Scaling of an anomalous metal-insulator transition in a two-dimensional system in silicon at B=0

Quantum scaling for the metal-insulator transition in a two-dimensional electron system

The quantum phase transition observed experimentally in two-dimensional (2D) electron systems has been a subject of theoretical and experimental studies for almost 30 years. We suggest Gaussian approximation to the mean-field theory of the second-order phase transition to explain the experimental data. Our approach explains self-consistently the universal value of the critical exponent 3/2 (found after scaling measured resistivities on both sides of the transition as a function of temperature) as the result of the divergence of the correlation length when the electron density approaches the critical value. We also provide numerical evidence for the stretched exponential temperature dependence of the metallic phase's resistivities in a wide range of temperatures and show that it leads to correct qualitative results. Finally, we interpret the phase diagram on the density-temperature plane exhibiting the quantum critical point, quantum critical trajectory and two crossover lines. Our research presents a theoretical description of the seminal experimental results.

Link between T-Linear Resistivity and Quantum Criticality in Ambipolar Black Phosphorus

The interplay between strong Coulomb interactions and kinetic energy leads to intricate many-body competing ground states owing to quantum fluctuations in 2D electron and hole gases. However, the simultaneous observation of quantum critical phenomena in both electron and hole regimes remains elusive. Here, we utilize anisotropic black phosphorus (BP) to show density-driven metal-insulator transition with a critical conductance ∼e2/h which highlights the significant role of quantum fluctuations in both hole and electron regimes. We observe a T-linear resistivity from the deep metallic phase to the metal-insulator boundary at moderate temperatures, while it turns to Fermi liquid behavior in the deep metallic phase at low temperatures in both regimes. An analysis of the resistivity suggests that disorder-dominated transport leads to T-linear behavior in the hole regime, while in the electron regime, the T-linear resistivity results from strong Coulomb interactions, suggestive of strange-metal behavior. Successful scaling collapse of the resistivity in the T-linear region demonstrates the link between quantum criticality and the T-linear resistivity in both regimes. Our study provides compelling evidence that ambipolar BP could serve as an exciting testbed for investigating exotic states and quantum critical phenomena in hole and electron regimes of 2D semiconductors.

Nature of the Metal Insulator Transition in High-Mobility 2D_Si-MOSFETs

Our investigation focuses on the analysis of the conductive properties of high-mobility 2D-Si-MOSFETs as they approach the critical carrier density, nsc (approximately 0.72×1011 cm-2), which marks the metal insulator transition (MIT). In close proximity to the nsc, the conductivity exhibits a linear dependence on the temperature (T). By examining the extrapolated conductivity at the absolute zero temperature (T = 0), denoted as σ0, as a function of the electron density ns, we identify two distinct regimes with varying σ0(ns) patterns, indicating the existence of two different phases. The transition from one of these two regimes to another, coinciding with nsc, is abrupt and serves as the focus of our investigation. Our aim is to establish the possibility of a percolation type transition in the 2D-Si-MOSFETs' sample. In fact, we observed that the model of percolation is applicable only for densities very close to nsc*=n2 (where n2 is the linear extrapolation of σ0), indicating the percolation type transition essentially represents a phase transition at the zero temperature.

Structural-disorder-driven critical quantum fluctuation and localization in two-dimensional semiconductors

Quantum fluctuations of wavefunctions in disorder-driven quantum phase transitions (QPT) exhibit criticality, as evidenced by their multifractality and power law behavior. However, understanding the metal-insulator transition (MIT) as a continuous QPT in a disordered system has been challenging due to fundamental issues such as the lack of an apparent order parameter and its dynamical nature. Here, we elucidate the universal mechanism underlying the structural-disorder-driven MIT in 2D semiconductors through autocorrelation and multifractality of quantum fluctuations. The structural disorder causes curvature-induced band gap fluctuations, leading to charge localization and formation of band tails near band edges. As doping level increases, the localization-delocalization transition occurs when states above a critical energy become uniform due to unusual band bending by localized charge. Furthermore, curvature induces local variations in spin-orbit interactions, resulting in non-uniform ferromagnetic domains. Our findings demonstrate that the structural disorder in 2D materials is essential to understanding the intricate phenomena associated with localization-delocalization transition, charge percolation, and spin glass with both topological and magnetic disorders.

