Abstract:
Interface bound states have been theoretically predicted to appear at isolated graphene-superconductor junctions. These states are formed at the interface due to the interplay between virtual Andreev and normal reflections and provide long range superconducting correlations on the graphene layer. We describe in detail the formation of these states from combining the Dirac equation with the Bogoliubov de Gennes equations of superconductivity. On the other hand, fluctuations of the low energy charge density in graphene have been confirmed as the dominating type of disorder. For analyzing the effect of disorder on these states we use a microscopic tight binding model. We show how the formation of these states is robust against the presence of disorder in the form of electron charge inhomogeneities in the graphene layer. We numerically compute the effect of disorder on the interface bound states and on the local density of states of graphene.

Abstract:
We suggest a way to characterize the coherence of the split Cooper pairs emitted by a double-quantum-dot based Cooper pair splitter (CPS), by studying the radiative response of such a CPS inside a microwave cavity. The coherence of the split pairs manifests in a strongly nonmonotonic variation of the emitted radiation as a function of the parameters controlling the coupling of the CPS to the cavity. The idea to probe the coherence of the electronic states using the tools of Cavity Quantum Electrodynamics could be generalized to many other nanoscale circuits.

Abstract:
Spin-orbit interaction provides a spin filtering effect in carbon nanotube based Cooper pair splitters that allows us to determine spin correlators directly from current measurements. The spin filtering axes are tunable by a global external magnetic field. By a bending of the nanotube the filtering axes on both sides of the Cooper pair splitter become sufficiently different that a test of entanglement of the injected Cooper pairs through the Bell inequality can be implemented. This implementation does not require noise measurements, supports imperfect splitting efficiency and disorder, and does not demand a full knowledge of the spin-orbit strength. Using a microscopic calculation we demonstrate that entanglement detection by violation of the Bell inequality is within the reach of current experimental setups.

Abstract:
We investigate the behavior of the dc electronic current, Jdc, in an interacting quantum dot driven by two ac local potentials oscillating with a frequency, Omega0, and a phase-lag, phi. We provide analytical functions to describe the fingerprints of the Coulomb interaction in an experimental Jdc vs phi characteristic curve. We show that the Kondo resonance reduces at low temperatures the frequency range for the linear behavior of Jdc in Omega0 to take place and determines the evolution of the dc-current as the temperature increases.

Abstract:
Using remarkably simple experimental techniques it is possible to gently break a metallic contact and thus form conducting nanowires. During the last stages of the pulling a neck-shaped wire connects the two electrodes, the diameter of which is reduced to single atom upon further stretching. For some metals it is even possible to form a chain of individual atoms in this fashion. Although the atomic structure of contacts can be quite complicated, as soon as the weakest point is reduced to just a single atom the complexity is removed. The properties of the contact are then dominantly determined by the nature of this atom. This has allowed for quantitative comparison of theory and experiment for many properties, and atomic contacts have proven to form a rich test-bed for concepts from mesoscopic physics. Properties investigated include multiple Andreev reflection, shot noise, conductance quantization, conductance fluctuations, and dynamical Coulomb blockade. In addition, pronounced quantum effects show up in the mechanical properties of the contacts, as seen in the force and cohesion energy of the nanowires. We review this reseach, which has been performed mainly during the past decade, and we discuss the results in the context of related developments.

Abstract:
We study the electronic and transport properties of a topological insulator nanowire including selective magnetic doping of its surfaces. We use a model which is appropriate to describe materials like Bi$_2$Se$_3$ within a k.p approximation and consider nanowires with a rectangular geometry. Within this model the magnetic doping at the (111) surfaces induces a Zeeman field which opens a gap at the Dirac cones corresponding to the surface states. For obtaining the transport properties in a two terminal configuration we use a recursive Green function method based on a tight-binding model which is obtained by discretizing the original continuous model. For the case of uniform magnetization of two opposite nanowire (111) surfaces we show that the conductance can switch from a quantized value of $e^2/h$ (when the magnetizations are equal) to a very small value (when they are opposite). We also analyze the case of non-uniform magnetizations in which the Zeeman field on the two opposite surfaces change sign at the middle of the wire. For this case we find that conduction by resonant tunneling through a chiral state bound at the middle of the wire is possible. The resonant level position can be tuned by imposing an Aharonov-Bohm flux through the nanowire cross section.

Abstract:
We demonstrate that due to their spin-orbit interaction carbon nanotube cross-junctions have attractive spin projective properties for transport. First, we show that the junction can be used as a versatile spin filter as a function of a backgate and a static external magnetic field. Switching between opposite spin filter directions can be achieved by small changes of the backgate potential, and a full polarization is generically obtained in an energy range close to the Dirac points. Second, we discuss how the spin filtering properties affect the noise correlators of entangled electron pairs, which allows us to obtain signatures of the type of entanglement that are different from the signatures in conventional semiconductor cross-junctions.

Abstract:
We investigate tunneling between two spinful Tomonaga-Luttinger liquids (TLLs) realized, e.g., as two crossed nanowires or quantum Hall edge states. When injecting into each TLL one electron of opposite spin, the dc current measured after the crossing differs for singlet, triplet, or product states. This is a striking new non-Fermi liquid feature because the (mean) current in a noninteracting beam splitter is insensitive to spin entanglement. It can be understood in terms of collective excitations subject to spin-charge separation. This behavior may offer an easier alternative to traditional entanglement detection schemes based on current noise, which we show to be suppressed by the interactions.

Abstract:
We calculate the time dependent nonequilibrium current through a single level quantum dot strongly coupled to a vibrational mode. The nonequilibrium real time dynamics caused by an instantaneous coupling of the leads to the quantum dot is discussed using an approximate method. The approach, which is specially designed for the strong polaronic regime, is based on the so-called polaron tunneling approximation. Considering different initial dot occupations, we show that a common steady state is reached after times much larger than the typical electron tunneling times due to a polaron blocking effect in the dot charge. A direct comparison is made with numerically exact data, showing good agreement for the time scales accessible by the diagrammatic Monte Carlo simulation method.

Abstract:
Electron correlation effects in Fe are analyzed using a first principles LCAO-scheme. In our approach, we first use a local orbital DFT-LDA solution to introduce a Hubbard Hamiltonian without fitting parameters. In a second step, we introduce a many-body solution to this Hamiltonian using a DMF approximation. Our analysis shows that magnetism in Fe is an effect associated with the first atomic Hund's rule. Moreover, we also find important correlation effects in the Fe-spin polarized DOS. The photoemision spectra is explained using a value of U_eff as large as 4 eV, provided the satellite peaks appearing around 3-5 eV below the Fermi energy are interpreted appropriately.