Critical Density Nc Research Articles

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.

An efficient approach to study membrane nano-inclusions: from the complex biological world to a simple representation.

Membrane nano-inclusions (NIs) are of great interest in biophysics, materials science, nanotechnology, and medicine. We hypothesized that the NIs within a biological membrane bilayer interact via a simple and efficient interaction potential, inspired by previous experimental and theoretical work. This interaction implicitly treats the membrane lipids but takes into account its effect on the NIs micro-arrangement. Thus, the study of the NIs is simplified to a two-dimensional colloidal system with implicit solvent. We calculated the structural properties from Molecular Dynamics simulations (MD), and we developed a Scaling Theory to discuss their behavior. We determined the thermal properties through potential energy per NI and pressure, and we discussed their variation as a function of the NIs number density. We performed a detailed study of the NIs dynamics using two approaches, MD simulations, and Dynamics Theory. We identified two characteristic values of number density, namely a critical number density nc = 3.67 × 10−3 Å−2 corresponded to the apparition of chain-like structures along with the liquid dispersed structure and the gelation number density ng = 8.40 × 10−3 Å−2 corresponded to the jamming state. We showed that the aggregation structure of NIs is of fractal dimension dF < 2. Also, we identified three diffusion regimes of membrane NIs, namely, normal for n < nc, subdiffusive for nc ≤ n < ng, and blocked for n ≥ ng. Thus, this paper proposes a simple and effective approach for studying the physical properties of membrane NIs. In particular, our results identify scaling exponents related to the microstructure and dynamics of membrane NIs.

Experimental Evidence for an Inhomogeneous State of the Correlated Two-Dimensional Electron System in the Vicinity of a Metal–Insulator Transition

From measurements of the oscillatory magnetoresistance in weak perpendicular magnetic fields, we found that the quantum oscillations in two-dimensional electron systems in Si-MOS structures are observed down to the critical carrier density nc of the transition to the strongly localized state. For such low densities, the oscillations exhibit an anticipated period, phase, and amplitude, even though the conductivity becomes less than e2/h, and, hence, the mean free path becomes less than the Fermi wavelength λF. We believe that this apparent contradiction with the Ioffe-Regel criterion for diffusive transport is caused by emergence of an inhomogeneous state of the 2D system, in which the regions of diffusive and hopping conduction are spatially separated.

The contributions of junctions and nanowires/nanotubes in conductive networks

Electrical transport in networked materials occurs through percolative clusters composed of a random distribution of two kinds of interconnected elements: elementary nanostructures and nanostructure-nanostructure junctions. Rationalizing the contribution of these microscopic elements to the macroscopic resistance of the system is a fundamental issue to develop this class of materials and related devices. Focusing on networks composed of high-aspect-ratio nanostructures, such as nanowires (NWs) or nanotubes (NTs), these concepts are still raising controversy in modeling and interpretation of experimental data. Despite these incongruences and the large variations induced by disorder in the electrical properties of such networked systems, this work shows that the ratio between the junction and the nanostructure resistance is nearly the same at the microscopic and macroscopic levels, regardless of the network features. In other words, this means that we may assess the relative contribution of nanostructures and junctions to the macroscopic network resistance directly from the knowledge of its microscopic building blocks. Based on experimental data available in the literature, this result is proven to hold for different materials and network densities, ranging from inorganic NWs to organic carbon NTs and from the percolation critical density nc up to, at least, five times nc, respectively.

Chirp assisted ion acceleration via relativistic self-induced transparency

We study the effect of the chirped laser pulse on the transmission and associated ion acceleration by the sub-wavelength target. In the chirped laser pulses, the pulse frequency has a temporal variation about its fundamental frequency, which manifests to the temporal dependence of the critical density (nc). In this work, we used a chirp model which is beyond the linear approximation. For negatively (positively) chirped pulses, the high (low) frequency component of the pulse interacts with the target initially followed by the low (high) frequency component. The threshold plasma density for the transmission of the pulse is found to be higher for the negatively chirped laser pulses as compared to the unchirped or positively chirped pulses. The enhanced transmission of the negatively chirped pulses for higher densities (6nc) results in very efficient heating of the target electrons, creating a very stable and persistent longitudinal electrostatic field behind the target. The void of the electrons results in expansion of the target ions in either direction, resulting in the broad energy spectrum. We have introduced a very thin, low density (&amp;lt;nc) secondary layer behind the primary layer. The ions from the secondary layer are then found to be accelerated as a mono-energetic bunch under the influence of the electrostatic field created by the primary layer upon interaction by the negatively chirped pulse. Under the optimum conditions, the maximum energy of the protons is found to be ∼100 MeV for 10 fs (intensity FWHM); Circularly Polarized; Gaussian; negatively chirped laser pulse with peak intensity ∼8.5 × 1020 W/cm2.

