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Quantum scattering beyond quasi one-dimensionnal systems

Abstract : Simulations in the field of quantum nanoelectronics are often restricted to a quasi one-dimensional geometries where the device is connected to the macroscopic world with one-dimensional electrodes. This thesis presents novel numerical methods that lift many of these restrictions, in particular rendering realistic simulations of three-dimensional systems possible.The first part introduces a robust and efficient algorithm for computing bound states of infinite tight-binding systems that are made up of a scattering region connected to semi-infinite leads. The method is formulated in close nalogy to the wave-matching approach used to compute the scattering matrix. It also allows one to calculate edge or surface states, e.g. the so-called Fermi arcs.The second part is dedicated to a new numerical method, based on the Green's function formalism, that allows to efficiently simulate systems that are infinite in 1, 2 or 3 dimensions and mostly invariant by translation. Compared to established approaches whose computational costs grow with system size and that are therefore plagued by finite size effects, the new method allows one to directly reach the thermodynamic limit. It provides a practical route for simulating 3D setups that have so far remained elusive.Both methods are illustrated by applications to several quantum systems(a disordered two-dimensional electron gas, a graphene device...) and topological materials (Majorana states in 1D superconducting nanowires, Fermi arcs in 3D Weyl semimetals...). The last application (resilience of Fermi arcs to disorder) combines all the algorithms that were introduced in this thesis.
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Mathieu Istas. Quantum scattering beyond quasi one-dimensionnal systems. Mesoscopic Systems and Quantum Hall Effect [cond-mat.mes-hall]. Université Grenoble Alpes, 2019. English. ⟨NNT : 2019GREAY023⟩. ⟨tel-02445475⟩

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