{c}$ correspond to the Fermi temperature $T_{F}$s. However, $T_{c}$ shows little $p$- dependence at $pT_{c}$ and a power-law part for $T [Preview Abstract]

Metal-insulator transition in 2D: comparison between experiment and Punnoose-Finkelstein's theory

New theory of the 2D metal-insulator transition (Punnoose and Finkelstein, Science 310, 289 (2005)) explains all most striking features of this phenomenon --- temperature- independent separatrix between metallic and insulating phases, destruction of the metallic state by magnetic field, critical behavior of the spin susceptibility and dramatic enhancement of the effective mass in the vicinity of the transition. We will report detailed comparison between our experiments and this theory.   

Hall coefficient and magnetoresistance of 2D spin-polarized eletron system

Recent measurements of the Hall resistance show that the Hall coefficient is independent on the applied in-plane magnetic field which gives rise to the spin-polarization of the system. We calculate the weak-field Hall coefficient and the magnetoresistance of a spin polarized system based on the screening theory. We solve the coupled kinetic equations of the two carrier system including electron-electron interaction. We find that the in-plane magnetic field dependence of the Hall coefficient can be suppressed by the weakening of the screening and the electron-electron interaction. However, the in-plane magnetoresistance is barely affected by the electron-electron interaction.   

Unified scaling picture for electronic transport in two-dimensions at low temperatures

We focus on generic features of the phase diagram for the 2D metal-insulator transition phenomenon. The diagram has a line of critical points corresponding to a conducting region (but not necessarily Fermi-liquid-like). The line terminates at a critical end point which controls an extended quantum critical region encompassing not only the conventional quantum critical sector but also a wide range of low temperature data extending deep into the insulator region. This permits us to unify analysis of transport data from the insulating region and the quantum critical sector, and allows us to determine the $z$ and $\nu$ critical exponents from a single experiment. We present strong evidence for the connection between data in the quantum critical sector and insulating critical region, pointing to the presence of a quantum critical point.   

Temperature-Dependent Weak Field Hall Resistance in 2D Carrier Systems

Das Sarma and Huang [1] have attempted to explain the T- dependent Hall coefficient R$_{H}$(T) of Gao et al. [2] for the 2D GaAs hole system solely with the T-dependent Hall factor r$_ {H}$(T) = $<$$\tau ^{2}$$>$/$<$$\tau$$>$$^{2}$. They employed R$_{H}$ = r$_{H}$(T)/en with n the total hole density which is independent of T. However r$_{H}$ = 1 at T=0 and r$_{H}$ $>$ 1 at finite T. Thus r$_{H}$(T) cannot explain the observed decrease of R$_{H}$(T) with increasing T. Employing the known relation R$_{H}$(T) = r$_{H}$/ep$_{i}$(T), where p$_{i}$(T) is the itinerant hole density, one can explain the decrease in R$_ {H}$ with increasing T with p$_{i}$(T) increasing faster than r$_{H}$(T). Using the mobility data [$\mu$(T) $\alpha$ $<$$\tau$$>$] one can determine r$_{H}$(T), which differs from the calculated curves in [1] in that it is asymmetrical about r$_{H,max}$. Using the Hall data and r$_{H}$(T) inferred from the data one can obtain the increase in p$_{i}$(T) with T and compare it with calculations of p$_{i}$(T) done with Fermi Liquid theory taking account of the soft Coulomb gap in the density-of-states. This approach gives good agreement, but doesn't take account of inhomogeneity. Other features of the Gao et al. data will be discussed. 1. S. Das Sarma and E.H. Huang, Phys.Rev.Lett.95, 0164011 (2005) 2. X.P.A. Gao et al., Phys.Rev.Lett.93, 256402 (2004)   

The transmission of a quantum particle through 2D disordered clusters.

We study quantum percolation model in two dimensions by directly calculating the conductance of finite disordered clusters. In extrapolating to the limit of very large clusters we find evidence that states are localized for any amount of disorder except at the limit of zero disorder where resonance transmission may occur. The nature of localization, however, depends on the amount of disorder present in the clusters. When disorder exceeds certain critical value, transmission decreases exponentially with the size of the clusters whereas below that value it is consistent with power laws. We also investigate how the energy affects the transmission in 2D disordered systems.   