Probing suprathermal electrons by trace rare gases optical emission spectroscopy in low pressure dipolar microwave plasmas excited at the electron cyclotron resonance

In microwave plasmas with the presence of a magnetic field, fast electrons could result from collisionless energy absorption under electron cyclotron resonance (ECR) conditions. In this case, electrons are trapped between the two poles of the magnetic field and rotate at the cyclotron frequency ωce. When crossing a zone where the cyclotron frequency equals the microwave frequency (ωce=ω), electrons see a steady electric field in their reference frame and are constantly accelerated by the right handed polarized (RHP) wave. When the plasma density reaches the so-called critical density nc at which ωpe2=ω2±ωωce, where ωpe is the plasma electron frequency, the left handed polarized (LHP) electromagnetic wave can excite electrostatic waves that can produce collisionless electron heating and fast electron generation by Landau damping. In this study, a combination of the Langmuir probe and trace rare gas optical emission spectroscopy (TRG-OES) is used to analyze the electron energy probability function (EEPF) in microwave (2.45 GHz) low-pressure argon plasmas excited at ECR in a dipolar magnetic field. While both TRG-OES and Langmuir probe measurements agree on the effective electron temperature (TeAll) from 1.6 to 50 mTorr, TRG-OES, which is more sensitive to high energy electrons, shows that the EEPF is the sum of two Maxwellian populations: one described by TeAll and a high energy tail characterized by a temperature TeTail. Spatially resolved-TRG-OES measurements show that the high-energy tail (TeTail) in the EEPF is spatially localized near the magnet, while the effective electron temperature (TeAll) stays constant. The ratio between the high energy tail and the effective temperatures is found to increase with the absorbed microwave power and decrease with increasing pressure. The former phenomenon is ascribed to a rise in ECR heating due to a stronger RHP wave electric field and to an enhanced absorption of the LHP waves. On the other hand, the decrease in the ratio is attributed to a smaller magnetic confinement of the electrons (increase in the collision frequency), which lessens ECR heating and to a decrease in the LHP field intensity at the resonant position, which impedes the conversion into electrostatic waves.

Continuous phase transitions in high-mobility Si MOSFETs at finite temperatures

We re-analyze earlier published data on two dimensional electron system Si-MOSFETs sample, in which a transition from metallic to insulator (MIT) behavior was observed. Our results indicate the existence of continuous phase transition at finite temperatures. We have focused our work around the critical density nc of the MIT, where nc≈0.712×1011cm−2, and we have found that the two suggestive phase transitions revealed in previous work, persist at finite temperatures by plotting log10ρ and dlog10σ/dns against carrier density ns. However, the graphics displaying log10ρ (ns) and dlog10σ/dns (ns) share a peak located almost at the same value of the carrier density ns∗≈1×1011cm-2 remarkably higher than the critical density nc in contrast to earlier work, where this peak is located just at nc.

Effective mass and Landé g-factor in Si-MOSFETs near the critical density

We analyze the electrical resistivity and conductivity of a dilute two-dimensional electron gas (2DEG) in a Si metal-oxide-semiconductor field-effect transistor. When a magnetic field is applied parallel to the plane of the 2DEG, a signature of complete spin polarization, as evidenced by the saturation of the resistivity, is observed. We measured the effective mass and the Lande g-factor near the metal-insulator transition (MIT) and found that the Lande g-factor remained almost constant and close to its value in bulk silicon. In contrast, we have observed a sharp increase in the effective mass near the critical density of the MIT. Our new results suggest that the sharp increase in the previously-observed spin susceptibility is mainly due to the enhanced effective mass. Therefore, renormalization of the effective mass could play an important role in a dilute spinpolarized 2DEG. The data indicate that electron-electron interactions strongly modify the effective mass but only weakly affect the g-factor in a dilute 2DEG. Moreover, our results indicate that Bc, which corresponds to the magnetic field at which the magnetoresistivity reaches saturation, vanishes at a characteristic density nχ higher than the critical density nc of the MIT. This is in contrast to the existing experimental results, and further studies are required if this discrepancy is to be understood.

