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

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

Small digital recording head has parallel bit channels, minimizes cross talk

A small digital recording head consists of closely spaced parallel wires, imbedded in a ferrite block to concentrate the magnetic flux. Parallel-recorded information bits are converted into serial bits on moving magnetic tape and cross talk is suppressed

Superconducting Plate in Transverse Magnetic Field: New State

A model to describe Cooper pairs near the transition point (on temperature and magnetic field), when the distance between them is big compared to their sizes, is proposed. A superconducting plate whose thickness is less than the pair size in the transverse magnetic field near the critical value $H_{c2}$ is considered as an application of the model. A new state that is energetically more favourable than that of Abrikosov vortex state within an interval near the transition point was obtained. The system's wave function in this state looks like that of Laughlin's having been used in fractional quantum Hall effect (naturally, in our case - for Cooper pairs as Bose-particles) and it corresponds to homogeneous incompressible liquid. The state energy is proportional to the first power of value $(1 - H/H_{c2})$, unlike the vortex state energy having this value squared. The interval of the new state existence is greater for dirty specimens.Comment: 7 page

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

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

Structure and consequences of vortex-core states in p-wave superfluids

It is now well established that in two-dimensional chiral p-wave paired superfluids, the vortices carry zero-energy modes which obey non-abelian exchange statistics and can potentially be used for topological quantum computation. In such superfluids there may also exist other excitations below the bulk gap inside the cores of vortices. We study the properties of these subgap states, and argue that their presence affects the topological protection of the zero modes. In conventional superconductors where the chemical potential is of the order of the Fermi energy of a non-interacting Fermi gas, there is a large number of subgap states and the mini-gap towards the lowest of these states is a small fraction of the Fermi energy. It is therefore difficult to cool the system to below the mini-gap and at experimentally available temperatures, transitions between the subgap states, including the zero modes, will occur and can alter the quantum states of the zero-modes. We show that compound qubits involving the zero-modes and the parity of the occupation number of the subgap states on each vortex are still well defined. However, practical schemes taking into account all subgap states would nonetheless be difficult to achieve. We propose to avoid this difficulty by working in the regime of small chemical potential mu, near the transition to a strongly paired phase, where the number of subgap states is reduced. We develop the theory to describe this regime of strong pairing interactions and we show how the subgap states are ultimately absorbed into the bulk gap. Since the bulk gap vanishes as mu -> 0 there is an optimum value mu_c which maximises the combined gap. We propose cold atomic gases as candidate systems where the regime of strong interactions can be explored, and explicitly evaluate mu_c in a Feshbach resonant K-40 gas.Comment: 19 pages, 10 figures; v2: main text as published version, additional detail included as appendice

Tailoring the ground state of the ferrimagnet La2Ni(Ni1/3Sb2/3)O6

We report on the magnetic and structural properties of La2Ni(Ni1/3Sb2/3)O6 in polycrystal, single crystal and thin film samples. We found that this material is a ferrimagnet (Tc ~ 100 K) which possesses a very distinctive and uncommon feature in its virgin curve of the hysteresis loops. We observe that bellow 20 K it lies outside the hysteresis cycle, and this feature was found to be an indication of a microscopically irreversible process possibly involving the interplay of competing antiferromagnetic interactions that hinder the initial movement of domain walls. This initial magnetic state is overcome by applying a temperature dependent characteristic field. Above this field, an isothermal magnetic demagnetization of the samples yield a ground state different from the initial thermally demagnetized one.Comment: 21 pages, 8 figures, submitted to JMM

Local properties of patterned vegetation: quantifying endogenous and exogenous effects

Dryland ecosystems commonly exhibit periodic bands of vegetation, thought to form due to competition between individual plants for heterogeneously distributed water. In this paper, we develop a Fourier method for locally identifying the pattern wavenumber and orientation, and apply it to aerial images from a region of vegetation patterning near Fort Stockton, Texas. We find that the local pattern wavelength and orientation are typically coherent, but exhibit both rapid and gradual variation driven by changes in hillslope gradient and orientation, the potential for water accumulation, or soil type. Endogenous pattern dynamics, when simulated for spatially homogeneous topographic and vegetation conditions, predict pattern properties that are much less variable than the orientation and wavelength observed in natural systems. Our local pattern analysis, combined with ancillary datasets describing soil and topographic variation, highlights a largely unexplored correlation between soil depth, pattern coherence, vegetation cover and pattern wavelength. It also, surprisingly, suggests that downslope accumulation of water may play a role in changing vegetation pattern properties