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

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

Near zero modes in condensate phases of the Dirac theory on the honeycomb lattice

We investigate a number of fermionic condensate phases on the honeycomb lattice, to determine whether topological defects (vortices and edges) in these phases can support bound states with zero energy. We argue that topological zero modes bound to vortices and at edges are not only connected, but should in fact be \emph{identified}. Recently, it has been shown that the simplest s-wave superconducting state for the Dirac fermion approximation of the honeycomb lattice at precisely half filling, supports zero modes inside the cores of vortices (P. Ghaemi and F. Wilczek, 2007). We find that within the continuum Dirac theory the zero modes are not unique neither to this phase, nor to half filling. In addition, we find the \emph{exact} wavefunctions for vortex bound zero modes, as well as the complete edge state spectrum of the phases we discuss. The zero modes in all the phases we examine have even-numbered degeneracy, and as such pairs of any Majorana modes are simply equivalent to one ordinary fermion. As a result, contrary to bound state zero modes in $p_x+i p_y$ superconductors, vortices here do \emph{not} exhibit non-Abelian exchange statistics. The zero modes in the pure Dirac theory are seemingly topologically protected by the effective low energy symmetry of the theory, yet on the original honeycomb lattice model these zero modes are split, by explicit breaking of the effective low energy symmetry.Comment: Final version including numerics, accepted for publication in PR

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

Interplane and intraplane heat transport in quasi two-dimensional nodal superconductors

We analyze the behavior of the thermal conductivity in quasi-two dimensional superconductors with line nodes. Motivated by measurements of the anisotropy between the interplane and intraplane thermal transport in CeIrIn_5 we show that a simple model of the open Fermi surface with vertical line nodes is insufficient to describe the data. We propose two possible extensions of the model taking into account a) additional modulation of the gap along the axial direction of the open Fermi surface; and b) dependence of the interplane tunneling on the direction of the in-plane momentum. We discuss the temperature dependence of the thermal conductivity anisotropy and its low T limit in these two models and compare the results with a model with a horizontal line of nodes (``hybrid gap''). We discuss possible relevance of each model for the symmetry of the order parameter in CeIrIn_5, and suggest further experiments aimed at clarifying the shape of the superconducting gap.Comment: 14pages, 12 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

Macroscopic parity violating effects and 3He-A

We discuss parity violating effects in relativistic quantum theory and their analogues in effective field theory of superfluid 3He-A. A mixed axial-gravitational Chern-Simons term in the relativistic effective action and its condensed matter analog are responsible for the chiral fermion flux along the rotation axis of the heat bath in relativistic system and for the unusual Omega-odd dependence of the zero-temperature density of the normal component on the rotation velocity in 3He-A.Comment: 6 pages, RevTex file, no figures, modified after referee repor

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

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

Vacuum energy and Universe in special relativity

The problem of cosmological constant and vacuum energy is usually thought of as the subject of general relativity. However, the vacuum energy is important for the Universe even in the absence of gravity, i.e. in the case when the Newton constant G is exactly zero, G=0. We discuss the response of the vacuum energy to the perturbations of the quantum vacuum in special relativity, and find that as in general relativity the vacuum energy density is on the order of the energy density of matter. In general relativity, the dependence of the vacuum energy on the equation of state of matter does not contain G, and thus is valid in the limit when G tends to zero. However, the result obtained for the vacuum energy in the world without gravity, i.e. when G=0 exactly, is different.Comment: LaTeX file, 7 pages, no figures, to appear in JETP Letters, reference is adde