Percolation-Based Metal-Insulator Transition in Black Phosphorus Field Effect Transistors

The existence of a novel phenomenon, such as the metal-insulator transition (MIT) in two-dimensional (2D) systems, affords emerging functional properties that provide new aspects for future electronics and optoelectronics. Here, we report the observation of the MIT in black phosphorus field effect transistors by tuning the carrier density (n) controlled by back-gate bias. We find that the conductivity follows an n dependence as σ(n) ∝ n^α with α ∼ 1, which indicates the presence of screened Coulomb impurity scattering at high carrier densities in the temperature range of 10-300 K. As n decreases, the screened Coulomb impurity scattering breaks down, developing strong charge density inhomogeneity leading to a percolation-based transition at the critical carrier density (n_C). At low carrier densities (n < n_C), the system is in the insulating regime, which is expressed by Mott variable range hopping that demonstrates the role of disorder in the system. In addition, the extracted average values of critical exponent δ are ∼1.29 ± 0.01 and ∼1.14 ± 0.01 for devices A and B, respectively, consistent with the 2D percolation exponent of ⁴/₃, confirming the 2D percolation-based MIT in BP devices. Our findings strongly suggest that the 2D MIT observed in BP is a classical percolation-based transition caused by charge inhomogeneity induced by screened Coulomb charge impurity scattering around a transition point controlled by n through back-gate bias.

Insulator-to-metal phase transition in a few-layered MoSe2 field effect transistor

The metal-to-insulator phase transition (MIT) in low-dimensional materials and particularly two-dimensional layered semiconductors is exciting to explore due to the fact that it challenges the prediction that a two-dimensional system must be insulating at low temperatures. Thus, the exploration of MITs in 2D layered semiconductors expands the understanding of the underlying physics. Here we report the MIT of a few-layered MoSe₂ field effect transistor under a gate bias (electric field) applied perpendicular to the MoSe₂ layers. With low applied gate voltage, the conductivity as a function of temperature from 150 K to 4 K shows typical semiconducting to insulating character. Above a critical applied gate voltage, V_c, the conductivity becomes metallic (i.e., the conductivity increases continuously as a function of decreasing temperature). Evidence of a metallic state was observed using an applied gate voltage or, equivalently, increasing the density of charge carriers within the 2D channel. We analyzed the nature of the phase transition using percolation theory, where conductivity scales with the density of charge carriers as σ ∝ (n - n_c)^δ. The critical exponent for a percolative phase transition, δ(T), has values ranging from 1.34 (at T = 150 K) to 2 (T = 20 K), which is close to the theoretical value of 1.33 for percolation to occur. Thus we conclude that the MIT in few-layered MoSe₂ is driven by charge carrier percolation. Furthermore, the conductivity does not scale with temperature, which is a hallmark of a quantum critical phase transition.

How to Recognize the Universal Aspects of Mott Criticality?

In this paper we critically discuss several examples of two-dimensional electronic systems displaying interaction-driven metal-insulator transitions of the Mott (or Wigner–Mott) type, including dilute two-dimension electron gases (2DEG) in semiconductors, Mott organic materials, as well as the recently discovered transition-metal dichalcogenide (TMD) moiré bilayers. Remarkably similar behavior is found in all these systems, which is starting to paint a robust picture of Mott criticality. Most notable, on the metallic side a resistivity maximum is observed whose temperature scale vanishes at the transition. We compare the available experimental data on these systems to three existing theoretical scenarios: spinon theory, Dynamical Mean Field Theory (DMFT) and percolation theory. We show that the DMFT and percolation pictures for Mott criticality can be distinguished by studying the origins of the resistivity maxima using an analysis of the dielectric response.

Low temperature injected-caused charge carrier instability in n-type silicon below insulator-to-metal transition

We report on the electric transport properties of Si heavily doped with Sb at concentration just below the insulator-to-metal transition in the temperature range 1.9-3.0 K for current density J  <  0.2 A cm^-2. The change in the sign of the temperature dependence of the differential resistivity [Formula: see text] was observed: the d[Formula: see text]/dT is positive if J  <  0.045 A cm^-2 whereas it becomes negative at J  >  0.045 A cm^-2. The effect is explained assuming the exchange by electrons between the upper Hubbard band (UHB) and the conduction band. The obtained J dependencies of the activation energy, nonequilibrium concentration, mobility and scattering time of the conduction electrons correspond well to this hypothesis. The reason for charge instability is the Coulomb repulsion between electrons occupying states both in the UHB and conduction band. The estimated J dependencies of the conduction electrons lifetime and concentration of the D^- states in the UHB strongly supports this assumption.

