Density of States and Conductivity of Granular Metal or Array of Quantum Dots

The conductivity of a granular metal or an array of quantum dots usually has the temperature dependence associated with variable range hopping within the soft Coulomb gap of density of states. This is difficult to explain because neutral dots have a hard charging gap at the Fermi level. We show that uncontrolled or intentional doping of the insulator around dots by donors leads to random charging of dots and finite bare density of states at the Fermi level. Then Coulomb interactions between electrons of distant dots results in the a soft Coulomb gap. We show that in a sparse array of dots the bare density of states oscillates as a function of concentration of donors and causes periodic changes in the temperature dependence of conductivity. In a dense array of dots the bare density of states is totally smeared if there are several donors per dot in the insulator.Comment: 13 pages, 15 figures. Some misprints are fixed. Some figures are dropped. Some small changes are given to improve the organizatio

Dyakonov-Perel spin relaxation near metal-insulator transition and in hopping transport

In a heavily doped semiconductor with weak spin-orbital interaction the Dyakonov-Perel spin relaxation rate is known to be proportional to the Drude conductivity. We argue that in the case of weak spin-orbital interaction this proportionality goes beyond the Drude mechanism: it stays valid through the metal-insulator transition and in the range of the exponentially small hopping conductivity.Comment: 3 page

Anomalously large capacitance of a plane capacitor with a two-dimensional electron gas

In electronic devices where a two-dimensional electron gas (2DEG) comprises one or both sides of a plane capacitor, the resulting capacitance $C$ can be larger than the "geometric capacitance" $C_g$ determined by the physical separation $d$ between electrodes. This larger capacitance is known to result from the Coulomb correlations between individual electrons within the low density 2DEG, which lead to a negative thermodynamic density of states (negative compressibility). Experiments on such systems generally operate in the regime where the average spacing between electrons $n^{-1/2}$ in the 2DEG is smaller than $d$, and these experiments observe $C > C_g$ by only a few percent. A recent experiment [1], however, has observed $C$ larger than $C_g$ by almost 40% while operating in the regime $nd^2 << 1$. In this paper we argue that at $nd^2 << 1$ correlations between the electronic charge of opposite electrodes become important. We develop a theory of the capacitance for the full range of $nd^2$. We show that, in the absence of disorder, the capacitance can be $4d/a$ times larger than the geometric value, where $a << d$ is the electron Bohr radius. Our results compare favorably with the experiment of Ref. [1] without the use of adjustable parameters.Comment: 8 pages, 6 figures; revised discussion of the zero density limit; some typos fixe

Percolation-to-hopping crossover in conductor-insulator composites

Here, we show that the conductivity of conductor-insulator composites in which electrons can tunnel from each conducting particle to all others may display both percolation and tunneling (i.e. hopping) regimes depending on few characteristics of the composite. Specifically, we find that the relevant parameters that give rise to one regime or the other are $D/\xi$ (where $D$ is the size of the conducting particles and $\xi$ is the tunneling length) and the specific composite microstructure. For large values of $D/\xi$, percolation arises when the composite microstructure can be modeled as a regular lattice that is fractionally occupied by conducting particle, while the tunneling regime is always obtained for equilibrium distributions of conducting particles in a continuum insulating matrix. As $D/\xi$ decreases the percolating behavior of the conductivity of lattice-like composites gradually crosses over to the tunneling-like regime characterizing particle dispersions in the continuum. For $D/\xi$ values lower than $D/\xi\simeq 5$ the conductivity has tunneling-like behavior independent of the specific microstructure of the composite.Comment: 8 pages, 5 figure

Analysis of broadband microwave conductivity and permittivity measurements of semiconducting materials

We perform broadband phase sensitive measurements of the reflection coefficient from 45 MHz up to 20 GHz employing a vector network analyzer with a 2.4 mm coaxial sensor which is terminated by the sample under test. While the material parameters (conductivity and permittivity) can be easily extracted from the obtained impedance data if the sample is metallic, no direct solution is possible if the material under investigation is an insulator. Focusing on doped semiconductors with largely varying conductivity, here we present a closed calibration and evaluation procedure for frequencies up to 5 GHz, based on the rigorous solution for the electromagnetic field distribution inside the sample combined with the variational principle; basically no limiting assumptions are necessary. A simple static model based on the electric current distribution proves to yield the same frequency dependence of the complex conductivity up to 1 GHz. After a critical discussion we apply the developed method to the hopping transport in Si:P at temperature down to 1 K.Comment: 9 pages, 10 figures, accepted for publication in the Journal of Applied Physic

