2D Metal-insulator Transition Research Articles

Density-tuned effective metal-insulator transitions in two-dimensional semiconductor layers: Anderson localization or Wigner crystallization

Electrons (or holes) confined in 2D semiconductor layers have served as model systems for studying disorder and interaction effects for almost 50 years. In particular, strong disorder drives the metallic 2D carriers into a strongly localized Anderson insulator (AI) at low densities whereas pristine 2D electrons in the presence of no (or little) disorder should solidify into a Wigner crystal at low carrier densities. Since the disorder in 2D semiconductors is mostly Coulomb disorder arising from random charged impurities, the applicable physics is complex as the carriers interact with each other as well as with the random charged impurities through the same long-range Coulomb coupling. By critically theoretically analyzing the experimental transport data in depth using a realistic transport theory to calculate the low-temperature 2D resistivity as a function of carrier density in 11 different experimental samples covering 9 different materials, we establish, utilizing the Ioffe-Regel-Mott criterion for strong localization, a direct connection between the critical localization density for the 2D metal-insulator transition (MIT) and the sample mobility deep into the metallic state, which for clean samples could lead to a localization density low enough to make the transition appear to be a Wigner crystallization. We believe that the insulating phase is always an effective Coulomb disorder-induced localized AI, which may have short-range WC-like correlations at low carrier densities. Our theoretically calculated disorder-driven critical MIT density agrees with experimental findings in all 2D samples, even for the ultra-clean samples. In particular, the extrapolated critical density for the 2D MIT seems to vanish when the high-density mobility goes to infinity, indicating that transport probes a disorder-localized insulating ground state independent of how low the carrier density might be.

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) ∝ nα 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 (nC). At low carrier densities (n < nC), 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.

Disorder-induced two-dimensional metal-insulator transition in moiré transition metal dichalcogenide multilayers

We develop a minimal theory for the recently observed metal-insulator transition (MIT) in two-dimensional (2D) moir\'e multilayer transition metal dichalcogenides (mTMD) using Coulomb disorder in the environment as the underlying mechanism. In particular, carrier scattering by random charged impurities leads to an effective 2D MIT approximately controlled by the Ioffe-Regel criterion, which is qualitatively consistent with the experiments. We find the necessary disorder to be around $5$-$10\times10^{10}$cm$^{-2}$ random charged impurities in order to quantitatively explain much, but not all, of the observed MIT phenomenology as reported by two different experimental groups. Our estimate is consistent with the known disorder content in TMDs.

Low-Temperature 2D/2D Ohmic Contacts in WSe2 Field-Effect Transistors as a Platform for the 2D Metal-Insulator Transition.

We report the fabrication of hexagonal-boron-nitride (hBN) encapsulated multiterminal WSe2 Hall bars with 2D/2D low-temperature Ohmic contacts as a platform for investigating the two-dimensional (2D) metal-insulator transition. We demonstrate that the WSe2 devices exhibit Ohmic behavior down to 0.25 K and at low enough excitation voltages to avoid current-heating effects. Additionally, the high-quality hBN-encapsulated WSe2 devices in ideal Hall-bar geometry enable us to accurately determine the carrier density. Measurements of the temperature (T) and density (ns) dependence of the conductivity σ(T, ns) demonstrate scaling behavior consistent with a metal-insulator quantum phase transition driven by electron-electron interactions but where disorder-induced local magnetic moments are also present. Our findings pave the way for further studies of the fundamental quantum mechanical properties of 2D transition metal dichalcogenides using the same contact engineering.

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 - nC)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.

An electronic avalanche model for metal–insulator transition in two dimensional electron gas

In this paper, we present an electronic avalanche model for the transport of electrons in the disordered two-dimensional (2D) electron gas which has the potential to describe the 2D metal–insulator transition (MIT) in the zero electron–electron interaction limit. The disorder is considered to be uncorrelated-Coulomb noise with a uniform distribution. In this model we sub-divide the system to some virtual cells each of which has a linear size of the order of phase coherence length of the system. Using Thomas-Fermi-Dirac theory we propose some simple energy functions for the cells and using the thermodynamics of 2DEG we develop some rules for the charge transfer between the cells. A second order transition line arises from our model with some similarities with the experiments. The compressibility of the system also diverges on this line. We characterize this (disorder-driven) phase transition which is between the non-percolating phase and the percolating phase (in which the system shows metallic behavior) and obtain some geometrical critical exponents. The fractal dimension of the exterior frontier of the electronic avalanches on the transition line is compatible with the percolation theory, whereas the other exponents are different. The exponents are robust against disorder in the low disordered 2DEGs and change considerably in the high disordered ones.

