827 research outputs found
Effects of interedge scattering on the Wigner crystallization in graphene nanoribbons
We investigate the effects of coupling between the two zigzag edges of
graphene nanoribbons on the Wigner crystallization of electrons and holes using
a combination of tight-binding, mean field Hubbard and many-body configuration
interaction methods. We show that the thickness of the nanoribbon plays a
crucial role in the formation of Wigner crystal. For ribbon widths smaller than
16 \mbox{\AA}, increased kinetic energy overcomes the long-range Coulomb
repulsion and suppresses the Wigner crystallization. For wider ribbons up to 38
\mbox{\AA} wide, strong Wigner localization is observed for even number of
electrons, revealing an even-odd effect also found in Coulomb blockade addition
spectrum. Interedge correlations are found to be strong enough to allow
simultaneous crystallization on both edges, although an applied electric field
can decouple the two edges. Finally, we show that Wigner crystallization can
also occurs for holes, albeit weaker than for electrons.Comment: Accepted for publication in PR
Estimation of Scale and Hurst Parameters of Semi-Selfsimilar Processes
The characteristic feature of semi-selfsimilar process is the invariance of
its finite dimensional distributions by certain dilation for specific scaling
factor. Estimating the scale parameter and the Hurst index of such
processes is one of the fundamental problem in the literature. We present some
iterative method for estimation of the scale and Hurst parameters which is
addressed for semi-selfsimilar processes with stationary increments. This
method is based on some flexible sampling scheme and evaluating sample variance
of increments in each scale intervals , . For such iterative method we find the initial estimation for the
scale parameter by evaluating cumulative sum of moving sample variances and
also by evaluating sample variance of preceding and succeeding moving sample
variance of increments. We also present a new efficient method for estimation
of Hurst parameter of selfsimilar processes. As an example we introduce simple
fractional Brownian motion (sfBm) which is semi-selfsimilar with stationary
increments. We present some simulations and numerical evaluation to illustrate
the results and to estimate the scale for sfBm as a semi-selfsimilar process.
We also present another simulation and show the efficiency of our method in
estimation of Hurst parameter by comparing its performance with some previous
methods.Comment: 15 page
Effect of long-range structural corrugations on magnetotransport properties of phosphorene in tilted magnetic field
Rippling is an inherent quality of two-dimensional materials playing an
important role in determining their properties. Here, we study the effect of
structural corrugations on the electronic and transport properties of monolayer
black phosphorus (phosphorene) in the presence of tilted magnetic field. We
follow a perturbative approach to obtain analytical corrections to the spectrum
of Landau levels induced by a long-wavelength corrugation potential. We show
that surface corrugations have a non-negligible effect on the electronic
spectrum of phosphorene in tilted magnetic field. Particularly, the Landau
levels are shown to exhibit deviations from the linear field dependence. The
observed effect become especially pronounced at large tilt angles and
corrugation amplitudes. Magnetotransport properties are further examined in the
low temperature regime taking into account impurity scattering. We calculate
magnetic field dependence of the longitudinal and Hall resistivities and find
that the nonlinear effects reflecting the corrugation might be observed even in
moderate fields (\mbox{ T})
- …