17 research outputs found
Symmetry of the charge density wave in cuprates
We derive and analyze an effective Ginzburg-Landau (GL) functional for a
charge density wave (CDW) for a model of electrons on a tight binding square
lattice with density-density interactions. We show, using realistic electronic
dispersions for the cuprates, that for the simplest GL theory, the preferred
symmetry is of the uni-directional (stripe) type, but upon inclusion of
third-order terms, the CDW may exhibit a transition from a uni-directional to a
checkerboard pattern depending on the strength and range of the interaction.Comment: 8 pages, 8 figure
Index theoretic characterization of d-wave superconductors in the vortex state
We employ index theoretic methods to study analytically the low energy
spectrum of a lattice d-wave superconductor in the vortex lattice state. This
allows us to compare singly quantized and doubly quantized
vortices, the first of which must always be accompanied by branch cuts.
For an inversion symmetric vortex lattice and in the presence of particle-hole
symmetry we prove an index theorem that imposes a lower bound on the number of
zero energy modes. Generic cases are constructed in which this bound exceeds
the number of zero modes of an equivalent lattice of doubly quantized vortices,
despite the identical point group symmetries. The quasiparticle spectrum around
the zero modes is doubly degenerate and exhibits a Dirac-like dispersion, with
velocities that become universal functions of in the limit of low
magnetic field. For weak particle-hole symmetry breaking, the gapped state can
be characterized by a topological quantum number, related to spin Hall
conductivity, which generally differs in the cases of the and
vortex lattices.Comment: 4 pages, 2 figures, 1 table (accepted for publication in PRL;
substantially rewritten for presentation clarity; references to quantum order
and visons omitted on referee's demand
Mixed state of a lattice d-wave superconductor
We study the mixed state in an extreme type-II lattice d-wave superconductor
in the regime of intermediate magnetic fields H_{c1} << H << H_{c2}. We analyze
the low energy spectrum of the problem dominated by nodal Dirac-like
quasiparticles with momenta near k_F=(\pm k_D,\pm k_D) and find that the
spectrum exhibits characteristic oscillatory behavior with respect to the
product of k_D and magnetic length l. The Simon-Lee scaling, predicted in this
regime, is satisfied only on average, with the magnitude of the oscillatory
part of the spectrum displaying the same 1/l dependence as its monotonous
``envelope'' part. The oscillatory behavior of the spectrum is due to the
inter-nodal interference enhanced by the singular nature of the low energy
eigenfunctions near vortices. We also study a separate problem of a single
vortex piercing an isolated superconducting grain of size L by L. Here we find
that the periodicity of the quasiparticle energy oscillations with respect to
k_D L is doubled relative to the case where the field is zero and the vortex is
absent, both such oscillatory behaviors being present at the leading order in
1/L. Finally, we review the overall features of the tunneling conductance
experiments in YBCO and BSCCO, and suggest an interpretation of the peaks at
5-20 meV observed in the tunneling local density of states in these materials.Comment: 16 pages, 11 figure
Dopant-modulated pair interaction in cuprate superconductors
Comparison of recent experimental STM data with single-impurity and
many-impurity Bogoliubov-de Gennes calculations strongly suggests that random
out-of-plane dopant atoms in cuprates modulate the pair interaction locally.
This type of disorder is crucial to understanding the nanoscale electronic
structure inhomogeneity observed in BSCCO-2212, and can reproduce observed
correlations between the positions of impurity atoms and various aspects of the
local density of states such as the gap magnitude and the height of the
coherence peaks. Our results imply that each dopant atom modulates the pair
interaction on a length scale of order one lattice constant.Comment: 5 pages, 4 figure
Andreev states near short-ranged pairing potential impurities
We study Andreev states near atomic scale modulations in the pairing
potential in both - and d-wave superconductors with short coherence lengths.
For a moderate reduction of the local gap, the states exist only close to the
gap edge. If one allows for local sign changes of the order parameter, however,
resonances can occur at energies close to the Fermi level. The local density of
states (LDOS) around such pairing potential defects strongly resembles the
patterns observed by tunneling measurements around Zn impurities in
BiSrCaCuO (BSCCO). We discuss how this phase impurity model
of the Zn LDOS pattern can be distinguished from other proposals
experimentally.Comment: 4 pages, 4 figure
Thermodynamic transitions in inhomogeneous d-wave superconductors
We study the spectral and thermodynamic properties of inhomogeneous d-wave
superconductors within a model where the inhomogeneity originates from atomic
scale pair disorder. This assumption has been shown to be consistent with the
small charge and large gap modulations observed by scanning tunnelling
spectroscopy (STS) on BSCCO. Here we calculate the specific heat within the
same model, and show that it gives a semi-quantitative description of the
transition width in this material. This model therefore provides a consistent
picture of both surface sensitive spectroscopy and bulk thermodynamic
properties.Comment: 4 pages, 4 figure
Fourier transform spectroscopy of d-wave quasiparticles in the presence of atomic scale pairing disorder
The local density of states power spectrum of optimally doped
BiSrCaCuO (BSCCO) has been interpreted in terms of
quasiparticle interference peaks corresponding to an "octet'' of scattering
wave vectors connecting k-points where the density of states is maximal. Until
now, theoretical treatments have not been able to reproduce the experimentally
observed weights and widths of these "octet'' peaks; in particular, the
predominance of the dispersing "q'' peak parallel to the Cu-O bond
directions has remained a mystery. In addition, such theories predict
"background'' features which are not observed experimentally. Here, we show
that most of the discrepancies can be resolved when a realistic model for the
out-of-plane disorder in BSCCO is used. Weak extended potential scatterers,
which are assumed to represent cation disorder, suppress large-momentum
features and broaden the low-energy "q''-peaks, whereas scattering at order
parameter variations, possibly caused by a dopant-modulated pair interaction
around interstitial oxygens, strongly enhances the dispersing "q''-peaks.Comment: 7 pages, 3 figure
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The genetic history of the Southern Arc: a bridge between West Asia and Europe
By sequencing 727 ancient individuals from the Southern Arc (Anatolia and its neighbors in Southeastern Europe and West Asia) over 10,000 years, we contextualize its Chalcolithic period and Bronze Age (about 5000 to 1000 BCE), when extensive gene flow entangled it with the Eurasian steppe. Two streams of migration transmitted Caucasus and Anatolian/Levantine ancestry northward, and the Yamnaya pastoralists, formed on the steppe, then spread southward into the Balkans and across the Caucasus into Armenia, where they left numerous patrilineal descendants. Anatolia was transformed by intra–West Asian gene flow, with negligible impact of the later Yamnaya migrations. This contrasts with all other regions where Indo-European languages were spoken, suggesting that the homeland of the Indo-Anatolian language family was in West Asia, with only secondary dispersals of non-Anatolian Indo-Europeans from the steppe
Pattern-Based Approach to Current Density Verification
Methodology of static verification of current density based on layout patterns common in IC designs is proposed. The methodology is based on pre-calculation of current density distribution for common layout patterns. Then using the obtained data to calculate current densities of large circuits by partitioning them to selected patterns. Presented experimental results show the effectiveness of the approach