Reappearance of linear hole transport in an ambipolar undoped GaAs/AlGaAs quantum well

We report the results of an investigation of ambipolar transport in a quantum well of 15 nm width in an undoped GaAs/AlGaAs structure, which was populated either by electrons or holes using positive or negative gate voltage Vtg, respectively. More attention was focussed on the low concentration of electrons n and holes p near the metal–insulator transition (MIT). It is shown that the electron mobility increases almost linearly with increase of n and is independent of temperature T in the interval 0.3 K–1.4 K, while the hole mobility depends non-monotonically on p and T. This difference is explained on the basis of the different effective masses of electrons and holes in GaAs. Intriguingly, we observe that at low p the source–drain current (ISD)–voltage (V) characteristics, which become non-linear beyond a certain ISD, exhibit a re-entrant linear regime at even higher ISD. We find, remarkably, that the departure and reappearance of linear behaviour are not due to non-linear response of the system, but due to an intrinsic mechanism by which there is a reduction in the net number of mobile carriers. This effect is interpreted as evidence of inhomogeneity of the conductive 2D layer in the vicinity of MIT and trapping of holes in ‘dead ends’ of insulating islands. Our results provide insights into transport mechanisms as well as the spatial structure of the 2D conducting medium near the 2D MIT.

Probing Spontaneous Spin Magnetization and Two-Phase State in Two-Dimensional Correlated Electron System

Strongly interacting two-dimensional (2D) carrier system has a tendency to spontaneous spin magnetization and mass divergence. Numerous experiments aimed to reveal these instabilities were not entirely convincing. In particular, spin susceptibility of itinerant electrons, determined from quantum oscillations, remains finite at the critical density of the 2D metal-insulator transition (MIT), n = nc. In contrast, the susceptibility and effective mass determined from high field magnetotransport were reported to diverge. Later, it became clear that as interactions grow, the homogeneous 2D Fermi liquid breaks into a two phase state which hampers interpretation of the experimental data. The thermodynamic magnetization measurements have revealed spontaneous formation of the spin-polarized collective electron droplets (“nanomagnets”) in the correlated 2D Fermi liquid, while the spin susceptibility of itinerant electrons in the surrounding 2D “Fermi sea” remains finite. Here, we report how the non Fermi-liquid two-phase state (dilute ferromagnet) reveals itself in magnetotransport and zero field transport. We found in the correlated 2D system a novel energy scale T∗<TF. At T≈T∗ the in-plane field magnetotransport and zero field transport exhibit features. Finally, in thermodynamic magnetization, the spin susceptibility per electron, ∂χ/∂n changes sign at T≈T∗. All three notable temperatures are close to each other, behave critically, \( \propto (n-n_{c})\); we associate, therefore, T∗ with a novel energy scale caused by interactions in the two-phase 2DE system.

‘Metal’-like transport in high-resistance, high aspect ratio two-dimensional electron gases

We investigate the striking absence of strong localisation observed in mesoscopic two-dimensional electron gases (2DEGs) (Baenninger et al 2008 Phys. Rev. Lett. 100 016805, Backes et al 2015 arXiv:1505.03444) even when their resistivity . In particular, we try to understand whether this phenomenon originates in quantum many-body effects, or simply percolative transport through a network of electron puddles. To test the latter scenario, we measure the low temperature (low-T) transport properties of long and narrow 2DEG devices in which percolation effects should be heavily suppressed in favour of Coulomb blockade. Strikingly we find no indication of Coulomb blockade and that the high-ρ, low-T transport is exactly similar to that previously reported in mesoscopic 2DEGs with different geometries. Remarkably, we are able to induce a ‘metal’-insulator transition (MIT) by applying a perpendicular magnetic field B. We present a picture within which these observations fit into the more conventional framework of the 2D MIT.

