Andreev bound states probed in three-terminal quantum dots

We demonstrate several new electron transport phenomena mediated by Andreev bound states (ABSs) that form on three-terminal carbon nanotube (CNT) QDs, with one superconducting (S) contact in the center and two adjacent normal metal (N) contacts. Three-terminal spectroscopy allows us to identify the coupling to the N contacts as the origin of the Andreev resonance (AR) linewidths and to determine the critical coupling strengths to S, for which a ground state transition S-QD systems can occur. We ascribe replicas of the lowest-energy ABS resonance to transitions between the ABS and odd-parity excited QD states, a process called excited state ABS resonances. In the conductance between the two N contacts we find a characteristic pattern of positive and negative differential subgap conductance, which we explain by considering two nonlocal processes, the creation of Cooper pairs in S by electrons from both N terminals, and a novel mechanism called resonant ABS tunneling. In the latter, electrons are transferred via the ABS without creating Cooper pairs in S. The three-terminal geometry also allows spectroscopy experiments with different boundary conditions, for example by leaving S floating. Surprisingly, we find that, depending on the boundary conditions, the experiments either show single-particle Coulomb blockade resonances, ABS characteristics, or both in the same measurements, seemingly contradicting the notion of ABSs replacing the single particle states as eigenstates of the QD. We qualitatively explain these results as originating from the finite time scale required for the coherent oscillations between the superposition states after a single electron tunneling event. These experiments demonstrate that three-terminal experiments on a single complex quantum object can also be useful to investigate charge dynamics otherwise not accessible due to the very high frequencies.Comment: 15 pages, 16 figure

Resonant and inelastic Andreev tunneling observed on a carbon nanotube quantum dot

We report the observation of two fundamental sub-gap transport processes through a quantum dot (QD) with a superconducting contact. The device consists of a carbon nanotube contacted by a Nb superconducting and a normal metal contact. First, we find a single resonance with position, shape and amplitude consistent with the theoretically predicted resonant Andreev tunneling (AT) through a single QD level. Second, we observe a series of discrete replicas of resonant AT at a separation of $\sim145\,\mu$eV, with a gate, bias and temperature dependence characteristic for boson-assisted, inelastic AT, in which energy is exchanged between a bosonic bath and the electrons. The magnetic field dependence of the replica's amplitudes and energies suggest that two different bosons couple to the tunnel process.Comment: 5 pages + 9 pages supplementary materia

Fork stamping of pristine carbon nanotubes onto ferromagnetic contacts for spin-valve devices

We present a fabrication scheme called 'fork stamping' optimized for the dry transfer of individual pristine carbon nanotubes (CNTs) onto ferromagnetic contact electrodes fabricated by standard lithography. We demonstrate the detailed recipes for a residue-free device fabrication and in-situ current annealing on suspended CNT spin-valve devices with ferromagnetic Permalloy (Py) contacts and report preliminary transport characterization and magnetoresistance experiments at cryogenic temperatures. This scheme can directly be used to implement more complex device structures, including multiple gates or superconducting contacts.Comment: 7 pages, 4 figures, submitted to IWEPNM 2015 conference proceedings (physica status solidi (b)

On Some Positivity Properties of the Interquark Potential in QCD

We prove that the Fourier transform of the exponential e^{-\b V(R)} of the {\bf static} interquark potential in QCD is positive. It has been shown by Eliott Lieb some time ago that this property allows in the same limit of static spin independent potential proving certain mass relation between baryons with different quark flavors.Comment: 6 pages, latex with one postscript figur

Hierarchic Superposition Revisited

Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably complete" even in the presence of free function symbols ranging into a background theory sort. The hierarchic superposition calculus of Bachmair, Ganzinger, and Waldmann already supports such symbols, but, as we demonstrate, not optimally. This paper aims to rectify the situation by introducing a novel form of clause abstraction, a core component in the hierarchic superposition calculus for transforming clauses into a form needed for internal operation. We argue for the benefits of the resulting calculus and provide two new completeness results: one for the fragment where all background-sorted terms are ground and another one for a special case of linear (integer or rational) arithmetic as a background theory

Contact resistance dependence of crossed Andreev reflection

We show experimentally that in nanometer scaled superconductor/normal metal hybrid devices and in a small window of contact resistances, crossed Andreev reflection (CAR) can dominate the nonlocal transport for all energies below the superconducting gap. Besides CAR, elastic cotunneling (EC) and nonlocal charge imbalance (CI) can be identified as competing subgap transport mechanisms in temperature dependent four-terminal nonlocal measurements. We demonstrate a systematic change of the nonlocal resistance vs. bias characteristics with increasing contact resistances, which can be varied in the fabrication process. For samples with higher contact resistances, CAR is weakened relative to EC in the midgap regime, possibly due to dynamical Coulomb blockade. Gaining control of CAR is an important step towards the realization of a solid state entangler.Comment: 5 pages, 4 figures, submitted to PR