Features of the conductivity and magnetoresistance of doped two-dimensional structures near a metal-insulator transition

Theoretical and experimental studies of the conductivity and magnetoresistance of selectively doped structures of GaAs/AlGaAs quantum well structures near a metal-insulator phase transition have been reviewed. Special attention is focused on the role of the structure of impurity bands, which are narrow in the absence of intentional compensation and, in the case of doping of barriers, include the partially filled upper Hubbard band. It has been shown that the indicated structures exhibit (i) specific mixed conductivity, which can, in particular, include the contribution from delocalized states in the impurity band; (ii) the virtual Anderson transition, which is suppressed with an increase in disorder owing to compensation or with an increase in the concentration of a dopant; (iii) slow relaxations of the hopping magnetoresistance caused by the Coulomb glass effects, including, in particular, the states of the upper Hubbard band; and (iv) the suppression of the negative interference magnetoresistance owing to the spin effects.     

Virtual Anderson transition in a narrow impurity band of doped <Emphasis Type="Italic">p</Emphasis>-GaAs/AlGaAs layers

In highly doped uncompensated layers of p-GaAs/AlGaAs quantum wells, activation conduction with low activation energies is observed at low temperatures and this conduction is not explained by known mechanisms (ε₄ conduction). Such behavior is attributed to the delocalization of electron states near the maximum of a narrow impurity band in the sense of the Anderson transition. In this case, conduction is implemented due to the activation of minority carriers from the Fermi level to the indicated delocalized-state band.     

Normal phase and superconducting instability in the attractive Hubbard model: a DMFT(NRG) study

We study the normal (nonsuperconducting) phase of the attractive Hubbard model within the dynamical mean field theory (DMFT) using the numerical renormalization group (NRG) as an impurity solver. A wide range of attractive potentials U is considered, from the weak-coupling limit, where superconducting instability is well described by the BCS approximation, to the strong-coupling region, where the superconducting transition is described by Bose condensation of compact Cooper pairs, which are formed at temperatures much exceeding the superconducting transition temperature. We calculate the density of states, the spectral density, and the optical conductivity in the normal phase for this wide range of U, including the disorder effects. We also present the results on superconducting instability of the normal state dependence on the attraction strength U and the degree of disorder. The disorder influence on the critical temperature T _c is rather weak, suggesting in fact the validity of Anderson’s theorem, with the account of the general widening of the conduction band due to disorder.     

Effects of bulk charged impurities on the bulk and surface transport in three-dimensional topological insulators

In the three-dimensional topological insulator (TI), the physics of doped semiconductors exists literally side-by-side with the physics of ultrarelativistic Dirac fermions. This unusual pairing creates a novel playground for studying the interplay between disorder and electronic transport. In this mini-review, we focus on the disorder caused by the three-dimensionally distributed charged impurities that are ubiquitous in TIs, and we outline the effects it has on both the bulk and surface transport in TIs. We present self-consistent theories for Coulomb screening both in the bulk and at the surface, discuss the magnitude of the disorder potential in each case, and present results for the conductivity. In the bulk, where the band gap leads to thermally activated transport, we show how disorder leads to a smaller-than-expected activation energy that gives way to variable-range hopping at low temperatures. We confirm this enhanced conductivity with numerical simulations that also allow us to explore different degrees of impurity compensation. For the surface, where the TI has gapless Dirac modes, we present a theory of disorder and screening of deep impurities, and we calculate the corresponding zero-temperature conductivity. We also comment on the growth of the disorder potential in passing from the surface of the TI into the bulk. Finally, we discuss how the presence of a gap at the Dirac point, introduced by some source of time-reversal symmetry breaking, affects the disorder potential at the surface and the mid-gap density of states.     

On the Optical Conductivity of Kondo Insulators

The temperature-dependent optical conductivity of a Kondo insulator for different temperatures with impurity doping on the conduction band is studied within the U = ∞ Anderson lattice model in the framework of a slave-boson mean-field theory under the coherent potential approximation. The results show that the depletion of the optical conductivity in low-frequency region decreases with increasing of the temperature, and the system exhibits a transition between a low-temperature insulating phase and a high-temperature metallic phase. With increasing of the impurity concentration, the effect of the impurity scattering could result in a nearly temperature-independent gap behavior. The numerical results on the localization of the electron and its variation with temperature are also discussed with the help of optical sum rule.     

Electrical conduction properties of Si δ-doped GaAs grown by MBE

The temperature dependent Hall effect and resistivity measurements of Si δ-doped GaAs are performed in a temperature range of 25–300 K. The temperature dependence of carrier concentration shows a characteristic minimum at about 200 K, which indicates a transition from the conduction band conduction to the impurity band conduction. The temperature dependence of the conductivity results are in agreement with terms due to conduction band conduction and localized state hopping conduction in the impurity band. It is found that the transport properties of Si δ-doped GaAs are mainly governed by the dislocation scattering mechanism at high temperatures. On the other hand, the conductivity follows the Mott variable range hopping conduction (VRH) at low temperatures in the studied structures.     