Euclidean resonance in a magnetic field

An analogy between Wigner resonant tunneling and tunneling across a static potential barrier in a static magnetic field is found. Whereas in the process of Wigner tunneling an electron encounters a classically allowed regions, where a discrete energy level coincides with its energy, in the magnetic field a potential barrier is a constant in the direction of tunneling. Along the tunneling path the certain regions are formed, where, in the classical language, the kinetic energy of the motion perpendicular to tunneling is negative. These regions play a role of potential wells, where a discrete energy level can coincide with the electron energy. Such phenomenon, which occurs at the certain magnetic field, is called Euclidean resonance and substantially depends on a shape of potential forces in the direction perpendicular to tunneling. Under conditions of Euclidean resonance a long distance underbarrier motion is possible.Comment: 7 pages, 4 figure

Cyclotron enhancement of tunneling

A state of an electron in a quantum wire or a thin film becomes metastable, when a static electric field is applied perpendicular to the wire direction or the film surface. The state decays via tunneling through the created potential barrier. An additionally applied magnetic field, perpendicular to the electric field, can increase the tunneling decay rate for many orders of magnitude. This happens, when the state in the wire or the film has a velocity perpendicular to the magnetic field. According to the cyclotron effect, the velocity rotates under the barrier and becomes more aligned with the direction of tunneling. This mechanism can be called cyclotron enhancement of tunneling

Solution of the tunneling-percolation problem in the nanocomposite regime

We noted that the tunneling-percolation framework is quite well understood at the extreme cases of percolation-like and hopping-like behaviors but that the intermediate regime has not been previously discussed, in spite of its relevance to the intensively studied electrical properties of nanocomposites. Following that we study here the conductivity of dispersions of particle fillers inside an insulating matrix by taking into account explicitly the filler particle shapes and the inter-particle electron tunneling process. We show that the main features of the filler dependencies of the nanocomposite conductivity can be reproduced without introducing any \textit{a priori} imposed cut-off in the inter-particle conductances, as usually done in the percolation-like interpretation of these systems. Furthermore, we demonstrate that our numerical results are fully reproduced by the critical path method, which is generalized here in order to include the particle filler shapes. By exploiting this method, we provide simple analytical formulas for the composite conductivity valid for many regimes of interest. The validity of our formulation is assessed by reinterpreting existing experimental results on nanotube, nanofiber, nanosheet and nanosphere composites and by extracting the characteristic tunneling decay length, which is found to be within the expected range of its values. These results are concluded then to be not only useful for the understanding of the intermediate regime but also for tailoring the electrical properties of nanocomposites.Comment: 13 pages with 8 figures + 10 pages with 9 figures of supplementary material (Appendix B

Compensation driven superconductor-insulator transition

The superconductor-insulator transition in the presence of strong compensation of dopants was recently realized in La doped YBCO. The compensation of acceptors by donors makes it possible to change independently the concentration of holes n and the total concentration of charged impurities N. We propose a theory of the superconductor-insulator phase diagram in the (N,n) plane. It exhibits interesting new features in the case of strong coupling superconductivity, where Cooper pairs are compact, non-overlapping bosons. For compact Cooper pairs the transition occurs at a significantly higher density than in the case of spatially overlapping pairs. We establish the superconductor-insulator phase diagram by studying how the potential of randomly positioned charged impurities is screened by holes or by strongly bound Cooper pairs, both in isotropic and layered superconductors. In the resulting self-consistent potential the carriers are either delocalized or localized, which corresponds to the superconducting or insulating phase, respectively

Local transport in a disorder-stabilized correlated insulating phase

We report the experimental realization of a correlated insulating phase in 2D GaAs/AlGaAs heterostructures at low electron densities in a limited window of background disorder. This has been achieved at mesoscopic length scales, where the insulating phase is characterized by a universal hopping transport mechanism. Transport in this regime is determined only by the average electron separation, independent of the topology of background disorder. We have discussed this observation in terms of a pinned electron solid ground state, stabilized by mutual interplay of disorder and Coulomb interaction.Comment: 4+delta pages, 4 figures, To appear in the Physical Review B (Rapid Comm