749 research outputs found
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
Hopf Term for a Two-Dimensional Electron Gas
In this Comment on the paper by W. Apel and Yu. A. Bychkov, cond-mat/9610040
and Phys. Rev. Lett. 78, 2188 (1997), we draw attention to our prior
microscopic derivations of the Hopf term for various systems and to
shortcomings of the Apel-Bychkov derivation. We explain how the value of the
Hopt term prefactor is expressed in terms of a topological invariant
in the momentum space and the quantized Hall conductivity of the system. (See
also related paper cond-mat/9703195)Comment: RevTeX, 1 page, no figure
Glass state of superfluid 3He-A in aerogel
Glass states formed in the superfluid He confined in aerogel are
discussed. If the short range order corresponds to the A-phase state, the glass
state is nonsuperfluid in the long wave length limit. The superfluidity can be
restored by application of a small mass current. Transitions between the
superfluid and nonsuperfluid glass states can be triggered by small magnetic
field and by the change of the tipping angle of magnetization in NMR
experiments.Comment: 6 pages, LaTeX file, no figures, submitted to JETP Letter
Random anisotropy disorder in superfluid 3He-A in aerogel
The anisotropic superfluid 3He-A in aerogel provides an interesting example
of a system with continuous symmetry in the presence of random anisotropy
disorder. Recent NMR experiments allow us to discuss two regimes of the
orientational disorder, which have different NMR properties. One of them, the
(s)-state, is identified as the pure Larkin-Imry-Ma state. The structure of
another state, the (f)-state, is not very clear: probably it is the
Larkin-Imry-Ma state contaminated by the network of the topological defects
pinned by aerogel.Comment: JETP Lett. style, 6 pages, no figures, discussion extended,
references added, version to be published in JETP Letter
Non-abelian statistics of half-quantum vortices in p-wave superconductors
Excitation spectrum of a half-quantum vortex in a p-wave superconductor
contains a zero-energy Majorana fermion. This results in a degeneracy of the
ground state of the system of several vortices. From the properties of the
solutions to Bogoliubov-de-Gennes equations in the vortex core we derive the
non-abelian statistics of vortices identical to that for the Moore-Read
(Pfaffian) quantum Hall state.Comment: 5 pages, 3 figures, REVTeX, epsf. Reference adde
Merging gauge coupling constants without Grand Unification
The merging of the running couplings constants of the weak, strong, and
electromagnetic fields does not require the unification of these gauge fields
at high energy. It can, in fact, be the property of a general fermionic system
in which gauge bosons are not fundamental.Comment: 11 pages, 1 figure, v3: to appear in JETP Letter
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 He-B, 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) of the bosonic excitations in each channel
with the mass (energy gap) of the condensed fermion as . Previously this relation was established by Nambu in \cite{Nambu}
for 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
Topological superfluid 3He-B in magnetic field and Ising variable
The topological superfluid 3He-B provides many examples of the interplay of
symmetry and topology. Here we consider the effect of magnetic field on
topological properties of 3He-B. Magnetic field violates the time reversal
symmetry. As a result, the topological invariant supported by this symmetry
ceases to exist; and thus the gapless fermions on the surface of 3He-B are not
protected any more by topology: they become fully gapped. Nevertheless, if
perturbation of symmetry is small, the surface fermions remain relativistic
with mass proportional to symmetry violating perturbation -- magnetic field.
The 3He-B symmetry gives rise to the Ising variable I=+/- 1, which emerges in
magnetic field and which characterizes the states of the surface of 3He-B. This
variable also determines the sign of the mass term of surface fermions and the
topological invariant describing their effective Hamiltonian. The line on the
surface, which separates the surface domains with different I, contains 1+1
gapless fermions, which are protected by combined action of symmetry and
topology.Comment: 5 pages, JETP Letters style, no figures, version submitted to JETP
Letter
Spontaneous mass current and textures of p-wave superfluids of trapped Fermionic atom gases at rest and under rotation
It is found theoretically based on the Ginzburg-Landau framework that p-wave
superfluids of neutral atom gases in three dimension harmonic traps exhibit
spontaneous mass current at rest, whose direction depends on trap geometry.
Under rotation various types of the order parameter textures are stabilized,
including Mermin-Ho and Anderson-Toulouse-Chechetkin vortices. In a cigar shape
trap spontaneous current flows longitudial to the rotation axis and thus
perpendicular to the ordinary rotational current. These features, spontaneous
mass current at rest and texture formation, can be used as diagnoses for p-wave
superfluidity.Comment: 5 pages, 5 figure
Phase slip phenomena in superconductors: from ordered to chaotic dynamics
We consider flux penetration to a 2D superconducting cylinder. We show that
in the low field limit the kinetics is deterministic. In the strong field limit
the dynamics becomes stochastic. Surprisingly the inhomogeneity in the cylinder
reduces the level of stochasticity because of the predominance of
Kelvin-Helmholtz vortices.Comment: 4 pages, 3 figures (main text) and 1 page, 1 figure (supplementary
material
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