2,378 research outputs found

### 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

### 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

### 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

### Discovery of parity-violating Majorana fermions in a chiral superconductor Sr2RuO4

We found parity-violating Majorana fermions in a chiral superconductor
Sr2RuO4. The current-voltage curves show an anomalous behavior: The induced
voltage is an even function of the bias current. The magnetic field dependent
results suggest the excitation of the Majorana fermions along the closed chiral
edge current of the single domain under bias current. We also discuss the
relationship between a change of the chirality and spontaneous magnetization of
the single domain Sr2RuO4

### 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

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