Gate-Induced Metal-Insulator Transition in 2D van der Waals Layers of Copper Indium Selenide Based Field-Effect Transistors

The existence of an exquisite phenomenon such as a metal-insulator transition (MIT) in two-dimensional (2D) systems, where completely different electronic functionalities in the same system can emerge simply by regulating parameters such as charge carrier density in them, is noteworthy. Such tunability in material properties can lead to several applications where precise tuning of function specific properties are desirable. Here, we report on our observation on the occurrence of MIT in the 2D material system of copper indium selenide (CuIn₇Se₁₁). Clear evidence of the metallic nature of conductivity (σ) under the influence of electrostatic doping via the gate, which crosses over to an insulating phase upon lowering the temperature, was observed by investigating the temperature and gate dependence of σ in CuIn₇Se₁₁ field-effect transistor devices. At higher charge carrier densities (n > 10¹² cm^-1), we found that σ ∼ (n)^α with α ∼ 2, which suggests the presence of bare Coulomb impurity scattering within the studied range of temperature (280 K > T > 20 K). Our analysis of the conductivity data following the principles of percolation theory of transition where σ ∼ (n - n_C)^δ show that the critical percolation exponent δ(T) has average values ∼1.57 ± 0.27 and 1.02 ± 0.35 within the measured temperature range for the two devices and it is close to the 2D percolation exponent value of 1.33. We believe that the 2D MIT seen in our system is due to the charge density inhomogeneity caused by electrostatic doping and unscreened charge impurity scattering that leads to a percolation driven transition. The findings reported here for CuIn₇Se₁₁ system provide a different material platform to investigate MIT in 2D and are crucial in order to understand the fundamental basis of electronic interactions and charge-transport phenomenon in other unexplored 2D electron systems.

Inter-cluster separation induced change in charge transport mechanism in Ni40Pd60 nanoclusters

Nanoclusters offer a fascinating possibility of studying the evolution of properties of a physical system by varying the number, size and inter-cluster separation of a given cluster to go from one limit to another. By systematically varying the inter-cluster separation in a nanocluster assembly of Ni₄₀Pd₆₀ alloy, that is known to be a metal in bulk, we observe an unusual and hitherto unreported, spatial dimension change as well as a change in the transport mechanism. In the nanocluster form, the temperature dependent resistance shows an activated behavior for virtually all inter-cluster separations, contrary to, the bulk metallic behaviour. At large average inter-cluster separation, the transport happens via three dimensional Efros-Shklovskii hopping, due to the opening of a Coulomb gap at the Fermi surface. With a reduction in the inter-cluster separation, the transport mechanism changes from three dimensional Efros-Shklovskii hopping to that of a three dimensional Mott variable range hopping (VRH) due to the closing up of the gap. With a further reduction in average inter-cluster separation, the three dimensional Mott VRH changes to that of a two dimensional Mott VRH with additional signatures of an insulator to a weak metal-like transition in this particular assembly. So, nanoclusters offer a paradigm for studying the important problem of evolution of charge transport in physical systems with the possibility of directly tuning the average inter-cluster separation enabling the system to go from insulating to metallic limit via intermediate changes in the charge transport mechanism.

Recent Developments in the Field of the Metal-Insulator Transition in Two Dimensions

We review the latest developments in the field of the metal-insulator transition in strongly-correlated two-dimensional electron systems. Particular attention is given to recent discoveries of a sliding quantum electron solid and interaction-induced spectrum flattening at the Fermi level in high-quality silicon-based structures.

Metal-to-Insulator Transitions in Strongly Correlated Regime

Transport results from measuring ultra-clean two-dimensional systems, containing tunable carrier densities from 7 × 10 8 cm − 2 to ∼ 1 × 10 10 cm − 2 , reveal a strongly correlated liquid up to r s ≈ 40 where a Wigner crystallization is anticipated. A critical behavior is identified in the proximity of the metal-to-insulator transition. The nonlinear DC responses for r s > 40 captures hard pinning modes that likely undergo a first order transition into an intermediate phase in the course of melting.

Systematic Quantum Cluster Typical Medium Method for the Study of Localization in Strongly Disordered Electronic Systems

