19 research outputs found
Charge modulation, spin response, and dual Hofstadter butterfly in high-Tc cuprates
The modulated density of states observed in recent STM experiments in
underdoped cuprates is argued to be a manifestation of the charge density wave
of Cooper pairs (CPCDW). CPCDW formation is due to superconducting phase
fluctuations enhanced by Mott-Hubbard correlations near half-filling. The
physics behind the CPCDW is related to a Hofstadter problem in a dual
superconductor. It is shown that CPCDW does not impact nodal fermions at the
leading order. An experiment is proposed to probe coupling of the CPCDW to the
spin carried by nodal quasiparticles.Comment: 4 pages. Streamlined introduction, corrected typos, added references.
To appear in PRL. For related work and information see cond-mat/0408344 and
visit http://www.pha.jhu.edu/people/faculty/zbt.htm
s-wave Cooper pair insulators and theory of correlated superconductors
The pseudogap state of cuprate high-temperature superconductors has been
often viewed as either a yet unknown competing order or a precursor state to
superconductivity. While awaiting the resolution of the pseudogap problem in
cuprates, we demonstrate that local pairing fluctuations, vortex liquid
dynamics and other precursor phenomena can emerge quite generally whenever
fermionic excitations remain gapped across the superconducting transition,
regardless of the gap origin. Our choice of a tractable model is a lattice band
insulator with short-range attractive interactions between fermions in the
s-wave channel. An effective crossover between Bardeen-Cooper-Schrieffer (BCS)
and Bose-Einstein condensate (BEC) regimes can be identified in any band
insulator above two dimensions, while in two dimensions only the BEC regime
exists. The superconducting transition is "unconventional" (non-pair-breaking)
in the BEC regime, identified by either the bosonic mean-field or XY
universality class. The insulator adjacent to the superconductor in the BEC
regime is a bosonic Mott insulator of Cooper pairs, which may be susceptible to
charge density wave ordering. We construct a function of the many-body
excitation spectrum whose non-analytic changes define a sharp distinction
between band and Mott insulators. The corresponding "second order transition"
can be observed out of equilibrium by driving a Cooper pair laser in the Mott
insulator. We explicitly show that the gap for charged bosonic excitations lies
below the threshold for Cooper pair breakup in any BEC regime, despite quantum
fluctuations. Our discussion ends with a view of possible consequences for
cuprates, where antinodal pair dynamics has certain features in common with our
simple s-wave picture.Comment: 18 pages, 4 figures, published versio
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
Quantum criticality of d-wave quasiparticles and superconducting phase fluctuations
We present finite temperature extension of the QED theory of underdoped
cuprates. The theory describes nodal quasiparticles whose interactions with
quantum proliferated vortex-antivortex pairs are represented by an emergent
U(1) gauge field. Finite temperature introduces a scale beyond which the long
wavelength fluctuations in the spatial components of vorticity are suppressed.
As a result, the spin susceptibility of the pseudogap state is bounded by
at low T and crosses over to at higher , while the low-
electronic specific heat scales as , reflecting the thermodynamics of
QED. The Wilson ratio vanishes as . This non-Fermi liquid behavior
originates from two general principles: spin correlations induced by ``gauge''
interactions of quasiparticles and fluctuating vortices and the
``relativistic'' scaling of the T=0 fixed point.Comment: 5 pages; published versio
Three-band superconductivity and the order parameter that breaks time-reversal symmetry
We consider a model of multiband superconductivity, inspired by iron
pnictides, in which three bands are connected via repulsive pair-scattering
terms. Generically, three distinct superconducting states arise within such a
model. Two of them are straightforward generalizations of the two-gap order
parameter while the third one corresponds to a time-reversal symmetry breaking
order parameter, altogether absent within the two-band model. Potential
observation of such a genuinely frustrated state would be a particularly vivid
manifestation of the repulsive interactions being at the root of iron-based
high temperature superconductivity. We construct the phase diagram of this
model and discuss its relevance to the iron pnictides family of high
temperature superconductors. We also study the case of the Josephson coupling
between a two-band s' (or extended s-wave) superconductor and a single-gap
s-wave superconductor, and the associated phase diagram.Comment: 9 pages, 9 figures. Added discussion and references, one new figure
(Fig. 3
Density of states of a type-II superconductor in a high magnetic field: Impurity effects