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.

Two-dimensional metal-insulator transition as a strong localization induced crossover phenomenon

Low-disorder and high-mobility 2D electron (or hole) systems undergo an apparent metal-insulator-transition (MIT) at low temperatures as the carrier density (n) is varied. In some situations, the 2D MIT can be caused at a fixed low carrier density by changing an externally applied in-plane magnetic field parallel to the 2D layer. d\rho/dT changes its sign at some nonuniversal sample-dependent critical carrier density n_c separating an effective 2D metal (d\rho/dT >0) for n>n_c from an effective 2D insulator (d\rho/dT<0) for n<n_c. We study the 2D MIT phenomenon as a possible strong localization induced crossover process controlled by the Ioffe-Regel criterion, k_F l=1. Calculating the quantum mean free path (l) in the effective metallic phase from a realistic transport theory including disorder scattering effects, we solve the integral equation defined by the Ioffe-Regel criterion to obtain the nonuniversal critical density n_c as a function of the applicable physical experimental parameters including disorder strength, in-plane magnetic field, spin and valley degeneracy, background dielectric constant and carrier effective mass, and temperature. The key physics underlying the nonuniversal parameter dependence of the n_c is the temperature and density dependence of the Coulomb disorder. Our calculated results for the crossover n_c appear to be in qualitative and semi-quantitative agreement with the available experimental data in different 2D semiconductor systems lending credence to the possibility that the apparent 2D MIT signals the onset of the strong localization crossover in disordered 2D systems. We provide some results for graphene where a low-temperature 2D MIT becomes possible in the presence of intervalley scattering. We also provide an extensive comparison with the theoretical results obtained on the basis of 2D MIT being considered as a percolation transition.

The Observation of a Percolation-Induced 2D Metal-Insulator Transition in AlAs

The nature of the metal-insulator transition at zero magnetic field in two-dimensional systems has remained a controversial enigma since the pioneering realization of the metallic behavior in high mobility Si-MOSFETs. In this paper the density (n) dependence of the conductivity of the two-dimensional electron gas in aluminum arsenide was analyzed in the metallic side (n ≥ 0.59×10^(11) cm^(-2)) at very low temperature. Our study reveals an inhomogeneity driven percolation type transition to an insulating state due to the breakdown of screening in the random charged impurities disordered background. The critical density found under this assumption is lower than that assumed by observing the sign of the temperature coefficient of conductivity. Experimental data are reprinted with permission from [S. J. Papadakis and M. Shayegan, Phys. Rev. B 57, R15068 (1998)].

Two-dimensional metal-insulator transition as a potential fluctuation driven semiclassical transport phenomenon

We theoretically consider the carrier density tuned (apparent) two-dimensional (2D) metal-insulator-transition (MIT) in semiconductor heterostructure-based 2D carrier systems as arising from a classical percolation phenomenon in the inhomogeneous density landscape created by the long-range potential fluctuations induced by random quenched charged impurities in the environment. The long-range Coulomb disorder inherent in semiconductors produces strong potential fluctuations in the 2D system where a fraction of the carriers gets trapped or classically localized, leading to a mixed 2-component semiclassical transport behavior at intermediate densities where a fraction of the carriers is mobile and another fraction immobile. At high carrier density, all the carriers are essentially mobile whereas at low carrier density all the carriers are essentially trapped since there is no possible percolating transport path through the lake-and-mountain inhomogeneous potential landscape. The low-density situation with no percolation would mimic an insulator whereas the high-density situation with allowed percolating paths through the lake-and-mountain energy landscape would mimic a metal with the system manifesting an apparent MIT in between. We calculate the transport properties as a function of carrier density, impurity density, impurity location, and temperature using a 2-component (trapped and mobile carriers) effective medium theory. Our theoretically calculated transport properties are in good qualitative agreement with the experimentally observed 2D MIT phenomenology in 2D electron and hole systems. We find a high (low) density metallic (insulating) temperature-dependence of the 2D resistivity, and an intermediate-density crossover behavior which could be identified with the experimentally observed 2D MIT.

