1,048 research outputs found
Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry
We study topological phases of time-reversal invariant singlet
superconductors in three spatial dimensions. In these particle-hole symmetric
systems the topological phases are characterized by an even-numbered winding
number . At a two-dimensional (2D) surface the topological properties of
this quantum state manifest themselves through the presence of flavors of
gapless Dirac fermion surface states, which are robust against localization
from random impurities. We construct a tight-binding model on the diamond
lattice that realizes a topologically nontrivial phase, in which the winding
number takes the value . Disorder corresponds to a (non-localizing)
random SU(2) gauge potential for the surface Dirac fermions, leading to a
power-law density of states . The bulk
effective field theory is proposed to be the (3+1) dimensional SU(2) Yang-Mills
theory with a theta-term at .Comment: 5 pages, 3 figure
Momentum space metric, non-local operator, and topological insulators
Momentum space of a gapped quantum system is a metric space: it admits a
notion of distance reflecting properties of its quantum ground state. By using
this quantum metric, we investigate geometric properties of momentum space. In
particular, we introduce a non-local operator which represents distance square
in real space and show that this corresponds to the Laplacian in curved
momentum space, and also derive its path integral representation in momentum
space. The quantum metric itself measures the second cumulant of the position
operator in real space, much like the Berry gauge potential measures the first
cumulant or the electric polarization in real space. By using the non-local
operator and the metric, we study some aspects of topological phases such as
topological invariants, the cumulants and topological phase transitions. The
effect of interactions to the momentum space geometry is also discussed.Comment: 13 pages, 4 figure
Fermion zero modes at the boundary of superfluid 3He-B
Superfluid 3He-B belongs to the important special class of time-reversal
invariant topological superfluids. It has Majorana fermions as edge states on
the surface of bulk 3He-B. On the rough wall these fermion zero modes have
finite density of states at E=0. It is possible that Lancaster experiments with
a wire vibrating in 3He-B have already probed Majorana fermions living on the
surface of the wire.Comment: 4 pages, no Figures, JETP Letters style, version to be published in
JETP Letter
Quasiparticle interference from different impurities on the surface of pyrochlore iridates: signatures of the Weyl phase
Weyl semimetals are gapless three-dimensional topological materials where two
bands touch at an even number of points in the bulk Brillouin zone. These
semimetals exhibit topologically protected surface Fermi arcs, which pairwise
connect the projected bulk band touchings in the surface Brillouin zone. Here,
we analyze the quasiparticle interference patterns of the Weyl phase when
time-reversal symmetry is explicitly broken. We use a multi-band -electron
Hubbard Hamiltonian on a pyrochlore lattice, relevant for the pyrochlore
iridate RIrO (where R is a rare earth). Using exact
diagonalization, we compute the surface spectrum and quasiparticle interference
(QPI) patterns for various surface terminations and impurities. We show that
the spin and orbital texture of the surface states can be inferred from the
absence of certain backscattering processes and from the symmetries of the QPI
features for non-magnetic and magnetic impurities. Furthermore, we show that
the QPI patterns of the Weyl phase in pyrochlore iridates may exhibit
additional interesting features that go beyond those found previously in TaAs.Comment: 15 pages, 16 figure
Screening in (d+s)-wave superconductors: Application to Raman scattering
We study the polarization-dependent electronic Raman response of untwinned
YBaCuO superconductors employing a tight-binding band
structure with anisotropic hopping matrix parameters and a superconducting gap
with a mixing of - and s-wave symmetry. Using general arguments we find
screening terms in the B^{\}_{1g} scattering channel which are required by
gauge invariance. As a result, we obtain a small but measurable softening of
the pair-breaking peak, whose position has been attributed for a long time to
twice the superconducting gap maximum. Furthermore, we predict
superconductivity-induced changes in the phonon line shapes that could provide
a way to detect the isotropic s-wave admixture to the superconducting gap.Comment: typos corrected, 6 pages, 3 figure
Influence of higher d-wave gap harmonics on the dynamical magnetic susceptibility of high-temperature superconductors
Using a fermiology approach to the computation of the magnetic susceptibility
measured by neutron scattering in hole-doped high-Tc superconductors, we
estimate the effects on the incommensurate peaks caused by higher d-wave
harmonics of the superconducting order parameter induced by underdoping. The
input parameters for the Fermi surface and d-wave gap are taken directly from
angle resolved photoemission (ARPES) experiments on Bi{2}Sr{2}CaCu{2}O{8+x}
(Bi2212). We find that higher d-wave harmonics lower the momentum dependent
spin gap at the incommensurate peaks as measured by the lowest spectral edge of
the imaginary part in the frequency dependence of the magnetic susceptibility
of Bi2212. This effect is robust whenever the fermiology approach captures the
physics of high-Tc superconductors. At energies above the resonance we observe
diagonal incommensurate peaks. We show that the crossover from parallel
incommensuration below the resonance energy to diagonal incommensuration above
it is connected to the values and the degeneracies of the minima of the
2-particle energy continuum.Comment: 13 pages, 7 figure
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