Great progress has been made in recent years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of disorder and electron-electronic interactions on equal footing. They include dynamical mean-field theory and the Coherent Potential Approximation, and their cluster extension, the dynamical cluster approximation. Despite their successes, these methods do not enable the first-principles study of the strongly disordered regime, including the effects of electronic localization. The main focus of this review is the recently developed typical medium dynamical cluster approximation for disordered electronic systems. This method has been constructed to capture disorder-induced localization and is based on a mapping of a lattice onto a quantum cluster embedded in an effective typical medium, which is determined self-consistently. Unlike the average effective medium-based methods mentioned above, typical medium-based methods properly capture the states localized by disorder. The typical medium dynamical cluster approximation not only provides the proper order parameter for Anderson localized states, but it can also incorporate the full complexity of Density-Functional Theory (DFT)-derived potentials into the analysis, including the effect of multiple bands, non-local disorder, and electron-electron interactions. After a brief historical review of other numerical methods for disordered systems, we discuss coarse-graining as a unifying principle for the development of translationally invariant quantum cluster methods. Together, the Coherent Potential Approximation, the Dynamical Mean-Field Theory and the Dynamical Cluster Approximation may be viewed as a single class of approximations with a much-needed small parameter of the inverse cluster size which may be used to control the approximation. We then present an overview of various recent applications of the typical medium dynamical cluster approximation to a variety of models and systems, including single and multiband Anderson model, and models with local and off-diagonal disorder. We then present the application of the method to realistic systems in the framework of the DFT and demonstrate that the resulting method can provide a systematic first-principles method validated by experiment and capable of making experimentally relevant predictions. We also discuss the application of the typical medium dynamical cluster approximation to systems with disorder and electron-electron interactions. Most significantly, we show that in the limits of strong disorder and weak interactions treated perturbatively, that the phenomena of 3D localization, including a mobility edge, remains intact. However, the metal-insulator transition is pushed to larger disorder values by the local interactions. We also study the limits of strong disorder and strong interactions capable of producing moment formation and screening, with a non-perturbative local approximation. Here, we find that the Anderson localization quantum phase transition is accompanied by a quantum-critical fan in the energy-disorder phase diagram.

Soft Coulomb gap and asymmetric scaling towards metal-insulator quantum criticality in multilayer MoS2

Quantum localization–delocalization of carriers are well described by either carrier–carrier interaction or disorder. When both effects come into play, however, a comprehensive understanding is not well established mainly due to complexity and sparse experimental data. Recently developed two-dimensional layered materials are ideal in describing such mesoscopic critical phenomena as they have both strong interactions and disorder. The transport in the insulating phase is well described by the soft Coulomb gap picture, which demonstrates the contribution of both interactions and disorder. Using this picture, we demonstrate the critical power law behavior of the localization length, supporting quantum criticality. We observe asymmetric critical exponents around the metal-insulator transition through temperature scaling analysis, which originates from poor screening in insulating regime and conversely strong screening in metallic regime due to free carriers. The effect of asymmetric scaling behavior is weakened in monolayer MoS₂ due to a dominating disorder.

The interplay between strong interactions and presence of disorder makes atomically thin transition metal dichalcogenides an ideal platform to study phase transitions and critical phenomena. Here, the authors observe asymmetric critical exponents around the metal-insulator-transition of multilayer MoS₂.

Non-Fermi Liquid Behavior and Continuously Tunable Resistivity Exponents in the Anderson-Hubbard Model at Finite Temperature

We employ a recently developed computational many-body technique to study for the first time the half-filled Anderson-Hubbard model at finite temperature and arbitrary correlation U and disorder V strengths. Interestingly, the narrow zero temperature metallic range induced by disorder from the Mott insulator expands with increasing temperature in a manner resembling a quantum critical point. Our study of the resistivity temperature scaling T^{α} for this metal reveals non-Fermi liquid characteristics. Moreover, a continuous dependence of α on U and V from linear to nearly quadratic is observed. We argue that these exotic results arise from a systematic change with U and V of the "effective" disorder, a combination of quenched disorder and intrinsic localized spins.

Scaling analysis of field-tuned superconductor-insulator transition in two-dimensional tantalum thin films

The superconductor–insulator (SI) transition in two-dimensional Ta thin films is investigated by controlling both film thickness and magnetic field. An intriguing metallic phase appears between a superconducting and an insulating phase within a range of film thickness and magnetic field. The temperature and electric field scaling analyses are performed to investigate the nature of the SI transition in the thickness-tuned metallic and superconducting samples. The critical exponents product of νz obtained from the temperature scaling analysis is found to be approximately 0.67 in the entire range of film thickness. On the other hand, an apparent discrepancy is measured in the product of ν(z + 1) by the electric filed analysis. The product values are found to be about 1.37 for the superconducting films and about 1.86 for the metallic films respectively. We find that the discrepancy is the direct consequence of electron heating that introduces additional dissipation channels in the metallic Ta films.

