Yusuf Amir Kinkhabwala

A numerical study of transport and shot noise in 2D hopping

We have used modern supercomputer facilities to carry out extensive Monte Carlo simulations of 2D hopping (at negligible Coulomb interaction) in conductors with a completely random distribution of localized sites in both space and energy, within a broad range of the applied electric field E and temperature T, both within and beyond the variable-range hopping region. The calculated properties include not only dc current and statistics of localized site occupation and hop lengths, but also the current fluctuation spectrum. Within the calculation accuracy, the model does not exhibit 1/f noise, so that the low-frequency noise at low temperatures may be characterized by the Fano factor F. For sufficiently large samples, F scales with conductor length L as (L(c)/L)(α), where α = 0.76 ± 0.08<1, and parameter L(c) is interpreted as the average percolation cluster length. At relatively low E, the electric field dependence of parameter L(c) is compatible with the law [Formula: see text] which follows from directed percolation theory arguments.

A numerical study of Coulomb interaction effects on 2D hopping transport

We have extended our supercomputer-enabled Monte Carlo simulations of hopping transport in completely disordered 2D conductors to the case of substantial electron-electron Coulomb interaction. Such interaction may not only suppress the average value of hopping current, but also affect its fluctuations rather substantially. In particular, the spectral density S(I)(f) of current fluctuations exhibits, at sufficiently low frequencies, a 1/f-like increase which approximately follows the Hooge scaling, even at vanishing temperature. At higher f, there is a crossover to a broad range of frequencies in which S(I)(f) is nearly constant, hence allowing characterization of the current noise by the effective Fano factor [Formula: see text]. For sufficiently large conductor samples and low temperatures, the Fano factor is suppressed below the Schottky value (F = 1), scaling with the length L of the conductor as F = (L(c)/L)(α). The exponent α is significantly affected by the Coulomb interaction effects, changing from α = 0.76 ± 0.08 when such effects are negligible to virtually unity when they are substantial. The scaling parameter L(c), interpreted as the average percolation cluster length along the electric field direction, scales as [Formula: see text] when Coulomb interaction effects are negligible and [Formula: see text] when such effects are substantial, in good agreement with estimates based on the theory of directed percolation.

Shot noise at hopping via two sites

The average current and the shot noise at correlated sequential tunneling via two localized sites are studied. At zero temperature the Fano factor averaged over the positions and energies of sites is shown to be 0.707. The noise dependence on temperature and frequency is analyzed numerically.

Shot Noise Suppression and Enhancement at 2D Hopping and in Single‐Electron Arrays

We have carried out numerical simulations of shot noise at two-dimensional (2D) hop- ping and in 2D arrays of single-electron islands with and without random background charges. Such key transport characteristics as the average (dc) current hIi, the single-particle density of states and the current fluctuation spectrum, have been calculated within a broad range of the applied electric field E and temperature T. Substantial Coulomb interaction effects are shown to not only suppress the average value of hopping current, but also affect its fluctuations rather substantially. In par- ticular, at sufficiently low frequencies ( f ! 0) the spectral density SI ( f ) of current fluctuations exhibits a 1= f -like increase which approximately follows the Hooge scaling. As f increases, there is a crossover to a broad range of frequencies in which SI ( f ) is nearly constant, hence allowing char- acterization of the current noise by the Fano factor F SI ( f )=2ehIi. For sufficiently large samples and low temperature, the Fano factor is suppressed below the Schottky value (F = 1), scaling with the sample length L as F = (Lc=L) α . The exponent α is significantly affected by the inclusion of Coulomb interaction effects, changing from α = 0:76 0:08 when such effects are negligible to virtually unity when they are substantial. The scaling parameter Lc, interpreted as the average per- colation cluster length along the electric field direction, scales as Lc ∝ E (0:98 0:08) when Coulomb interaction effects are negligible and Lc ∝ E (1:26 0:15) when such effects are substantial, in good agreement with results of directed percolation theory. In arrays of single-electron islands with completely random background charges, the current noise is strongly colored at low currents, and its spectral density levels off at very low frequen- cies. The Fano factor may be much larger than unity, due to the remnants of single-electron/hole avalanches. However, even very small thermal fluctuations reduced the Fano factor below unity for almost any bias.