String Field Theory Vertices, Integrability and Boundary States

We study Neumann coefficients of the various vertices in the Witten's open string field theory (SFT). We show that they are not independent, but satisfy an infinite set of algebraic relations. These relations are identified as so-called Hirota identities. Therefore, Neumann coefficients are equal to the second derivatives of tau-function of dispersionless Toda Lattice hierarchy (this tau-function is just the partition sum of normal matrix model). As a result, certain two-vertices of SFT are identified with the boundary states, corresponding to boundary conditions on an arbitrary curve. Such two-vertices can be obtained by the contraction of special surface states with Witten's three vertex. We analyze a class of SFT surface states,which give rise to boundary states under this procedure. We conjecture that these special states can be considered as describing D-branes and other non-perturbative objects as "solitons" in SFT. We consider some explicit examples, one of them is a surface states corresponding to orientifold.Comment: 28pages plus appendices, acknowledgments adde

Non-renormalization of two and three Point Correlators of N=4 SYM in N=1 Superspace

Certain two and three point functions of gauge invariant primary operators of ${\cal N}=4$ SYM are computed in ${\cal N}=1$ superspace keeping all the $\th$-components. This allows one to read off many component descendent correlators. Our results show the only possible $g^2_{YM}$ corrections to the free field correlators are contact terms. Therefore they vanish for operators at separate points, verifying the known non-renormalization theorems. This also implies the results are consistent with ${\cal N}=4$ supersymmetry even though the Lagrangian we use has only ${\cal N}=1$ manifest supersymmetry. We repeat some of the calculations using supersymmetric Landau gauge and obtain, as expected, the same results as those of supersymmetric Feynman gauge.Comment: 10 pages, 20 eps figures, references adde

Reduced leakage current in Josephson tunnel junctions with codeposited barriers

Josephson junctions were fabricated using two different methods of barrier formation. The trilayers employed were Nb/Al-AlOx/Nb on sapphire, where the first two layers were epitaxial. The oxide barrier was formed either by exposing the Al surface to O2 or by codepositing Al in an O2 background. The codeposition process yielded junctions that showed the theoretically predicted subgap current and no measurable shunt conductance. In contrast, devices with barriers formed by thermal oxidation showed a small shunt conductance in addition to the predicted subgap current.Comment: 3 pages, 4 figure

Quantum phase slips in a confined geometry

We consider tunneling of vortices across a superconducting film that is both narrow and short (and connected to bulk superconducting leads at the ends). We find that in the superconducting state the resistance, at low values of the temperature (T) and current, does not follow the power-law dependence on T characteristic of longer samples but is exponential in 1/T. The coefficient of 1/T in the exponent depends on the length or, equivalently, the total normal-state resistance of the sample. These conclusions persist in the one-dimensional limit, which is similar to the problem of quantum phase slips in an ultra-narrow short wire.Comment: 14 pages, 1 figure; published in Phys. Rev.

Josephson effect in graphene SBS junctions

We study Josephson effect in graphene superconductor- barrier- superconductor junctions with short and wide barriers of thickness $d$ and width $L$, which can be created by applying a gate voltage $V_0$ across the barrier region. We show that Josephson current in such graphene junctions, in complete contrast to their conventional counterparts, is an oscillatory function of both the barrier width $d$ and the applied gate voltage $V_0$. We also demonstrate that in the thin barrier limit, where $V_0 \to \infty$ and $d \to 0$ keeping $V_0 d$ finite, such an oscillatory behavior can be understood in terms of transmission resonance of Dirac-Bogoliubov-de Gennes quasiparticles in superconducting graphene. We discuss experimental relevance of our work.Comment: 7 Pg., 6 Figs, extended version submitted to PR

Impurity band in clean superconducting weak links

Weak impurity scattering produces a narrow band with a finite density of states near the phase difference $\phi =\pi$ in the mid-gap energy spectrum of a macroscopic superconducting weak link. The equivalent distribution of transmission coefficients of various cunducting quantum channels is found.Comment: 4 pages, 4 figures, changed conten

Aharonov-Bohm differential conductance modulation in defective metallic single-wall carbon nanotubes

Using a perturbative approach, the effects of the energy gap induced by the Aharonov-Bohm (AB) flux on the transport properties of defective metallic single-walled carbon nanotubes (MSWCNTs) are investigated. The electronic waves scattered back and forth by a pair of impurities give rise to Fabry-Perot oscillations which constitutes a coherent backscattering interference pattern (CBSIP). It is shown that, the CBSIP is aperiodically modulated by applying a magnetic field parallel to the nanotube axis. In fact, the AB-flux brings this CBSIP under control by an additional phase shift. As a consequence, the extrema as well as zeros of the CBSIP are located at the irrational fractions of the quantity $\Phi_\rho={\Phi}/{\Phi_0}$, where $\Phi$ is the flux piercing the nanotube cross section and $\Phi_{0}=h/e$ is the magnetic quantum flux. Indeed, the spacing between two adjacent extrema in the magneto-differential conductance (MDC) profile is decreased with increasing the magnetic field. The faster and higher and slower and shorter variations is then obtained by metallic zigzag and armchair nanotubes, respectively. Such results propose that defective metallic nanotubes could be used as magneto-conductance switching devices based on the AB effect.Comment: 11 pages, 4 figure

The theory of the reentrant effect in susceptibility of cylindrical mesoscopic samples

A theory has been developed to explain the anomalous behavior of the magnetic susceptibility of a normal metal-superconductor ($NS$) structure in weak magnetic fields at millikelvin temperatures. The effect was discovered experimentally by A.C. Mota et al \cite{10}. In cylindrical superconducting samples covered with a thin normal pure metal layer, the susceptibility exhibited a reentrant effect: it started to increase unexpectedly when the temperature lowered below 100 mK. The effect was observed in mesoscopic $NS$ structures when the $N$ and $S$ metals were in good electric contact. The theory proposed is essentially based on the properties of the Andreev levels in the normal metal. When the magnetic field (or temperature) changes, each of the Andreev levels coincides from time to time with the chemical potential of the metal. As a result, the state of the $NS$ structure experiences strong degeneracy, and the quasiparticle density of states exhibits resonance spikes. This generates a large paramagnetic contribution to the susceptibility, which adds up to the diamagnetic contribution thus leading to the reentrant effect. The explanation proposed was obtained within the model of free electrons. The theory provides a good description for experimental results [10]