Screening and transport in 2D semiconductor systems at low temperatures

Low temperature carrier transport properties in 2D semiconductor systems can be theoretically well-understood within RPA-Boltzmann theory as being limited by scattering from screened Coulomb disorder arising from random quenched charged impurities in the environment. In this work, we derive a number of analytical formula, supported by realistic numerical calculations, for the relevant density, mobility, and temperature range where 2D transport should manifest strong intrinsic (i.e., arising purely from electronic effects) metallic temperature dependence in different semiconductor materials arising entirely from the 2D screening properties, thus providing an explanation for why the strong temperature dependence of the 2D resistivity can only be observed in high-quality and low-disorder 2D samples and also why some high-quality 2D materials manifest much weaker metallicity than other materials. We also discuss effects of interaction and disorder on the 2D screening properties in this context as well as compare 2D and 3D screening functions to comment why such a strong intrinsic temperature dependence arising from screening cannot occur in 3D metallic carrier transport. Experimentally verifiable predictions are made about the quantitative magnitude of the maximum possible low-temperature metallicity in 2D systems and the scaling behavior of the temperature scale controlling the quantum to classical crossover.

Metal-insulator transition in the quasi-one-dimensional transport of fractional quantum Hall states

We investigate edge state transmission in quantum point contacts (QPCs) in the fractional quantum-Hall regime, finding behavior reminiscent of a metal-insulator transition. The transition is suggested by an unusual behavior of the differential conductance in the fractional-quantum-Hall regime, and by the presence of a fixed point and universal scaling in the temperature dependence of the linear conductance. Noting that the 0.7 feature evolves continuously into a last fractional plateau at high magnetic fields, we suggest that this still unresolved feature may itself be viewed as a manifestation of a local, microscopic, metal-insulator transition.

Critical Behavior of a Strongly Disordered 2D Electron System: The Cases of Long-Range and Screened Coulomb Interactions

A study of the temperature (T) and density (ns) dependence of conductivity σ(ns,T) of a highly disordered, two-dimensional (2D) electron system in Si demonstrates scaling behavior consistent with the existence of a metal-insulator transition (MIT). The same critical exponents are found when the Coulomb interaction is screened by the metallic gate and when it is unscreened or long range. The results strongly suggest the existence of a disorder-dominated 2D MIT, which is not directly affected by the range of the Coulomb interactions.

Renormalization group study of random quantum magnets

We have developed a very efficient numerical algorithm of the strong disorder renormalization group method to study the critical behaviour of the random transverse field Ising model, which is a prototype of random quantum magnets. With this algorithm we can renormalize an N-site cluster within a time NlogN, independently of the topology of the graph, and we went up to N ∼ 4 × 10(6). We have studied regular lattices with dimension D ≤ 4 as well as Erdős-Rényi random graphs, which are infinite dimensional objects. In all cases the quantum critical behaviour is found to be controlled by an infinite disorder fixed point, in which disorder plays a dominant role over quantum fluctuations. As a consequence the renormalization procedure as well as the obtained critical properties are asymptotically exact for large systems. We have also studied Griffiths singularities in the paramagnetic and ferromagnetic phases and generalized the numerical algorithm for other random quantum systems.

Metallic behavior of cyclotron relaxation time in two-dimensional systems

Cyclotron resonance of two-dimensional electrons is studied at low temperatures down to 0.4 K for a high-mobility Si/SiGe quantum well which exhibits a metallic temperature dependence of dc resistivity ρ. The relaxation time τ(CR) shows a negative temperature dependence, which is similar to that of the transport scattering time τ(t) obtained from ρ. The ratio τ(CR)/τ(t) at 0.4 K increases as the electron density N(s) decreases, and exceeds unity when N(s) approaches the critical density for the metal-insulator transition.

Local versus global equilibration near the bosonic Mott-insulator-superfluid transition

We study the time scales for adiabaticity of trapped cold bosons subject to a time-varying lattice potential using a dynamic Gutzwiller mean-field theory. We explain apparently contradictory experimental observations by demonstrating a clear separation of time scales for local dynamics (~ ms) and global mass redistribution (~1 s). We provide a simple explanation for the short and fast time scales, finding that while density or energy transport is dominated by low energy phonons, particle-hole excitations set the adiabaticity time for fast ramps. We show how mass transport shuts off within Mott-insulator domains, leading to a chemical potential gradient that fails to equilibrate on experimental time scales.

Soft hubbard gaps in disordered itinerant models with short-range interaction

We study the Anderson-Hubbard model in the Hartree-Fock approximation and the exact diagonalization under the coexistence of short-range interaction and diagonal disorder. We show that there exist unconventional soft gaps, where the single-particle (SP) density of states (DOS) A follows a scaling in energy E as A(E) proportional, variantexp[-(-gammalog|E-E_{F}|);{d}] irrespective of electron filling and long-range order. Here, d is the spatial dimension, E_{F} the Fermi energy and gamma a nonuniversal constant. We propose a multivalley energy landscape as their origin. Possible experiments to verify the present theory are proposed.

