Knots in a Spinor Bose-Einstein Condensate

We show that knots of spin textures can be created in the polar phase of a spin-1 Bose-Einstein condensate, and discuss experimental schemes for their generation and probe, together with their lifetime.Comment: 4 pages, 3 figure

Birman-Schwinger and the number of Andreev states in BCS superconductors

The number of bound states due to inhomogeneities in a BCS superconductor is usually established either by variational means or via exact solutions of particularly simple, symmetric perturbations. Here we propose estimating the number of sub-gap states using the Birman-Schwinger principle. We show how to obtain upper bounds on the number of sub-gap states for small normal regions and derive a suitable Cwikel-Lieb-Rozenblum inequality. We also estimate the number of such states for large normal regions using high dimensional generalizations of the Szego theorem. The method works equally well for local inhomogeneities of the order parameter and for external potentials.Comment: Final version to appear in Phys Rev

Conductance enhancement due to the resonant tunneling into the subgap vortex core states in normal metal/superconductor ballistic junctions

We investigate the low-energy quantum transport in the ballistic normal metal-insulator -superconductor junction in the presence of magnetic field creating Abrikosov vortices in the superconductor. Within the Bogolubov- de Gennes theory we show that the presence of the subgap quasiparticle states localized within the vortex cores near the junction interface leads to the strong resonant enhancement of the Andreev reflection probability, and the normal-to supercurrent conversion. The corresponding increase of the charge conductance of the junction is determined by the distance from the vortex chain to the junction interface, which can be controlled by the applied magnetic field. The effect that we study provides a tool for probing the vortex core states by the measurements of charge transport across the applied magnetic field.Comment: 8 pages, 3 figure

Nodal Structure of Superconductors with Time-Reversal Invariance and Z2 Topological Number

A topological argument is presented for nodal structures of superconducting states with time-reversal invariance. A generic Hamiltonian which describes a quasiparticle in superconducting states with time-reversal invariance is derived, and it is shown that only line nodes are topologically stable in single-band descriptions of superconductivity. Using the time-reversal symmetry, we introduce a real structure and define topological numbers of line nodes. Stability of line nodes is ensured by conservation of the topological numbers. Line nodes in high-Tc materials, the polar state in p-wave paring and mixed singlet-triplet superconducting states are examined in detail.Comment: 11 pages, 8 figure

Coexistence of different vacua in the effective quantum field theory and Multiple Point Principle

According to the Multiple Point Principle our Universe is on the coexistence curve of two or more phases of the quantum vacuum. The coexistence of different quantum vacua can be regulated by the exchange of the global fermionic charges between the vacua, such as baryonic, leptonic or family charge. If the coexistence is regulated by the baryonic charge, all the coexisting vacua exhibit the baryonic asymmetry. Due to the exchange of the baryonic charge between the vacuum and matter which occurs above the electroweak transition, the baryonic asymmetry of the vacuum induces the baryonic asymmetry of matter in our Standard-Model phase of the quantum vacuum. The present baryonic asymmetry of the Universe indicates that the characteristic energy scale which regulates the equilibrium coexistence of different phases of quantum vacua is about 10^6 GeV.Comment: 12 pages, 1 figure, modified version submitted to JETP letter

Fermions on half-quantum vortex

The spectrum of the fermion zero modes in the vicinity of the vortex with fractional winding number is discussed. This is inspired by the observation of the 1/2 vortex in high-temperature superconductors (Kirtley, et al, Phys. Rev. Lett. 76 (1996) 1336). The fractional value of the winding number leads to the fractional value of the invariant, which describes the topology of the energy spectrum of fermions. This results in the phenomenon of the "half-crossing": the spectrum approaches zero but does not cross it, being captured at the zero energy level. The similarity with the phenomenon of the fermion condensation is discussed.Comment: In revised version the discussion is extended and 4 references are added. The paper is accepted for publication in JETP Letters. 10 pages, LaTeX file, 3 figures are available at ftp://boojum.hut.fi/pub/publications/lowtemp/LTL-96004.p

Spin-Hall effect in triplet chiral superconductors and graphene

We study spin-Hall effects in time-reversal symmetry (TRS) broken systems such as triplet chiral superconductors and TRS preserved ones such as graphene. For chiral triplet superconductors, we show that the edge states carry a quantized spin-Hall current in response to an applied Zeeman magnetic field $B$ along the ${\bf d}$ vector \cite{leggett1}, whereas the edge spin-current for ${\bf B} \perp {\bf d}$ is screened by the condensate. We also derive the bulk spin-Hall current for chiral triplet superconductors for arbitrary relative orientation of ${\bf B}$ and ${\bf d}$ and discuss its relation with the edge spin-current. For TRS invariant system graphene, we show that the bulk effective action, unlike its TRS broken counterparts, does not support a SU(2) Hopf term but allows a crossed Hopf term in the presence of an external electromagnetic field, which yields a quantized bulk spin-Hall current in response to an electric field. We also present an analytical solution of the edge problem for armchair edges of graphene and contrast the properties of these edge states with their time reversal symmetry broken counterparts in chiral superconductors. We propose possible experiments to test our results.Comment: v2; minor changes, additional ref

Magnetic resonance within vortex cores in the B phase of superfluid 3^3He

We investigate a magnetic susceptibility of vortices in the B phase of multicomponent triplet superfluid $^3$He focusing on a contribution of bound fermionic states localized within vortex cores. Several order parameter configurations relevant to different types of quantized vortices in $^3$He B are considered. It is shown quite generally that an ac magnetic susceptibility has a sharp peak at the frequency corresponding to the energy of interlevel spacing in the spectrum of bound fermions. We suggest that measuring of a magnetic resonance within vortex cores can provide a direct probe of a discrete spectrum of bound vortex core excitations

Gravity of Monopole and String and Gravitational Constant in 3He-A

We discuss the effective metric produced in superfluid 3He-A by such topological objects as radial disgyration and monopole. In relativistic theories these metrics are similar to that of the local string and global monopole correspondingly. But in 3He-A they have the negative angle deficit, which corresponds to the negative mass of the topological objects. The effective gravitational constant G in superfluid 3He-A, derived from the comparison with relativistic theories, is inversely proportional to the square of the gap amplitude Delta, which plays the part of the Planck energy cut-off. G depends on temperature and increases with T, which corresponds to the vacuum screening of the Newton's constant.Comment: Latex file, 10 pages, no figure

The Nambu sum rule and the relation between the masses of composite Higgs bosons

We review the known results on the bosonic spectrum in various NJL models both in the condensed matter physics and in relativistic quantum field theory including $^3$He-B, $^3$He-A, the thin films of superfluid He-3, and QCD (Hadronic phase and the Color Flavor Locking phase). Next, we calculate bosonic spectrum in the relativistic model of top quark condensation suggested in \cite{Miransky}. In all considered cases the sum rule appears that relates the masses (energy gaps) $M_{boson}$ of the bosonic excitations in each channel with the mass (energy gap) of the condensed fermion $M_f$ as $\sum M_{boson}^2 = 4 M_f^2$. Previously this relation was established by Nambu in \cite{Nambu} for $^3$He-B and for the s - wave superconductor. We generalize this relation to the wider class of models and call it the Nambu sum rule. We discuss the possibility to apply this sum rule to various models of top quark condensation. In some cases this rule allows to calculate the masses of extra Higgs bosons that are the Nambu partners of the 125 GeV Higgs.Comment: Latex, 15 page