Entanglement detection from conductance measurements in carbon nanotube Cooper pair splitters

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.Comment: 8 pages, 5 figure

Subradiant split Cooper pairs

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.Comment: Main text + Supplemental material file (15 pages, 5 figures), to appear in Physical Review Letter

Non adiabatic features of electron pumping through a quantum dot in the Kondo regime

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.Comment: 8 pages, 7 figure

Transport in Selectively Magnetically Doped Topological Insulator Wires

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.Comment: 8 pages, 7 figure

Quantum properties of atomic-sized conductors

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.Comment: Review, 120 pages, 98 figures. In view of the file size figures have been compressed. A higher-resolution version can be found at: http://lions1.leidenuniv.nl/wwwhome/ruitenbe/review/QPASC-hr-ps-v2.zip (5.6MB zip PostScript

Spin filtering and entanglement detection due to spin-orbit interaction in carbon nanotube cross-junctions

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.Comment: 14 pages, 8 figures. Final versio

Effects of the electrostatic environment on superlattice Majorana nanowires

Finding ways of creating, measuring, and manipulating Majorana bound states (MBSs) in superconducting-semiconducting nanowires is a highly pursued goal in condensed matter physics. It was recently proposed that a periodic covering of the semiconducting nanowire with superconductor fingers would allow both gating and tuning the system into a topological phase while leaving room for a local detection of the MBS wave function. We perform a detailed, self-consistent numerical study of a three-dimensional (3D) model for a finite-length nanowire with a superconductor superlattice including the effect of the surrounding electrostatic environment, and taking into account the surface charge created at the semiconductor surface. We consider different experimental scenarios where the superlattice is on top or at the bottom of the nanowire with respect to a back gate. The analysis of the 3D electrostatic profile, the charge density, the low-energy spectrum, and the formation of MBSs reveals a rich phenomenology that depends on the nanowire parameters as well as on the superlattice dimensions and the external back-gate potential. The 3D environment turns out to be essential to correctly capture and understand the phase diagram of the system and the parameter regions where topological superconductivity is establishedWe thank E. J. H. Lee, H. Beidenkopf, E. G. Michel, N. Avraham, H. Shtrikman, and J. Nygård for valuable discussions. Research supported by the Spanish MINECO through Grants No. FIS2016-80434-P, No. BES-2017-080374, and No. FIS2017-84860-R (AEI/FEDER, EU), the European Union's Horizon 2020 research and innovation programme under the FETOPEN Grant Agreement No. 828948 and Grant Agreement LEGOTOP No. 788715, the Ramón y Cajal programme RYC-2011-09345, the María de Maeztu Programme for Units of Excellence in R&D (MDM-2014-0377), the DFG (CRC/Transregio 183, EI 519/7- 1), the Israel Science Foundation (ISF), and the Binational Science Foundation (BSF

Signatures of triplet superconductivity in nu=2-chiral Andreev states

We study the behavior of the conductance and the current-noise in three-terminal configurations of edge modes of a quantum Hall system in the nu=2 filling factor with normal and s-wave superconducting contacts. We discuss the impact of spin-orbit coupling in the quantum Hall system and the possibility of effectively inducing triplet pairing in the egde states. We show that the presence of these correlations imprints very clear signatures in both the non-linear conductance and noise in these type of devices.Comment: 5 pages, 3 figures, supplemental materia