Coherent electron transport in nanostructures

Abstract

In this thesis we theoretically investigate coherent properties of quantum transport, especially photon-assisted electron transport as well as the frequency dependence of the noise spectral function for ballistic conductors. In chapter 2 we will briefly introduce the basic theoretical formalism of scattering theory as developed by Landauer and Büttiker. We will apply it to the model of a single resonant level between two metallic reservoirs in chapters 3 and 4. Dc and ac-bias voltages modify the current (chapter 3) and the current noise spectrum (chapter 4) via photon absorption and emission. We show how electron anti-bunching at small frequencies and electron bunching at high frequencies are modified by the interplay of Pauli’s exclusion principle and PAT.The special band structure of graphene provides the basis for novel phenomena in solid- state quantum physics. In chapter 5 we introduce the theoretical description of electronic transport in graphene in terms of the Dirac Hamiltonian and scattering theory. The purpose of the two main sections in there is to apply the scattering formalism and study the current and current noise in two different systems. i) A strongly electronically doped graphene sheet from where PAT events are injected into a graphene sheet around the charge neutrality point (section 5.3), and ii) a double barrier system with metallic leads where a short but wide graphene sheet is sandwiched in between (section 5.4). Characteristics of the graphene setup in comparison to the single-level model will be pointed out, such as the impact of Klein tunneling or distinguished interference patterns of transmission functions, which affect the noise spectrum.The last part before summarizing, chapter 6, is devoted to superconductor-normal metal- superconductor (SNS) junctions. We use the momentum averaged green function formalism to discuss the influence of non-ideal interfaces on the local density of states (DOS) inside the diffusive normal metal wire and how they influence properties of phase-coherent electron transport in matters of the current-phase relation.