We have calculated the density of states of a dirty but
homogeneous superconductor in a high magnetic field. We assume a dilute
concentration of scalar impurities and find how behaves as one
crosses from the weak scattering to the strong scattering limit. At low
energies, for small values of the impurity
concentration and scattering strength. When the disorder becomes stronger than
some critical value, a finite density of states is created at the Fermi
surface. These results are a consequence of the gapless nature of the
quasiparticle excitation spectrum in a high magnetic field.Comment: 20 pages in RevTeX, 4 figures, to appear in Phys. Rev. B (July 1,
1997
Low-Magnetic Field Critical Behavior in Strongly Type-II Superconductors
A new description is proposed for the low-field critical behavior of type-II
superconductors. The starting point is the Ginzburg-Landau theory in presence
of an external magnetic field H. A set of fictitious vortex variables and a
singular gauge transformation are used to rewrite a finite H Ginzburg-Landau
functional in terms of a complex scalar field of zero average vorticity. The
continuum limit of the transformed problem takes the form of an H = 0
Ginzburg-Landau functional for a charged field coupled to a fictitious `gauge'
potential which arises from long wavelength fluctuations in the background
liquid of field-induced vorticity. A possibility of a novel phase transition
involving zero vorticity degrees of freedom and formation of a uniform
condensate is suggested. A similarity to the superconducting [Higgs]
electrodynamics and the nematic-smectic-A transition in liquid crystals is
noted. The experimental situation is discussed.Comment: 19 pages RevTeX, one figure available by fax [email requests to
[email protected]], to appear in Physical Review B
Critical fluctuations in superconductors and the magnetic field penetration depth
The superconducting transition is studied within the one-loop renormalization
group in fixed dimension and at the critical point. A tricritical
behavior is found, and for , an attractive charged fixed
point, distinct from that of a neutral superfluid. The critical exponents of
the continuous transition are evaluated, and it is shown that the anomalous
dimension of the gauge field equals unity. This implies the proportionality of
the magnetic field penetration depth and the superconducting correlation length
below the transition. The penetration depth exponent is nonclassical. We argue
that it can not be extracted from the dual theory in a straightforward manner
since it is not renormalized by fluctuations of the dual field.Comment: 12 pages, LaTex, two figures available upon reques
Two-Dimensional Nature of Four-Layer Superconductors by Inequivalent Hole Distribution
The magnetization of the four-layer superconductor
CuBa_{2}Ca_{3}Cu_4O_{12-\delta} with T_c\simeq117 K is presented. The
high-field magnetization around T_c(H) follows the exact two-dimensional
scaling function given by Te\v{s}anovi\'{c} and Andreev. This feature is
contrary to the inference that the interlayer coupling becomes strong if the
number of CuO_2 planes in a unit cell increases. Also, the fluctuation-induced
susceptibility in the low-field region was analyzed by using the modified
Lawrence-Doniach model. The effective number of independently fluctuating CuO_2
layers per unit cell, g_{\rm eff}, turned out to be \simeq 2 rather than 4,
which indicated that two among the four CuO_2 layers were in states far from
their optimal doping levels. This result could explain why
CuBa_{2}Ca_{3}Cu_4O_{12-\delta} shows two-dimensional behavior.Comment: 5 pages and 4 figure
3D Lowest Landau Level Theory Applied to YBCO Magnetization and Specific Heat Data: Implications for the Critical Behavior in the H-T Plane
We study the applicability of magnetization and specific heat equations
derived from a lowest-Landau-level (LLL) calculation, to the high-temperature
superconducting (HTSC) materials of the YBaCuO (YBCO)
family. We find that significant information about these materials can be
obtained from this analysis, even though the three-dimensional LLL functions
are not quite as successful in describing them as the corresponding
two-dimensional functions are in describing data for the more anisotropic HTSC
Bi- and Tl-based materials. The results discussed include scaling fits, an
alternative explanation for data claimed as evidence for a second order flux
lattice melting transition, and reasons why 3DXY scaling may have less
significance than previously believed. We also demonstrate how 3DXY scaling
does not describe the specific heat data of YBCO samples in the critical
region. Throughout the paper, the importance of checking the actual scaling
functions, not merely scaling behavior, is stressed.Comment: RevTeX; 10 double-columned pages with 7 figures embedded. (A total of
10 postscript files for the figures.) Submitted to Physical Review