Effect of disorder on carrier transport in ZnO thin films grown by atomic layer deposition at different temperatures

We have grown ∼200 nm thick ZnO films on (0001) sapphire substrates using atomic layer deposition at different substrate temperatures ranging from ∼150 to 350 °C. X-ray diffraction and photoluminescence spectra of these films showed that crystalline and compositional native defects were strongly dependent on the substrate temperature. Room temperature Hall measurement showed that all the films were degenerate with carrier concentration exceeding the Mott's critical density nc required for metallic conduction. The lowest value of room temperature resistivity ∼3.6 × 10−3 Ω cm was achieved for the film deposited at ∼200 °C, which had an estimated carrier concentration ∼5.7 × 1019 cm−3 and mobility ∼30 cm2/V s. The films deposited both below and above ∼200 °C showed increased resistivity and decreased mobility presumably due to the intensified defects and deteriorated crystalline quality of these films. To investigate the effect of disorder on the underlying charge transport mechanisms in these films, the electrical resistivity was measured in the temperature range of ∼4.2 to 300 K. The films grown at ∼150, 300, and 350 °C were found to be semiconducting in the entire range of the measurement temperature due to the intensified disorder which impeded the metallic transport in these films. However, the films grown at ∼200 and 250 °C showed a transition from metallic to semiconducting transport behaviour at lower temperatures due to the reduced defects and improved crystalline quality of these films. The observed semiconducting behaviour below the transition temperature for these films could be well explained by considering quantum corrections to the Boltzmann conductivity which includes the effect of disorder induced weak localization and coulomb electron-electron interactions.

Hot-electron generation from laser–pre-plasma interactions in cone-guided fast ignition

Two-dimensional particle-in-cell (PIC) simulations were performed for the cone-in-shell integrated fast-ignition experiments at the Omega Laser Facility [W. Theobald et al., Phys. Plasmas 18, 056305 (2011)]. The initial plasma density profile in the PIC simulations was taken from hydrodynamic simulations of the prepulse interaction with the gold cone. Hot-electron generation from laser–pre-plasma interactions and transport up to 100× the critical density (nc) was studied. The simulation showed a mean divergence half-angle of 68° and 50% absorption for the hot electrons. The simulation results show that the generated hot electrons were dominated in number by low-energy electrons but in energy by multi-MeV electrons. Electron transport between 5 and 100 nc was ballistic. In the late stage of the simulation, all the results were largely independent of polarization, indicating a stochastic hot-electron–generation mechanism.

Phase transitions of dense neutron matter with generalized Skyrme interaction to superfluid states with triplet pairing in strong magnetic field

A generalized non-relativistic Fermi-liquid approach was used to find analytical formulas for temperatures Tc1(n, H) and Tc2(n, H) (which are functions nonlinear of density n and linear of magnetic field H) of phase transitions in spatially uniform dense pure neutron matter from normal to superfluid states with spin-triplet p-wave pairing (similar to anisotropic superfluid phases 3He-A1 and 3He-A2) in steady and homogeneous strong magnetic field (but |μn| H ≪ Ec < ∊F(n), where μn is the magnetic dipole moment of a neutron, Ec is the cutoff energy and ∊F(n) is the Fermi energy in neutron matter). General formulas for Tc1, 2 (n, H) (valid for arbitrary parameterization of the effective Skyrme interaction in neutron matter) are specified here for generalized BSk18 parameterization of the Skyrme forces (with additional terms dependent on density n) on the interval 0.3 n0 < n < nc (BSk18) ≍ 2.7952 · n0, where n0 = 0.17 fm−3 is nuclear density and at critical density nc(BSk18) triplet superfluidity disappears, Tc0(n, cH = 0) = 0. Expressions for phase transition temperatures Tc0(n)<0.09MeV (at Ec = 10MeV) and Tc1, 2(n, H) are realistic non-monotone functions of density n for BSk18 parameterization of the Skyrme forces (contrary to their monotone increase for all previous BSk parameterizations). Phase transitions to superfluid states of such type might occur in liquid outer core of magnetars (strongly magnetized neutron stars).

