Topologically stable gapless phases of time-reversal invariant superconductors

We show that time-reversal invariant superconductors in d=2 (d=3) dimensions can support topologically stable Fermi points (lines), characterized by an integer topological charge. Combining this with the momentum space symmetries present, we prove analogs of the fermion doubling theorem: for d=2 lattice models admitting a spin X electron-hole structure, the number of Fermi points is a multiple of four, while for d=3, Fermi lines come in pairs. We show two implications of our findings for topological superconductors in d=3: first, we relate the bulk topological invariant to a topological number for the surface Fermi points in the form of an index theorem. Second, we show that the existence of topologically stable Fermi lines results in extended gapless regions in a generic topological superconductor phase diagram.Comment: 7 pages, 1 figure; v3: expanded versio

Black-hole horizon and metric singularity at the brane separating two sliding superfluids

An analog of black hole can be realized in the low-temperature laboratory. The horizon can be constructed for the `relativistic' ripplons (surface waves) living on the brane. The brane is represented by the interface between two superfluid liquids, 3He-A and 3He-B, sliding along each other without friction. Similar experimental arrangement has been recently used for the observation and investigation of the Kelvin-Helmholtz type of instability in superfluids (cond-mat/0111343). The shear-flow instability in superfluids is characterized by two critical velocities. The lowest threshold measured in recent experiments (cond-mat/0111343) corresponds to appearance of the ergoregion for ripplons. In the modified geometry this will give rise to the black-hole event horizon in the effective metric experienced by ripplons. In the region behind the horizon, the brane vacuum is unstable due to interaction with the higher-dimensional world of bulk superfluids. The time of the development of instability can be made very long at low temperature. This will allow us to reach and investigate the second critical velocity -- the proper Kelvin-Helmholtz instability threshold. The latter corresponds to the singularity inside the black hole, where the determinant of the effective metric becomes infinite.Comment: LaTeX file, 12 pages, 3 Figures, version accepted in JETP Letter

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

Electron dynamics in the normal state of cuprates: spectral function, Fermi surface and ARPES data

An influence of the electron-phonon interaction on excitation spectrum and damping in a narrow band electron subsystem of cuprates has been investigated. Within the framework of the t-J model an approach to solving a problem of account of both strong electron correlations and local electron-phonon binding with characteristic Einstein mode $\omega _0$ in the normal state has been presented. In approximation Hubbard-I it was found an exact solution to the polaron bands. We established that in the low-dimensional system with a pure kinematic part of Hamiltonian a complicated excitation spectrum is realized. It is determined mainly by peculiarities of the lattice Green's function. In the definite area of the electron concentration and hopping integrals a correlation gap may be possible on the Fermi level. Also, in specific cases it is observed a doping evolution of the Fermi surface. We found that the strong electron-phonon binding enforces a degree of coherence of electron-polaron excitations near the Fermi level and spectrum along the nodal direction depends on wave vector module weakly. It corresponds to ARPES data. A possible origin of the experimentally observed kink in the nodal direction of cuprates is explained by fine structure of the polaron band to be formed near the mode -$\omega _0$

Nucleon QCD sum rules in nuclear matter including radiative corrections

We calculate the nucleon parameters in nuclear matter using the QCD sum rules method. The radiative corrections to the leading operator product expansion terms are included, with the corrections of the order \alpha_s beyond the logarithmic approximation taken into account. The density dependence of the influence of radiative corrections on the nucleon parameters is obtained. At saturation density the radiative corrections increase the values of vector and scalar self-energies by about 40 MeV, and 30 MeV correspondingly. The results appear to be stable with respect to possible variations of the value of \Lambda_{QCD}.Comment: 16 pages, 2 figure