On C*-algebras generated by pairs of q-commuting isometries

We consider the C*-algebras O_2^q and A_2^q generated, respectively, by isometries s_1, s_2 satisfying the relation s_1^* s_2 = q s_2 s_1^* with |q| < 1 (the deformed Cuntz relation), and by isometries s_1, s_2 satisfying the relation s_2 s_1 = q s_1 s_2 with |q| = 1. We show that O_2^q is isomorphic to the Cuntz-Toeplitz C*-algebra O_2^0 for any |q| < 1. We further prove that A_2^{q_1} is isomorphic to A_2^{q_2} if and only if either q_1 = q_2 or q_1 = complex conjugate of q_2. In the second part of our paper, we discuss the complexity of the representation theory of A_2^q. We show that A_2^q is *-wild for any q in the circle |q| = 1, and hence that A_2^q is not nuclear for any q in the circle.Comment: 18 pages, LaTeX2e "article" document class; submitted. V2 clarifies the relationships between the various deformation systems treate

Critical Current 0-π\pi Transition in Designed Josephson Quantum Dot Junctions

We report on quantum dot based Josephson junctions designed specifically for measuring the supercurrent. From high-accuracy fitting of the current-voltage characteristics we determine the full magnitude of the supercurrent (critical current). Strong gate modulation of the critical current is observed through several consecutive Coulomb blockade oscillations. The critical current crosses zero close to, but not at, resonance due to the so-called 0-$\pi$ transition in agreement with a simple theoretical model.Comment: 5 pages, 4 figures, (Supplementary information available at http://www.fys.ku.dk/~hij/public/nl_supp.pdf

Electron transport in single wall carbon nanotube weak links in the Fabry-Perot regime

We fabricated reproducible high transparency superconducting contacts consisting of superconducting Ti/Al/Ti trilayers to gated single-walled carbon nanotubes (SWCNTs). The reported semiconducting SWCNT have normal state differential conductance up to $3e^2/h$ and exhibit clear Fabry-Perot interference patterns in the bias spectroscopy plot. We observed subharmonic gap structure in the differential conductance and a distinct peak in the conductance at zero bias which is interpreted as a manifestation of a supercurrent. The gate dependence of this supercurrent as well as the excess current are examined and compared to a coherent theory of superconducting point contacts with good agreement.Comment: 10 pages, 4 figure

Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm

The primal-dual optimization algorithm developed in Chambolle and Pock (CP), 2011 is applied to various convex optimization problems of interest in computed tomography (CT) image reconstruction. This algorithm allows for rapid prototyping of optimization problems for the purpose of designing iterative image reconstruction algorithms for CT. The primal-dual algorithm is briefly summarized in the article, and its potential for prototyping is demonstrated by explicitly deriving CP algorithm instances for many optimization problems relevant to CT. An example application modeling breast CT with low-intensity X-ray illumination is presented.Comment: Resubmitted to Physics in Medicine and Biology. Text has been modified according to referee comments, and typos in the equations have been correcte

Superconductivity-enhanced bias spectroscopy in carbon nanotube quantum dots

We study low-temperature transport through carbon nanotube quantum dots in the Coulomb blockade regime coupled to niobium-based superconducting leads. We observe pronounced conductance peaks at finite source-drain bias, which we ascribe to elastic and inelastic cotunneling processes enhanced by the coherence peaks in the density of states of the superconducting leads. The inelastic cotunneling lines display a marked dependence on the applied gate voltage which we relate to different tunneling-renormalizations of the two subbands in the nanotube. Finally, we discuss the origin of an especially pronounced sub-gap structure observed in every fourth Coulomb diamond

A triple quantum dot in a single wall carbon nanotube

A top-gated single wall carbon nanotube is used to define three coupled quantum dots in series between two electrodes. The additional electron number on each quantum dot is controlled by top-gate voltages allowing for current measurements of single, double and triple quantum dot stability diagrams. Simulations using a capacitor model including tunnel coupling between neighboring dots captures the observed behavior with good agreement. Furthermore, anti-crossings between indirectly coupled levels and higher order cotunneling are discussed.Comment: Supporting Information is available at Nano Lett. website (see link below

On boson algebras as Hopf algebras

Certain types of generalized undeformed and deformed boson algebras which admit a Hopf algebra structure are introduced, together with their Fock-type representations and their corresponding $R$-matrices. It is also shown that a class of generalized Heisenberg algebras including those algebras including those underlying physical models such as that of Calogero-Sutherland, is isomorphic with one of the types of boson algebra proposed, and can be formulated as a Hopf algebra.Comment: LaTex, 18 page

The tunnel magnetoresistance in chains of quantum dots weakly coupled to external leads

We analyze numerically the spin-dependent transport through coherent chains of three coupled quantum dots weakly connected to external magnetic leads. In particular, using the diagrammatic technique on the Keldysh contour, we calculate the conductance, shot noise and tunnel magnetoresistance (TMR) in the sequential and cotunneling regimes. We show that transport characteristics greatly depend on the strength of the interdot Coulomb correlations, which determines the spacial distribution of electron wave function in the chain. When the correlations are relatively strong, depending on the transport regime, we find both negative TMR as well as TMR enhanced above the Julliere value, accompanied with negative differential conductance (NDC) and super-Poissonian shot noise. This nontrivial behavior of tunnel magnetoresistance is associated with selection rules that govern tunneling processes and various high-spin states of the chain that are relevant for transport. For weak interdot correlations, on the other hand, the TMR is always positive and not larger than the Julliere TMR, although super-Poissonian shot noise and NDC can still be observed