Localization-delocalization transition in a two-dimensional quantum percolation model

We study the hopping transport of a quantum particle through randomly diluted percolation clusters in two dimensions realized both on the square and triangular lattices. We investigate the nature of localization of the particle by calculating the transmission coefficient as a function of energy ( -2<E<2 in units of the hopping integral in the tight-binding Hamiltonian) and disorder, q (probability that a given site of the lattice is not available to the particle). Our study based on finite-size scaling suggests the existence of delocalized states that depends on energy and the amount of disorder present in the system. For energies away from the band center (E=0) , delocalized states appear only at low disorder (q<15%) . The transmission near the band center is generally very small for any amount of disorder and therefore makes it difficult to locate the transition to delocalized states if any, but our study does indicate a behavior that is weaker than power-law localization. Apart from this localization-delocalization transition, we also find the existence of two different kinds of localization regimes depending on energy and the amount of disorder. For a given energy, states are exponentially localized for sufficiently high disorder. As the disorder decreases, states first show power-law localization before showing a delocalized behavior.

Metal-insulator transition in two dimensions: experimental test of the two-parameter scaling

We report a detailed scaling analysis of resistivity rho(T,n) measured for several high-mobility 2D electron systems in the vicinity of the 2D metal-insulator transition. We analyzed the data using the two-parameter scaling approach and general scaling ideas. This enables us to determine the critical electron density, two critical indices, and temperature dependence for the separatrix in the self-consistent manner. In addition, we reconstruct the empirical scaling function describing a two-parameter surface which fits well the rho(T,n) data.

Electron-phonon interaction and localization of surface-state carriers in a metallic monolayer

Temperature-dependent electron transport in a metallic surface superstructure, Si(111)sqrt[3] x sqrt[3]-Ag, was studied by a micro-four-point probe method and photoemission spectroscopy. The surface-state conductivity exhibits a sharp transition from metallic conduction to strong localization at approximately 150 K. The metallic regime is due to electron-phonon interaction while the localization seemingly originates from coherency of electron waves. Random potential variations, caused by Friedel oscillations of surface electrons around defects, likely induce strong carrier localization.

Irradiation-induced confinement in a quasi-one-dimensional metal

The anisotropic resistivity of PrBa(2)Cu(4)O(8) has been measured as a function of electron irradiation fluence. Localization effects are observed for extremely small amounts of disorder corresponding to electron mean free paths of order 100 unit cells. Estimates of the localization corrections suggest that this anomalous localization threshold heralds a crossover to a ground state with pronounced one-dimensional character in which conduction electrons become confined to a small cluster of chains.

Disappearance of metal-like behavior in GaAs two-dimensional holes below 30 mK

The zero-field temperature dependence of the resistivity of two-dimensional holes is observed to exhibit two qualitatively different characteristics for a fixed carrier density for which only the metallic behavior of the so-called metal-insulator transition is anticipated. As T is lowered from 150 to 0.5 mK, the sign of the derivative of the resistivity with respect to T changes from being positive to negative when the temperature is lowered below approximately 30 mK and the resistivity continuously rises with cooling down to 0.5 mK, suggesting a crossover from being metal-like to insulatorlike.

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.

Inhomogeneous metallic phase in a disordered Mott insulator in two dimensions

We show that, with increasing randomness, the spectral gap in a 2D Mott-Hubbard insulator is destroyed first at a disorder V(c1), while antiferromagnetism persists up to a higher V(c2). Most unexpectedly, between V(c1) and V(c2) the system is metallic and is sandwiched between the Mott insulator below V(c1) and the Anderson insulator above V(c2). The metal is formed when the spectral gap gets destroyed locally in regions where the disorder potential is high enough to overcome the interelectron repulsion. This generates puddles with enhanced charge fluctuations that percolate with increasing disorder, resulting in a spatially inhomogeneous metallic phase.

Exotic versus conventional scaling and universality in a disordered bilayer quantum heisenberg antiferromagnet

We present Monte Carlo simulations of a two-dimensional bilayer quantum Heisenberg antiferromagnet with random dimer dilution. In contrast with exotic scaling scenarios found in other random quantum systems, the quantum phase transition in this system is characterized by a finite-disorder fixed point with power-law scaling. After accounting for corrections to scaling, with a leading irrelevant exponent of omega approximately 0.48, we find universal critical exponents z=1.310(6) and nu=1.16(3). We discuss the consequences of these findings and suggest new experiments.