PLASMA EFFECTS ON FAST PAIR BEAMS IN COSMIC VOIDS

The interaction of TeV gamma rays from distant blazars with the extragalactic background light produces relativistic electron-positron pair beams by the photon- photon annihilation process. The created pair beam distribution is unstable to linear two-stream instabilities of both electrostatic and electromagnetic nature in the unmagnetized intergalactic medium (IGM). The maximum electrostatic growth rate occurs at angles of 392 with respect to the pair beam direction, and is more than three orders of magnitude greater than the maximum Weibel growth rate, indicating that the linear oblique electrostatic instability operates much faster than the Weibel instability. The dissipation of the generated electrostatic turbulence is different for intense and weak gamma-ray blazars. For intense blazars, the normalized number of generated pairs n 22 = nb /[10–22 cm–3] exceeds the critical density nc (T) = 4.8 × 10–3 T 4 for given normalized IGM temperature T 4 = T/[104 K] necessary for the onset of the modulation instability, so that all free kinetic pair energy is dissipated in heating the IGM in cosmic voids. For weak blazars, half of the initial energy density of the beam particles is transferred to the electrostatic and electromagnetic fluctuations on timescales smaller than the inverse Compton energy loss timescale of the pairs. In both cases, this prevents the development of a full electromagnetic pair cascade as in vacuum. For weak blazars, the superluminal electrostatic fluctuations are dissipated by the inverse Compton scattering into transverse electromagnetic waves by the relaxed relativistic pair particles to optical frequencies, implying the occurrence of optical electrostatic bremsstrahlung pair halos from weak blazars with spectral flux densities below 50 μJy.

Enhancement of Kα emission through efficient hot electron generation in carbon nanotubes on intense laser pulse irradiation

Near complete absorption of the energy of intense ultra-short laser pulses (45 fs, intensity ∼1.6 × 1016 to 2.5 × 1017 W/cm2) is observed in carbon nanotubes deposited on a planar molybdenum substrate. The hollow structure of the nanotube plasma facilitates resonant electric field enhancement during its ionization phase. This resonantly enhanced localized field at a density much larger than the critical density nc leads to efficient hot electron generation, which results in enhanced Kα emission of Mo at 17.5 keV. It is observed that for nanotubes, depending on the degree of hollowness, there is an optimum laser intensity for maximum x-ray enhancement compared to a planar uncoated target.

Topology and transport in the edge region of RFX-mod helical regimes

New edge diagnostics and detailed analysis of magnetic topology have significantly improved the comprehension of the processes developing at the boundary of a reversed-field pinch (RFP) plasma in RFX-mod (a = 0.46 m, R = 2 m).An upper critical density nC ≈ 0.4 nG (nG Greenwald density) is found to limit the operational space for the improved quasi-single helical (QSH) regime: magnetic topology reconstructions and diagnostic observations suggest that this limit is due to a helical plasma–wall interaction which determines toroidally and poloidally localized edge density accumulation and cooling.The experimental evidence is provided by a variety of diagnostics: the magnetic boundary as reconstructed from equilibrium codes reveals a helical deformation, which is well correlated with the modulation of edge pressure profile as reconstructed from the thermal helium beam diagnostic. Correlations with the helical deformation are also observed on the space- and time-resolved patterns of the floating potential measured at the wall, and with the edge plasma flow, obtained from different diagnostics. The relevance of these findings is that understanding the mechanisms that limit the operational space of QSH is decisive in achieving the goal of high-density stationary helical RFP equilibrium.

Magnetic field generation and relativistic electron dynamics in circularly polarized intense laser interaction with dense plasma

The generation of both axial and azimuthal magnetic field components by the intense laser-dense plasma interaction and relativistic electron dynamics are studied in theoretical analysis and three-dimensional particle-in-cell simulations. For a circularly polarized laser, the cylindrical symmetry can be applied. Interacting with this laser, both axial and the azimuthally magnetic fields are generated and play an essential role in hot electron beam collimation, stabilization, and shaping. It is significantly different from the linearly polarized case, where the azimuthal current and the axial magnetic field are absent, therefore the axial current density gets filamentary early in the ramp plasma and is focused into a single channel in the dense (with a density larger than the critical density nc) plasma later, and the electron and ion density distributions as well as the azimuthally magnetic field profile are broadened in the polarized direction to form an ellipse-like structure in the transverse plane. Instead, the results for the circularly polarized laser analytically and numerically show a much better collimation of the relativistic electron beams than in the case of the linearly polarized laser, due to the axial field component generated by azimuthal electron dynamics.

Electromagnetic Wave Propagation in an Inhomogeneous Highly Collisional Plasma

It is shown that in a highly collisional plasma, electromagnetic waves can propagate beyond the critical density nc. When the electromagnetic wave propagates obliquely to the plasma density gradient, there exists a critical angle of incidence, below which there is no reflection. When the incident angle is larger than the critical angle, there are two reflection points. One is at a density lower than 2nc, corresponding to the EM wave incident from low to high density regions. The other one is at a density higher than 2nc, corresponding to that from high to low density regions.