Transition from strong to weak localization in the split-off impurity band in two-dimensional <Emphasis Type="Italic">p</Emphasis>-GaAs/AlGaAs structures

A crossover from strongly localized behavior to weak localization (SL-WL) was observed in two-dimensional modulation-doped GaAs/Al_0.3Ga_0.7 As structures as the impurity concentration increased. In this case, it was observed that the low-temperature dependence of the conductivity changed its character (from exponential to logarithmic) and the magnetoresistance changed its sign (from linear negative to root positive). For 2D structures, it is shown that this transition proceeds in the impurity band separated from the valence band by the mobility gap, whereas the effective mass in the impurity band is larger than in the valence band.     

Influence of weak nonlinearity on the 1D Anderson model with long-range correlated disorder

We investigate theoretically the nature of the states and the localization properties in a one-dimensional Anderson model with long-range correlated disorder and weak nonlinearity. Using the stationary discrete nonlinear Schrödinger equation, we calculate the disorder-averaged logarithm of the transmittance and the localization length in the fixed input case in a numerically exact manner. Unlike in many previous studies, we strictly fix the intensity of the incident wave and calculate the localization length as a function of other parameters. We also calculate the wave functions in a given disorder configuration. In the linear case, flat phased localized states appear near the bottom of the band and staggered localized states appear near the top of the band, while a continuum of extended states appears near the band center. We find that the focusing Kerr-type nonlinearity enhances the Anderson localization of flat phased states and suppresses that of staggered states. We observe that there exists a perfect symmetry relationship for the localization length between focusing and defocusing nonlinearities. Above a critical value of the strength of nonlinearity, delocalization due to the long-range correlations of disorder is destroyed and all states become localized.     

Ginzburg–Landau expansion in strongly disordered attractive Anderson–Hubbard model

We have studied disordering effects on the coefficients of Ginzburg–Landau expansion in powers of superconducting order parameter in the attractive Anderson–Hubbard model within the generalized DMFT+Σ approximation. We consider the wide region of attractive potentials U from the weak coupling region, where superconductivity is described by BCS model, to the strong coupling region, where the superconducting transition is related with Bose–Einstein condensation (ВЕС) of compact Cooper pairs formed at temperatures essentially larger than the temperature of superconducting transition, and a wide range of disorder—from weak to strong, where the system is in the vicinity of Anderson transition. In the case of semielliptic bare density of states, disorder’s influence upon the coefficients A and В of the square and the fourth power of the order parameter is universal for any value of electron correlation and is related only to the general disorder widening of the bare band (generalized Anderson theorem). Such universality is absent for the gradient term expansion coefficient C. In the usual theory of “dirty” superconductors, the С coefficient drops with the growth of disorder. In the limit of strong disorder in BCS limit, the coefficient С is very sensitive to the effects of Anderson localization, which lead to its further drop with disorder growth up to the region of the Anderson insulator. In the region of BCS–ВЕС crossover and in ВЕС limit, the coefficient С and all related physical properties are weakly dependent on disorder. In particular, this leads to relatively weak disorder dependence of both penetration depth and coherence lengths, as well as of related slope of the upper critical magnetic field at superconducting transition, in the region of very strong coupling.     

Delocalization and Heisenberg's uncertainty relation

In the one-dimensional Anderson model the eigenstates are localized for arbitrarily small amounts of disorder. In contrast, the Aubry-André model with its quasiperiodic potential shows a transition from extended to localized states. The difference between the two models becomes particularly apparent in phase space where Heisenberg's uncertainty relation imposes a finite resolution. Our analysis points to the relevance of the coupling between momentum eigenstates at weak potential strength for the delocalization of a quantum particle. Received 3 May 2002 / Received in final form 2 October 2002 Published online 29 November 2002     

d+s波超导体磁掺杂转变

研究了Anderson掺杂极限Δs/Δd《1的情况下,d+s波对称下的超导态。此模型包括哈密顿量中类似BSC项和自恰平均场似下的Anderson掺杂。随着掺杂中心数的增加或比率Δs/Δd的减小,可推出从低能下在费米能级附近具有双峰的态到N(0)≈(Δs/Δd)2态的转变。如果掺杂共振的能量为最小能量标度,则转变不连续。     

Localization in the CPA frame for alloys

To describe electron localization in substitutionally random alloysA _c B _1–c the coherent potential approximation (CPA) is incorporated into the self-consistent theory of Anderson localization in the form developed by Vollhardt and Wölfle. Modifications of the localization theory arise from the tight-binding model with bimodal diagonal disorder of arbitrary strength. The mean-free path, correlation and localization lengths, and the zero-temperature conductivity are calculated at dimensionalityd=3. The metal-insulator transition is studied numerically for a CPA-induced band structure under semielliptical model assumptions.     