Electric field effect in correlated oxide systems

Semiconducting field-effect transistors are the workhorses of the modern electronics era. Recently, application of the field-effect approach to compounds other than semiconductors has created opportunities to electrostatically modulate types of correlated electron behaviour--including high-temperature superconductivity and colossal magnetoresistance--and potentially tune the phase transitions in such systems. Here we provide an overview of the achievements in this field and discuss the opportunities brought by the field-effect approach.

Interacting electrons in a two-dimensional disordered environment: effect of a zeeman magnetic field

The effect of a Zeeman magnetic field coupled to the spin of the electrons on the conducting properties of the disordered Hubbard model is studied. Using the determinant quantum Monte Carlo method, the temperature- and magnetic-field-dependent conductivity is calculated, as well as the degree of spin polarization. We find that the Zeeman magnetic field suppresses the metallic behavior present for certain values of interaction and disorder strength and is able to induce a metal-insulator transition at a critical field strength. It is argued that the qualitative features of magnetoconductance in this microscopic model containing both repulsive interactions and disorder are in agreement with experimental findings in two-dimensional electron and hole gases in semiconductor structures.

Dilute electron gas near the metal-insulator transition: role of valleys in silicon inversion layers

We emphasize the role of valleys in the transport properties of the dilute electron gas in Si-MOSFETs. Close to the critical region of the metal-insulator transition the decrease in the resistivity up to 5 times has been captured in the correct temperature interval by a renormalization group analysis of the interplay of interaction and disorder. No adjustable parameters are involved in the analysis if the electron band is assumed to have two distinct valleys. The considerable variance in the data obtained from Si-MOSFET samples of different quality is attributed to the sample-dependent scattering rate across the two valleys, while universal behavior is expected to hold when the intervalley scattering is negligible.

Cooling of electrons in a silicon inversion layer

Low temperature cooling of two-dimensional electrons in silicon-metal-oxide semiconductor field effect transistors is studied experimentally and found to be more effective than expected from the bulk electron-phonon coupling in silicon. The extracted heat transfer rate to phonons depends cubically on electron temperature, suggesting that piezoelectric coupling, which is absent in bulk silicon, dominates over deformation potential. As a result, at 100 mK, electrons farther than approximately 100 microm from the contacts are mostly cooled by phonons. Using long devices and low excitation voltage we measure electron resistivity down to approximately 100 mK and find that some of the "metallic" curves turn insulating below approximately 300 mK.

Metallic behavior in dilute two-dimensional hole systems

We have studied the metallic behavior in low-density two-dimensional p-GaAs systems, close to the apparent metal-insulator transition. Two observations are made concerning the origins of the metallic-like behavior. Within a given sample the strength of the metallic behavior is almost independent of the asymmetry of the confining potential, and is predominantly determined by the low-temperature resistivity (i.e., by k(F)l). In all our samples we find that at low densities, close to the transition from insulating to metallic behavior, the fractional decrease in conductivity with increasing temperature scales as T/T(F).

Exclusion of quantum coherence as the origin of the 2D metallic state in high-mobility silicon inversion layers

The temperature and density dependence of the phase coherence time tau(phi) in high-mobility silicon inversion layers was determined from the magnetoresistivity due to weak localization. The upper temperature limit for single-electron quantum interference effects was delineated by comparing tau(phi) with the momentum relaxation time tau. A comparison between the density dependence of the borders for quantum interference effects and the strong resistivity drop reveals that these effects are not related to each other. As the strong resistivity drop occurs in the Drude regime, the apparent metallic behavior cannot be caused by quantum coherent effects.

Scaling of the magnetoconductivity of silicon MOSFETs: evidence for a quantum phase transition in two dimensions

For a broad range of electron densities n and temperatures T, the in-plane magnetoconductivity of the two-dimensional system of electrons in silicon MOSFETs can be scaled onto a universal curve with a single parameter H(sigma)(n,T), where H(sigma) obeys the empirical relation H(sigma) = A(n) [Delta(n)(2)+T2](1/2). The characteristic energy k(B)Delta associated with the magnetic field dependence of the conductivity decreases with decreasing density, and extrapolates to 0 at a critical density n(0), signaling the approach to a zero-temperature quantum phase transition. We show that H(sigma) = AT for densities near n(0).

