محاسبه حالت هاي مقيد اندريف در پيوندهاي SNS با استفاده از روش KPM و محاسبه ابر جريان جوزفسون در گرافين

چكيده انگليسي :

Calculation of Andreev bound states in SNS junctions using KPM and Calculation of Josephson supercurrent in Graphene Esameel Sarvestani e sarvestani@ph iut ac ir 4 16 2011 Department of Physics Isfahan University of Technology Isfahan 84156 83111 IranDegree M Sc Language PersianSupervisor Dr S A Jafari akbar jafari@gmail comAbstractIn this thesis we focused our attention to two problems in inhomogenities in superconductor systems The rst one is the calculation of Andreev Bound States in the junctions of superconductor and normalmetal Solving the Bogoliubov deGennes mean eld equation for nonhomogeneous superconductorsystems gives the bound and quantized states with energy below the superconductor energy gap Itis possible to solve this equation analytically for one dimensional systems as well as two or threedimensional systems with simple geometry But for more complex geometries numerical methodsare inevitable In this regard a new numerical method Kernel Polynomial Method KPM hasbeen adopted This method is based on the expansion of the physical quantities specially electronicDensity of States DOS in terms of the Chebishev polynomial In chapter 2 we took advanatage ofKPM for solving the Bogoliubov deGennes equation for superconductor normal metal junctions We have used the local density of states to distinguish the bound states from propagating ones i e local DOS for bound states has a nite value in the normal region while it vanishes rapidly in thesuperconductor region The second topic presented in this thesis is calculation of the supercurrent in the Graphene JosephsonJunction Graphene is a two dimensional 2D structure of carbon atoms with a thicknes of onlyone atom Carbon atoms in graphene arranged on a honeycomb structure which is composed oftwo sublattices Recently some experiments have been conducted to see the Josephson effect in theJunctions based on the Graphene and measure the supercurrent in these systems Consequently thisquantity has been calculated using various methods such as scattering matrix self consistent methodand Cooper pair propagator Temprature and lenghth dependency of the supercurrent have beendetermined In a very recently experiment current phase relation has been measured In this work we introduced a new method for performing this task that is the perturbative Green s Function methodin framework of the path integral using the tunneling Hamiltonian between superconductor regionand graphene normal region The main feature of our work is that we assumed that superconductivitywill be induced on the honycomb lattice of graphene while the pairing occures between electronson different valleys It will be shown that the fourth order is the lowest order of perturbation thatcontributes in the Josephson supercurrent Tunneling Hamiltonian involves the two kinds of tunnling interavalley and intervalley Considering the intervalley tunnlling we achieved results that havenot been seen in previous works We have seen sharp oscillations in the diagrams which show thedependency of the supercurrent on the distance between the superconductors electrods But if wesolely include intravalley tunnlling our result will match exactly to the others works Keywords Bogoliubov de Gennes equation KPM Andreev bound states Graphene Josephson supercurrent

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محاسبه حالت هاي مقيد اندريف در پيوندهاي SNS با استفاده از روش KPM و محاسبه ابر جريان جوزفسون در گرافين

معادله بوگوليوبوف , دوژن