17 research outputs found
Geometrical enhancement of the proximity effect in quantum wires with extended superconducting tunnel contacts
We study Andreev reflection in a ballistic one-dimensional channel coupled in
parallel to a superconductor via a tunnel barrier of finite length . The
dependence of the low-energy Andreev reflection probability on
reveals the existence of a characteristic length scale beyond which
is enhanced up to unity despite the low interfacial transparency. The
Andreev reflection enhancement is due to the strong mixing of particle and hole
states that builds up in contacts exceeding the coherence length ,
leading to a small energy gap (minigap) in the density of states of the normal
system. The role of the geometry of such hybrid contacts is discussed in the
context of the experimental observation of zero-bias Andreev anomalies in the
resistance of extended carbon nanotube/superconductor junctions in field effect
transistor setups.Comment: 11 pages, 8 figures; minor revisions including added Ref. 7 and inset
to Fig. 3b; version as accepted for publication to Phys. Rev.
Nonmonotonic inelastic tunneling spectra due to surface spin excitations in ferromagnetic junctions
The paper addresses inelastic spin-flip tunneling accompanied by surface spin
excitations (magnons) in ferromagnetic junctions. The inelastic tunneling
current is proportional to the magnon density of states which is
energy-independent for the surface waves and, for this reason, cannot account
for the bias-voltage dependence of the observed inelastic tunneling spectra.
This paper shows that the bias-voltage dependence of the tunneling spectra can
arise from the tunneling matrix elements of the electron-magnon interaction.
These matrix elements are derived from the Coulomb exchange interaction using
the itinerant-electron model of magnon-assisted tunneling. The results for the
inelastic tunneling spectra, based on the nonequilibrium Green's function
calculations, are presented for both parallel and antiparallel magnetizations
in the ferromagnetic leads.Comment: 9 pages, 4 figures, version as publishe
Nonquasiparticle states in half-metallic ferromagnets
Anomalous magnetic and electronic properties of the half-metallic
ferromagnets (HMF) have been discussed. The general conception of the HMF
electronic structure which take into account the most important correlation
effects from electron-magnon interactions, in particular, the spin-polaron
effects, is presented. Special attention is paid to the so called
non-quasiparticle (NQP) or incoherent states which are present in the gap near
the Fermi level and can give considerable contributions to thermodynamic and
transport properties. Prospects of experimental observation of the NQP states
in core-level spectroscopy is discussed. Special features of transport
properties of the HMF which are connected with the absence of one-magnon
spin-flip scattering processes are investigated. The temperature and magnetic
field dependences of resistivity in various regimes are calculated. It is shown
that the NQP states can give a dominate contribution to the temperature
dependence of the impurity-induced resistivity and in the tunnel junction
conductivity. First principle calculations of the NQP-states for the prototype
half-metallic material NiMnSb within the local-density approximation plus
dynamical mean field theory (LDA+DMFT) are presented.Comment: 27 pages, 9 figures, Proceedings of Berlin/Wandlitz workshop 2004;
Local-Moment Ferromagnets. Unique Properties for Moder Applications, ed. M.
Donath, W.Nolting, Springer, Berlin, 200
Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters
We prove the following theorems:
1) The Laurent expansions in epsilon of the Gauss hypergeometric functions
2F1(I_1+a*epsilon, I_2+b*epsilon; I_3+p/q + c epsilon; z),
2F1(I_1+p/q+a*epsilon, I_2+p/q+b*epsilon; I_3+ p/q+c*epsilon;z),
2F1(I_1+p/q+a*epsilon, I_2+b*epsilon; I_3+p/q+c*epsilon;z), where
I_1,I_2,I_3,p,q are arbitrary integers, a,b,c are arbitrary numbers and epsilon
is an infinitesimal parameter, are expressible in terms of multiple
polylogarithms of q-roots of unity with coefficients that are ratios of
polynomials; 2) The Laurent expansion of the Gauss hypergeometric function
2F1(I_1+p/q+a*epsilon, I_2+b*epsilon; I_3+c*epsilon;z) is expressible in terms
of multiple polylogarithms of q-roots of unity times powers of logarithm with
coefficients that are ratios of polynomials; 3) The multiple inverse rational
sums (see Eq. (2)) and the multiple rational sums (see Eq. (3)) are expressible
in terms of multiple polylogarithms; 4) The generalized hypergeometric
functions (see Eq. (4)) are expressible in terms of multiple polylogarithms
with coefficients that are ratios of polynomials.Comment: 48 pages in LaTe
Multilevel preconditioning operators on locally modified grids
Systems of grid equations that approximate elliptic boundary value problems on locally modified grids are considered. The triangulation, which approximates the boundary with second order of accuracy, is generated from an initial uniform triangulation by shifting nodes near the boundary according to special rules. This ”locally modified” grid possesses several significant features: this triangulation has a regular structure, the generation of the triangulation is rather fast, this construction allows to use multilevel preconditioning (BPX-like) methods. The proposed iterative methods for solving elliptic boundary value problems approximately are based on two approaches: The fictitious space method, i.e. the reduction of the original problem to a problem in a
Multilevel preconditioning operators on locally modified grids
Systems of grid equations that approximate elliptic boundary value problems on locally modified grids are considered. The triangulation, which approximates the boundary with second order of accuracy, is generated from an initial uniform triangulation by shifting nodes near the boundary according to special rules. This "locally modified" grid possesses several significant features: this triangulation has a regular structure, the generation of the triangulation is rather fast, this construction allows to use multilevel preconditioning (BPX-like) methods. The proposed iterative methods for solving elliptic boundary value problems approximately are based on two approaches: The fictitious space method, i.e. the reduction of the original problem to a problem in an auxiliary (fictitious) space, and the multilevel decomposition method, i.e. the construction of preconditioners by decomposing functions on hierarchical grids. The convergence rate of the corresponding iterative process with the preconditioner obtained is independent of the mesh size. The construction of the grid and the preconditioning operator for the three dimensional problem can be done in the same way