Disk-shaped electronic bubbles in gaseous helium

The structure of 2D anions placed on a hydrogen substrate in the presence of gaseous helium is discussed. It is shown that these structures, shaped like quasi-two-dimensional disks, are created in a threshold-like manner in the vicinity of critical density nc∼1020 cm−3, which is appreciably lower than the critical density for the appearance of spherical electronic bubbles in gas and linearly depends on temperature. Experiment confirms the existence of such autolocalized states.

On the stability of homogeneous solutions to some aggregation models

Vasculogenesis, i.e. self-assembly of endothelial cells leading to capillary network formation, has been the object of many experimental in- vestigations in recent years, due to its relevance both in physiological and in pathological conditions. We performed a detailed linear stability analysis of two models of in vitro vasculogenesis, with the aim of checking their potential for structure formation starting from initial data representing a continuum cell monolayer. The first model turns out to be unstable at low cell densities, while pressure stabilizes it at high densities. The second model is instead stable at low cell densities. Detailed information about the instability regions and the structure of the critical wave numbers are obtained in several interesting limit- ing cases. We expect that altogether, this information will be useful for further comparison of the two models with experiments. 1. Introduction. In living beings, complex structures arise from the aggregation of separate constituents. A typical example is given by the formation of the vascular network in vertebrates, where vascular endothelial cells migrate over long distances and finally coalesce to form complex vascular structures (11, 7). The process takes place during the early stages of embryo development and is therefore difficult to observe in its dynamical details. To circumvent this difficulty, severalin vitro as- says have been devised (4). In the experiments, cells are randomly seeded on the plain surface of a gel substratum and their migration and aggregation observed through videomicroscopy. In this way, the process of formation of a capillary-like network can be accurately tracked (1). Tracking of individual trajectories shows marked persistence in the direction of cell motion, with a small random component superimposed. Cells migrate over distances which are an order of magnitude larger than their radius and stick together when they get in contact with their neigh- bours. Motion is apparently directed towards zones of higher cell concentration, suggesting that chemotactic factors play a relevant role in the process. In a time of the order of some hours cells form a continuous multicellular network which can be described as a collection of nodes connected by chords (Fig. 1a). It is exper- imentally observed that i) the mean chord lengthis approximately independent on the initial cell density ( ¯ l ≃ 200 ±20¹ m); ii) connected networks are formed only above a critical density nc ∼ 100 cells/mm 2 (a phenomenon known as a percolative transition (12)); iii) at higher cell densities the chord thickness grows in order to ac- commodate a larger number of cells (Fig. 1b), until around 400 cells/mm 2 , a sort of

The Fe xxii I (11.92 )/ I (11.77 ) Density Diagnostic Applied to the Chandra High Energy Transmission Grating Spectrum of EX Hydrae

Using the Livermore X-ray Spectral Synthesizer, which calculates spectral models of highly charged ions based primarily on HULLAC atomic data, we investigate the temperature, density, and photoexcitation dependence of the I(11.92 A)/I(11.77 A) line ratio of Fe XXII. We find that this line ratio has a critical density nc ≈ 5 × 1013 cm-3, is approximately 0.3 at low densities and 1.5 at high densities, and is very insensitive to temperature and photoexcitation; therefore, it is a useful density diagnostic for sources like magnetic cataclysmic variables, in which the plasma densities are high and in which the efficacy of the He-like ion density diagnostic is compromised by the presence of a bright ultraviolet continuum. Applying this diagnostic to the Chandra High Energy Transmission Grating spectrum of the intermediate polar EX Hya, we find that the electron density of its Te ≈ 12 MK plasma is ne = 1.0 × 1014 cm-3, which is orders of magnitude greater than that typically observed in the Sun or other late-type stars.

COHERENT MOTIONS AND CLUSTERS IN A DISSIPATIVE MORSE RING CHAIN

We study a one-dimensional ring chain of length L with N particles interacting via Morse potentials and influenced by dissipative forces (passive and active friction). We show that by negative friction the system can be driven far from the thermodynamic equilibrium states. For over-critical pumping with free energy several types of coherent motions including uniform rotations, optical oscillations and waves emerge in the ring. We also show the existence of a critical particle density nc= N/Lc, below that the particles spontaneously organize into clusters which can actively rotate. Additionally, the influence of white noise on the clustering is discussed.