Mean-field description of Anderson localization transition

The Anderson model of noninteracting disordered electrons is studied in high spatial dimensions. In this limit the coupled Bethe-Salpeter equations determining two-particle vertices (parquet equations) reduce to a single algebraic equation for a local vertex. We find a disorder-driven bifurcation point in this equation signaling vanishing of electron diffusion and onset of Anderson localization. There is no bifurcation in $d=1,2$ where all states are localized. In dimensions $d\geq 3$ the mobility edge separating metallic and insulating phase is found for various types of disorder and compared with results of other treatments.   

Anomalously Localized States at the Anderson Transition

Anomalously localized states (ALS) at the critical point of the disorder induced metal-insulator transition, namely, the Anderson transition, are investigated. ALS are states in which most of amplitudes of a wave function concentrate on a narrow spatial region even in a metallic phase. While the existence of ALS in the metallic phase was analytically predicted and confirmed by numerical and experimental works, ALS at the critical point are far from understood due to lack of proper analytical methods describing critical phenomena of this phase transition. In this work, it is numerically shown that ALS exist at the critical point of the Anderson transition in both the three-dimensional orthogonal class and the two-dimensional symplectic class by quantifying non-multifractality of critical wave functions due to a characteristic length originating in their concentration nature of ALS. These results may suggest that the existence of non-multifractal states at criticality is generic in many disordered systems.   

New Glassy Phases of Electrons in Disordered Potentials

Critical disorders are found analytically for the Anderson model of independent electrons in two and three-dimensional random potentials. At large disorders the states are exponentially localized, then with decreasing disorder the model goes through a sequence of less strongly localized phases ending with power-law localization just above the transition to extended states. These results follow from an analytic transformation of the Anderson model into augmented space where disorder is removed from matrix-elements by constructing a basis of extended states correlated with the potential. For different disorders, the states are dominated asymptotically by different sectors of augmented space, and these sectors are identified by path-counting.   

Noise in an Electron Glass, Amorphous Indium Oxide

Amorphous Indium Oxide is a material that manifests a rich spectrum of physical phenomena. It undergoes both the disorder driven and the magnetic field driven superconductor to insulator transitions. In addition, in highly disordered samples, it shows electron glass behavior, where correlations amongst the electrons leads to memory and aging effects. It is hypothesized that this glassy behavior is the consequence of a hierarchy of multielectron relaxation processes. To study this hierarchical relaxation we are measuring conductance fluctuations in samples in the glassy regime, where the spectrum of fluctuations is related to the relaxation processes, leading to a 1/f type of spectral dependence.   

Proposal for a pre-exponential dependent Efros-Shklovskii regime

We address the variable range hopping regime in the range for which the measured temperatures are of the order of the characteristic Mott or Efros-Shklovskii temperatures $T_M$ and $T_{ES}$ respectively. In such a range present theories imply $R_{hop}/\xi<1$ where $R_{hop}$ is the hopping length and $\xi$ is the localization length. Using the Mott optimization procedure, including prefactor corrections in the wavefunction overlap, we obtain expressions for the dependence on temperature for the typical hopping length and the resistivity in an Anderson insulator with coulombic interactions. Such expressions lead to a regular Efros-Shklovskii law when $T<1$. We propose that the optimization procedure can consistently explain contradictory results in the critical regime and recent experimental results showing a maximum in resistivity due to a interplay between prefactor and exponential terms.   

Universal and Non-universal Behavior at the Metal Insulator Transition.

A metal-insulator transition in amorphous metal semiconductor alloys is known to exist at dopant concentrations much higher ($\sim $ 12 at. {\%}) than their crystalline counterparts[1].~ We have studied the MIT in alloys grown using MBE for a series of semiconductor matrices, Si, Ge and both C and H-C (hydrogenated carbon) for various dopants (magnetic Gd and non-magnetic Y and Nb), as a function of concentration and magnetic field tuning. We compare the temperature dependence of the DC conductivity in the magnetically doped systems to the non-magnetic systems and to crystalline doped semiconductors (i.e. Si:P).~ Results are discussed in terms of a theoretical model that incorporates both disorder and electronic correlations[2]. This model correctly describes many universally observed aspects including the remarkably similar temperature dependence of the metallic and insulating DC conductivity of crystalline and amorphous systems, despite the vastly different disorder and electron concentration.~~ There are however very significant variations in the prefactors that control the magnitude of the conductivity, which we correlate with the microscopic physics of each system. [1] F. Hellman et al. PRL 77, 4652 [2] Lee and Ramakrishnan RMP 57, 287