Connecting the Reentrant Insulating Phase and the Zero-Field Metal-Insulator Transition in a 2D Hole System

We present the transport and capacitance measurements of 10 nm wide GaAs quantum wells with hole densities around the critical point of the 2D metal-insulator transition (critical density p(c) down to 0.8 × 10(10)/cm2, r(s) ∼ 36). For metallic hole density p(c) < p < p(c) + 0.15 × 10(10)/cm2, a reentrant insulating phase (RIP) is observed between the ν = 1 quantum Hall state and the zero-field metallic state and it is attributed to the formation of pinned Wigner crystal. Through studying the evolution of the RIP versus 2D hole density, we show that the RIP is incompressible and continuously connected to the zero-field insulator, suggesting a similar origin for these two phases.

A METAL–INSULATOR TRANSITION IN 2D: ESTABLISHED FACTS AND OPEN QUESTIONS

The discovery of a metallic state and a metal–insulator transition (MIT) in two-dimensional (2D) electron systems challenges one of the most influential paradigms of modern mesoscopic physics, namely, that "there is no true metallic behavior in two dimensions". However, this conclusion was drawn for systems of noninteracting or weakly interacting carriers, while in all 2D systems exhibiting the metal–insulator transition, the interaction energy greatly exceeds all other energy scales. We review the main experimental findings and show that, although significant progress has been achieved in our understanding of the MIT in 2D, many open questions remain.

Self-doping instability of the Wigner-Mott insulator

We present a theory describing the mechanism for the two-dimensional (2D) metal-insulator transition (MIT) in the absence of disorder. A two-band Hubbard model is introduced, describing vacancy-interstitial pair excitations within the Wigner crystal. Kinetic energy gained by delocalizing such excitations is found to lead to an instability of the insulator to self-doping above a critical carrier concentration $n={n}_{c}$, mapping the problem to a density-driven Mott MIT. This mechanism provides a natural explanation of several puzzling experimental features, including the large effective mass enhancement, the large resistivity drop, and the large positive magnetoresistance on the metallic side of the transition. We also present a global phase diagram for the clean 2D electron gas as a function of $n$ and parallel magnetic field ${B}_{\ensuremath{\parallel}}$, which agrees well with experimental findings in ultraclean samples.

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–electron interactions in the 2D electron system

In this paper, we report studies of the electron–electron interaction effects in 2D electron systems. The interaction manifests in renormalization of the effective spin susceptibility, effective mass, g ∗ -factor, conductivity etc. By applying in-plane magnetic field, we tuned the effective interaction between the electrons and compared with theory the temperature dependence of the conductivity. We find a good agreement with interaction corrections calculated within the Fermi liquid theory. To address the question on the origin of the metal–insulator transition (MIT) in 2D, we explored transport and magnetotransport properties in the vicinity of the MIT and compared our data with solutions of two equations of the renormalization group (RG) theory, which describes temperature evolutions of the resistivity and interaction parameters for 2D electron system. We found a good agreement between the ρ ( T , B ∥ ) data and the RG-theory in a wide range of the in-plane fields. These results support the Fermi liquid type origin of the metallic state and the interpretation of the observed 2D MIT as the true quantum phase transition.

TRANSPORT PROPERTIES OF 2D ELECTRON GAS IN AN n-InGaAs/GaAs DQW IN A VICINITY OF LOW MAGNETIC-FIELD-INDUCED HALL INSULATOR–QUANTUM HALL LIQUID TRANSITION

The resistivity (ρ) of low mobility dilute 2D electron gas in an n- InGaAs / GaAs double quantum well (DQW) exhibits the monotonic "insulating-like" temperature dependence (dρ/dT &lt; 0) at T = 1.8–70 K in zero magnetic field. This temperature interval corresponds to a ballistic regime (kBTτ/ħ &gt; 0.1–3.5) for our samples, and the electron density is on an "insulating" side of the so-called B = 0 2D metal–insulator transition. We show that the observed features of localization and Landau quantization in a vicinity of the low magnetic-field-induced insulator–quantum Hall liquid transition is due to the σxy(T) anomalous T-dependence.