Quasi-Ferromagnet Spintronics in Graphene Nanodisk-Lead System

A zigzag graphene nanodisk can be interpreted as a quantum dot with an internal degree of freedom. It is well described by the infinite-range Heisenberg model. We have investigated its thermodynamical properties. There exists a quasi-phase transition between the quasi-ferromagnet and quasi-paramagnet states, as signaled by a sharp peak in the specific heat and in the susceptability. We have also analyzed how thermodynamical properties are affected when two leads are attached to the nanodisk. It is shown that lead effects are described by the many-spin Kondo Hamiltonian. There appears a new peak in the specific heat, and the multiplicity of the ground state becomes just one half of the system without leads. Another lead effect is to enhance the ferromagnetic order. Being a ferromagnet, a nanodisk can be used as a spin filter. Furthermore, since the relaxation time is finite, it is possible to control the spin of the nanodisk by an external spin current. We then propose a rich variety of spintronic devices made of nanodisks and leads, such as spin memory, spin amplifier, spin valve, spin-field-effect transistor, spin diode and spin logic gates such as spin-XNOR gate and spin-XOR gate. Graphene nanodisks could well be basic components of future nanoelectronic and spintronic devices.Comment: 12 pages, 13 figures, invited paper to "focus on graphene

Theory of 4e versus 2e supercurrent in frustrated Josepshon-junction rhombi chain

We consider a chain of Josepshon-junction rhombi (proposed originally in \cite{Doucot}) in quantum regime, and in the realistic case when charging effects are determined by junction capacitances. In the maximally frustrated case when magnetic flux through each rhombi $\Phi_r$ is equal to one half of superconductive flux quantum $\Phi_0$, Josepshon current is due to correlated transport of {\em pairs of Cooper pairs}, i.e. charge is quantized in units of $4e$. Sufficiently strong deviation $\delta\Phi \equiv |\Phi_r-\Phi_0/2| > \delta\Phi^c$ from the maximally frustrated point brings the system back to usual $2e$-quantized supercurrent. We present detailed analysis of Josepshon current in the fluctuation-dominated regime (sufficiently long chains) as function of the chain length, $E_J/E_C$ ratio and flux deviation $\delta\Phi$. We provide estimates for the set of parameters optimized for the observation of $4e$-supercurrent.Comment: 23 pages, 9 figure

Random walk of magnetic field lines for different values of the energy-range spectral index

An analytical nonlinear description of field-line wandering in partially statistically magnetic systems was proposed recently [A. Shalchi, I. Kourakis, Astronomy and Astrophysics, 470, 405 (2007)]. In this article we investigate the influence of the wave-spectrum in the energy-range onto field line random walk by applying this formulation. It is demonstrated that in all considered cases we clearly obtain a superdiffusive behaviour of the field-lines. If the energy-range spectral index exceeds unity a free-streaming behaviour of the field-lines can be found for all relevant length-scales of turbulence. Since the superdiffusive results obtained for the slab model are exact, it seems that superdiffusion is the normal behavior of field line wandering.Comment: Submitted to Physics of Plasmas; 13 pages, no figure

Traveling waves and Compactons in Phase Oscillator Lattices

We study waves in a chain of dispersively coupled phase oscillators. Two approaches -- a quasi-continuous approximation and an iterative numerical solution of the lattice equation -- allow us to characterize different types of traveling waves: compactons, kovatons, solitary waves with exponential tails as well as a novel type of semi-compact waves that are compact from one side. Stability of these waves is studied using numerical simulations of the initial value problem.Comment: 22 pages, 25 figure

PT-Invariant Periodic Potentials with a Finite Number of Band Gaps

We obtain the band edge eigenstates and the mid-band states for the complex, PT-invariant generalized associated Lam\'e potentials V^{PT}(x)=-a(a+1)m \sn^2(y,m)-b(b+1)m {\sn^2 (y+K(m),m)} -f(f+1)m {\sn^2 (y+K(m)+iK'(m),m)}-g(g+1)m {\sn^2 (y+iK'(m),m)}, where $y \equiv ix+\beta$, and there are four parameters $a,b,f,g$. This work is a substantial generalization of previous work with the associated Lam\'e potentials V(x)=a(a+1)m\sn^2(x,m)+b(b+1)m{\sn^2 (x+K(m),m)} and their corresponding PT-invariant counterparts $V^{PT}(x)=-V(ix+\beta)$, both of which involving just two parameters $a,b$. We show that for many integer values of $a,b,f,g$, the PT-invariant potentials $V^{PT}(x)$ are periodic problems with a finite number of band gaps. Further, usingsupersymmetry, we construct several additional, new, complex, PT-invariant, periodic potentials with a finite number of band gaps. We also point out the intimate connection between the above generalized associated Lam\'e potential problem and Heun's differential equation.Comment: 30 pages, 0 figure

Persistent current in superconducting nanorings

The superconductivity in very thin rings is suppressed by quantum phase slips. As a result the amplitude of the persistent current oscillations with flux becomes exponentially small, and their shape changes from sawtooth to a sinusoidal one. We reduce the problem of low-energy properties of a superconducting nanoring to that of a quantum particle in a sinusoidal potential and show that the dependence of the current on the flux belongs to a one-parameter family of functions obtained by solving the respective Schrodinger equation with twisted boundary conditions.Comment: 5 pages, 1 figur

Scattering states of a particle, with position-dependent mass, in a double heterojunction

In this work we obtain the exact analytical scattering solutions of a particle (electron or hole) in a semiconductor double heterojunction - potential well / barrier - where the effective mass of the particle varies with position inside the heterojunctions. It is observed that the spatial dependence of mass within the well / barrier introduces a nonlinear component in the plane wave solutions of the continuum states. Additionally, the transmission coefficient is found to increase with increasing energy, finally approaching unity, whereas the reflection coefficient follows the reverse trend and goes to zero.Comment: 7 pages, 6 figure

Gluon recombination in high parton density QCD: inclusive pion production

We argue that the collinear factorization of the fragmentation functions in high energy hadron and nuclei collisions breaks down at transverse momenta kT < Qs/g due to high parton densities in the colliding hadrons and/or nuclei. We calculate, at next-to-leading order in projectile parton density and to all orders in target parton density, the double-inclusive cross section for production of a pair of gluons in the scalar J^(PC)=0^(++) channel. Using the low energy theorems of QCD we find the inclusive cross section for pi-meson production.Comment: 24 pages, 5 figure

Matching factors for Delta S=1 four-quark operators in RI/SMOM schemes

The non-perturbative renormalization of four-quark operators plays a significant role in lattice studies of flavor physics. For this purpose, we define regularization-independent symmetric momentum-subtraction (RI/SMOM) schemes for Delta S=1 flavor-changing four-quark operators and provide one-loop matching factors to the MS-bar scheme in naive dimensional regularization. The mixing of two-quark operators is discussed in terms of two different classes of schemes. We provide a compact expression for the finite one-loop amplitudes which allows for a straightforward definition of further RI/SMOM schemes.Comment: 22 pages, 5 figure

Selective transmission of Dirac electrons and ballistic magnetoresistance of \textit{n-p} junctions in graphene

We show that an electrostatically created n-p junction separating the electron and hole gas regions in a graphene monolayer transmits only those quasiparticles that approach it almost perpendicularly to the n-p interface. Such a selective transmission of carriers by a single n-p junction would manifest itself in non-local magnetoresistance effect in arrays of such junctions and determines the unusual Fano factor in the current noise universal for the n-p junctions in graphene.Comment: 4 pages, 2 fig