Numbers of donors and acceptors from transport measurements in graphene

A method is suggested to separately determine the surface density of positively and negatively charged impurities that limit the mobility in a graphene monolayer. The method is based on the exact result for the transport cross-section, according to which the massless carriers are scattered more strongly when they are attracted to a charged impurity than when they are repelled from it.Comment: 3 pages, 1 figur

Asymptotic behavior of the mean square displacement of the Brownian parametric oscillator near the singular point

A parametric oscillator with damping driven by white noise is studied. The mean square displacement (MSD) in the long-time limit is derived analytically for the case that the static force vanishes, which was not treated in the past work \cite{tashiro07}. The formula is asymptotic but is applicable to a general periodic function. On the basis of this formula, some periodic functions reducing MSD remarkably are proposed

New global stability estimates for the Gel'fand-Calderon inverse problem

We prove new global stability estimates for the Gel'fand-Calderon inverse problem in 3D. For sufficiently regular potentials this result of the present work is a principal improvement of the result of [G. Alessandrini, Stable determination of conductivity by boundary measurements, Appl. Anal. 27 (1988), 153-172]

Temperature-dependent Drude transport in a two-dimensional electron gas

We consider transport of dilute two-dimensional electrons, with temperature between Fermi and Debye temperatures. In this regime, electrons form a nondegenerate plasma with mobility limited by potential disorder. Different kinds of impurities contribute unique signatures to the resulting temperature-dependent Drude conductivity, via energy-dependent scattering. This opens up a way to characterize sample disorder composition. In particular, neutral impurities cause a slow decrease in conductivity with temperature, whereas charged impurities result in conductivity growing as a square root of temperature. This observation serves as a precaution for literally interpreting metallic or insulating conductivity dependence, as both can be found in a classical metallic system.Comment: 5 pages, 2 figures, published versio

Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

For the Schrodinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. For the case of zero background potential these results were obtained in [R.G.Novikov, Multidimensional inverse spectral problem for the equation -\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22, (1988)]

New global stability estimates for monochromatic inverse acoustic scattering

We give new global stability estimates for monochromatic inverse acoustic scattering. These estimates essentially improve estimates of [P. Hahner, T. Hohage, SIAM J. Math. Anal., 33(3), 2001, 670-685] and can be considered as a solution of an open problem formulated in the aforementioned work

Dirac fermion wave guide networks on topological insulator surfaces

Magnetic texturing on the surface of a topological insulator allows the design of wave guide networks and beam splitters for domain-wall Dirac fermions. Guided by simple analytic arguments we model a Dirac fermion interferometer consisting of two parallel pathways, whereby a newly developed staggered-grid leap-frog discretization scheme in 2+1 dimensions with absorbing boundary conditions is employed. The net transmission can be tuned between constructive to destructive interference, either by variation of the magnetization (path length) or an applied bias (wave length). Based on this principle, a Dirac fermion transistor is proposed. Extensions to more general networks are discussed.Comment: Submitted to PR