Topological invariants for spin-orbit coupled superconductor nanowires

We show that a spin-orbit coupled semiconductor nanowire with Zeeman splitting and s-wave superconductivity is in symmetry class BDI (not D as is commonly thought) of the topological classification of band Hamiltonians. The class BDI allows for an integer Z topological invariant equal to the number of Majorana fermion (MF) modes at each end of the quantum wire protected by the chirality symmetry (reality of the Hamiltonian). Thus it is possible for this system (and all other d=1 models related to it by symmetry) to have an arbitrary integer number, not just 0 or 1 as is commonly assumed, of MFs localized at each end of the wire. The integer counting the number of MFs at each end reduces to 0 or 1, and the class BDI reduces to D, in the presence of terms in the Hamiltonian that break the chirality symmetry.Comment: 4+ pages, no figure

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

Reentrant violation of special relativity in the low-energy corner

In the effective relativistic quantum field theories the energy region, where the special relativity holds, can be sandwiched from both the high and low energies sides by domains where the special relativity is violated. An example is provided by 3He-A where the relativistic quantum field theory emerges as the effective theory. The reentrant violation of the special relativity in the ultralow energy corner is accompanied by the redistribution of the momentum-space topological charges between the fermionic flavors. At this ultralow energy an exotic massless fermion with the topological charge $N_3=2$ arises, whose energy spectrum mixes the classical and relativistic behavior. This effect can lead to neutrino oscillations if neutrino flavors are still massless at this energy scale.Comment: RevTeX file, 5 pages, one figure, submitted to JETP Let

Single particle Green's functions and interacting topological insulators

We study topological insulators characterized by the integer topological invariant Z, in even and odd spacial dimensions. These are well understood in case when there are no interactions. We extend the earlier work on this subject to construct their topological invariants in terms of their Green's functions. In this form, they can be used even if there are interactions. Specializing to one and two spacial dimensions, we further show that if two topologically distinct topological insulators border each other, the difference of their topological invariants is equal to the difference between the number of zero energy boundary excitations and the number of zeroes of the Green's function at the boundary. In the absence of interactions Green's functions have no zeroes thus there are always edge states at the boundary, as is well known. In the presence of interactions, in principle Green's functions could have zeroes. In that case, there could be no edge states at the boundary of two topological insulators with different topological invariants. This may provide an alternative explanation to the recent results on one dimensional interacting topological insulators.Comment: 16 pages, 2 figure

Local density of states of a strongly type-II d-wave superconductor: The binary alloy model in a magnetic field

We calculate self-consistently the local density of states (LDOS) of a d-wave superconductor considering the scattering of the quasiparticles off randomly distributed impurities and off externally induced vortices. The impurities and the vortices are randomly distributed but the vortices are preferably located near the impurities. The increase of either the impurity repulsive potential or the mpurity density only affects the density of states (DOS) slightly. The dominant effect is due to the vortex scattering. The results for the LDOS agree qualitatively with experimental results considering that most vortices are pinned at the impurities.Comment: To be published in Physical Review

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

On thermodynamic and quantum fluctuations of cosmological constant

We discuss from the condensed-matter point of view the recent idea that the Poisson fluctuations of cosmological constant about zero could be a source of the observed dark energy. We argue that the thermodynamic fluctuations of Lambda are much bigger. Since the amplitude of fluctuations is proportional to V^{-1/2}, where V is the volume of the Universe, the present constraint on the cosmological constant provides the lower limit for V, which is much bigger than the volume within the cosmological horizon.Comment: 4 pages, version submitted to JETP Letter

Stability of half quantum vortex in rotating superfluid 3He-A between parallel plates

We have found the precise stability region of the half quantum vortex (HQV) for superfluid $^3$He A phase confined in parallel plates with a narrow gap under rotation. Standard Ginzburg-Landau free energy, which is well established, is solved to locate the stability region spanned by temperature $T$ and rotation speed ($/Omega$). This $/Omega$-$T$ stability region is wide enough to check it experimentally in available experimental setup. The detailed order parameter structure of HQV characterized by A$_1$ core is given to facilitate the physical reasons of its stability over other vortices or textures.Comment: 5 pages, 4 figure

Detecting the Majorana fermion surface state of 3^3He-B through spin relaxation

The concept of the Majorana fermion has been postulated more than eighty years ago; however, this elusive particle has never been observed in nature. The non-local character of the Majorana fermion can be useful for topological quantum computation. Recently, it has been shown that the 3He-B phase is a time-reversal invariant topological superfluid, with a single component of gapless Majorana fermion state localized on the surface. Such a Majorana surface state contains half the degrees of freedom of the single Dirac surface state recently observed in topological insulators. We show here that the Majorana surface state can be detected through an electron spin relaxation experiment. The Majorana nature of the surface state can be revealed though the striking angular dependence of the relaxation time on the magnetic field direction, $1/T_1 \propto sin^2 \theta$ where $\theta$ is the angle between the magnetic field and the surface normal. The temperature dependence of the spin relaxation rate can reveal the gapless linear dispersion of the Majorana surface state. We propose a spin relaxation experiment setup where we inject an electron inside a nano-sized bubble below the helium liquid surface.Comment: 6 pages, 2 figures; reformatted with reference adde