Möbius transformations and electronic transport properties of large networks

Details Möbius transformations and electronic transport properties of large networks Möbius transformations and electronic transport properties of large networks

2011-04-14

arxiv.org/abs/1104.2820v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

latex, 5 figs, submitted to Phys. Rev. Lett

Scientific paper

We show that the insulating and conducting phases of large regular networks of scatterers can be described by negative and zero Lyapunov exponents, respectively, of M\"obius maps that relate the scattering matrix of systems with 2n scatterers to their next generation with 2(n+1). It is demonstrated that such a correspondence between dynamical properties of the underlying M\"obius transformation in the complex plane and the general metal-insulating transition scenarios is a generic property shared by classes of symmetric network structures with uniformly-distributed scatterers. Our conclusions have been verified for serial as well as parallel stub and ring mesoscopic structures. We have also tested our theory on dissipative transport systems, and have found that in this case the Lyapunov exponent is not a convincing indicator for conductance transitions.

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