Delocalization in the anderson model due to a local measurement

We study a one-dimensional Anderson model in which one site interacts with a detector monitoring the occupation of that site. We demonstrate that such an interaction, no matter how weak, leads to total delocalization of the Anderson model, and we discuss the experimental consequences.     

Two-dimensional metal-insulator transition as a percolation transition in a high-mobility electron system

By carefully analyzing the low temperature density dependence of 2D conductivity in undoped high-mobility n-GaAs heterostructures, we conclude that the 2D metal-insulator transition in this 2D electron system is a density inhomogeneity driven percolation transition due to the breakdown of screening in the random charged impurity disorder background. In particular, our measured conductivity exponent of approximately 1.4 approaches the 2D percolation exponent value of 4/3 at low temperatures and our experimental data are inconsistent with there being a zero-temperature quantum critical point in our system.     

Polarons in crystalline and non-crystalline materials

The current state of polaron theory as applicable to transition metal oxides is reviewed, including problems such as impurity conduction where disorder plays a role. An estimate is given of the conditions under which polaron formation leads to an enhancement of the mass but no hopping energy. The binding energy of a polaron to a donor or acceptor in narrow-band semiconductors is discussed. The experimental evidence about the conductivity of TiO₂ and NiO is reviewed. Impurity conduction in NiO and conduction in glasses containing transition metal ions is discussed and it is emphasized that the activation energy for hopping nearly all vanishes at low temperatures. Pollak's theory of a.c. impurity conductivity is reviewed and applied to the problem of dielectric loss in these materials.     

Polarons in crystalline and non-crystalline materials

The current state of polaron theory as applicable to transition metal oxides is reviewed, including problems such as impurity conduction where disorder plays a role. An estimate is given of the conditions under which polaron formation leads to an enhancement of the mass but no hopping energy. The binding energy of a polaron to a donor or acceptor in narrow-band semiconductors is discussed. The experimental evidence about the conductivity of TiO 2 and NiO is reviewed. Impurity conduction in NiO and conduction in glasses containing transition metal ions is discussed and it is emphasized that the activation energy for hopping nearly all vanishes at low temperatures. Pollak's theory of a.c. impurity conductivity is reviewed and applied to the problem of dielectric loss in these materials.     

Chebyshev expansion approach to the AC conductivity of the Anderson model

We propose an advanced Chebyshev expansion method for the numerical calculation of linear response functions at finite temperature. Its high stability and the small required resources allow for a comprehensive study of the optical conductivity of non-interacting electrons in a random potential (Anderson model) on large three-dimensional clusters. For low frequency the data follows the analytically expected power-law behaviour with an exponent that depends on disorder and has its minimum near the metal-insulator transition, where also the extrapolated DC conductivity continuously goes to zero. In view of the general applicability of the Chebyshev approach we briefly discuss its formulation for interacting quantum systems.Received: 6 June 2004, Published online: 12 August 2004PACS: 78.20.Bh Theory, models, and numerical simulation - 72.15.Rn Localisation effects (Anderson or weak localisation) - 05.60.Gg Quantum transport     

Attractive Hubbard model: Homogeneous Ginzburg–Landau expansion and disorder

We derive a Ginzburg–Landau (GL) expansion in the disordered attractive Hubbard model within the combined Nozieres–Schmitt-Rink and DMFT+Σ approximation. Restricting ourselves to the homogeneous expansion, we analyze the disorder dependence of GL expansion coefficients for a wide range of attractive potentials U, from the weak BCS coupling region to the strong-coupling limit, where superconductivity is described by Bose–Einstein condensation (BEC) of preformed Cooper pairs. We show that for the a semielliptic “bare” density of states of the conduction band, the disorder influence on the GL coefficients A and B before quadratic and quartic terms of the order parameter, as well as on the specific heat discontinuity at the superconducting transition, is of a universal nature at any strength of the attractive interaction and is related only to the general widening of the conduction band by disorder. In general, disorder growth increases the values of the coefficients A and B, leading either to a suppression of the specific heat discontinuity (in the weak-coupling limit), or to its significant growth (in the strong-coupling region). However, this behavior actually confirms the validity of the generalized Anderson theorem, because the disorder dependence of the superconducting transition temperature T_c, is also controlled only by disorder widening of the conduction band (density of states).     

Insulator-to-metal transition in sulfur-doped silicon

We observe an insulator-to-metal transition in crystalline silicon doped with sulfur to nonequilibrium concentrations using ion implantation followed by pulsed-laser melting and rapid resolidification. This insulator-to-metal transition is due to a dopant known to produce only deep levels at equilibrium concentrations. Temperature-dependent conductivity and Hall effect measurements for temperatures T>1.7 K both indicate that a transition from insulating to metallic conduction occurs at a sulfur concentration between 1.8 and 4.3×10(20) cm(-3). Conduction in insulating samples is consistent with variable-range hopping with a Coulomb gap. The capacity for deep states to effect metallic conduction by delocalization is the only known route to bulk intermediate band photovoltaics in silicon.