Novel metallic behavior in two dimensions

Experiments on a sufficiently disordered two-dimensional (2D) electron system in silicon reveal a new and unexpected kind of metallic behavior, where the conductivity decreases as sigma(n(s),T) = sigma(n(s),T = 0)+A(n(s))T(2) (where n(s) is carrier density) to a nonzero value as temperature T-->0. In 2D, the existence of a metal with dsigma/dT>0 is very surprising. In addition, a novel type of a metal-insulator transition obtains, which is unlike any known quantum phase transition in 2D.

Nonperturbative saddle point for the effective action of disordered and interacting electrons in 2D

We find a nonperturbative saddle-point solution for the nonlinear sigma model proposed by Finkelstein for interacting and disordered electronic systems. Spin rotation symmetry, present in the original saddle-point solution, is spontaneously broken at one loop, as in the Coleman-Weinberg mechanism. The new solution is singular in both the disorder and triplet interaction strengths, and it also explicitly demonstrates that a nontrivial ferromagnetic state appears in a theory where the disorder average is carried out from the outset.

Small-angle shubnikov-de haas measurements in a 2D electron system: the effect of a strong In-plane magnetic field

Measurements in magnetic fields applied at small angles relative to the electron plane in silicon MOSFETs indicate a factor of 2 increase of the frequency of Shubnikov-de Haas oscillations at H>H(sat). This signals the onset of full spin polarization above H(sat), the parallel field above which the resistivity saturates to a constant value. For H<H(sat), the phase of the second harmonic of the oscillations relative to the first is consistent with scattering events that depend on the overlap instead of the sum of the spin-up and spin-down densities of states. This unusual behavior may reflect the importance of many-body interactions.

Partially suppressed shot noise in hopping conduction: observation in SiGe quantum wells

We have observed shot noise in the hopping conduction of two-dimensional carriers confined in a p-type SiGe quantum well at a temperature of 4 K. Moreover, shot noise is suppressed relative to its "classical" value 2eI by an amount that depends on the length of the sample and the carrier density. We have found a suppression factor to the classical value of about one-half for a 2 &mgr;m long sample, and of one-fifth for a 5 &mgr;m sample. In each case, the factor decreased slightly as the density increased toward the insulator-metal transition. We explain these results in terms of the characteristic length ( approximately 1 &mgr;m in our case) of the inherent inhomogeneity of hopping transport, obtained from percolation theory.

Tenfold magnetoconductance in a nonmagnetic metal film

We present magnetoconductance (MC) measurements of homogeneously disordered Be films whose zero field sheet conductance ( G) is described by the Efros-Shklovskii hopping law G(T) = (2e(2)/h)exp-(T0/T)(1/2). The low field MC of the films is negative with G decreasing a factor of 2 below 1 T. In contrast the MC above 1 T is strongly positive. At 8 T, G increases tenfold in perpendicular field and fivefold in parallel field. In the simpler parallel case, we observe field enhanced variable range hopping characterized by an attenuation of T0 via the Zeeman interaction.

Correlated random band matrices: localization-delocalization transitions

We study the statistics of eigenvectors in correlated random band matrix models. These models are characterized by two parameters, the bandwidth B(N) of a Hermitian NxN matrix and the correlation parameter C(N) describing correlations of matrix elements along diagonal lines. The correlated band matrices show a much richer phenomenology than models without correlation as soon as the correlation parameter scales sufficiently fast with matrix size. In particular, for B(N) approximately sqrt[N] and C(N) approximately sqrt[N], the model shows a localization-delocalization transition of the quantum Hall type.

Unexpected behavior of the local compressibility near the B = 0 metal-insulator transition

We have measured the local electronic compressibility of a two-dimensional hole gas as it crosses the B = 0 metal-insulator transition. In the metallic phase, the compressibility follows the mean-field Hartree-Fock (HF) theory and is found to be spatially homogeneous. In the insulating phase it deviates by more than an order of magnitude from the HF predictions and is spatially inhomogeneous. The crossover density between the two types of behavior agrees quantitatively with the transport critical density, suggesting that the system undergoes a thermodynamic change at the transition.

Weak localization, hole-hole interactions, and the "Metal"-insulator transition in two dimensions

A detailed investigation of the metallic behavior in high-quality GaAs-AlGaAs two-dimensional hole systems reveals the presence of quantum corrections to the resistivity at low temperatures. Despite the low density ( r(s)>10) and high quality of these systems, both weak localization (observed via negative magnetoresistance) and weak hole-hole interactions (giving a correction to the Hall constant) are present in the so-called metallic phase where the resistivity decreases with decreasing temperature. If these quantum corrections persist down to T = 0, the results suggest that even at high r(s) there is no metallic phase in two dimensions.