A novel approach to cuprate SC ?

Here is a seemingly very interesting paper recently published in PRX. It contains an exotic treatment of the superconducting gap (not the pseudogap) in LSCO.

A generic theory of the quasiparticle superconducting gap in underdoped cuprates is derived in the strong-coupling limit, and found to describe the experimental ‘‘second gap’’ in absolute scale. In drastic contrast to the standard pairing gap associated with Bogoliubov quasiparticle excitations, the quasiparticle gap is shown to originate from anomalous kinetic (scattering) processes, with a size unrelated to the
pairing strength. Consequently, the k dependence of the gap deviates significantly from the pure dx2 y2 wave of the order parameter. Our study reveals a new paradigm for the nature of the superconducting gap, and is expected to reconcile numerous apparent contradictions among existing experiments and point
toward a more coherent understanding of high-temperature superconductivity.

Two pieces of work on cuprates

Just to highlight them here, because they seemingly represent something defying the cliche.
1. Electron-spin excitation coupling in an electron-doped copper oxide superconductor [Nphy, 7:719(2011)]

High-temperature (high-Tc) superconductivity in the copper oxides arises from electron or hole doping of their antiferromagnetic (AF) insulating parent compounds. The evolution of the AF phase with doping and its spatial coexistence with superconductivity are governed by the nature of charge and spin correlations, which provides clues to the mechanism of high-Tc superconductivity. Here we use neutron scattering and scanning tunnelling spectroscopy (STS) to study the evolution of the bosonic excitations in electron-doped superconductor Pr0:88LaCe0:12CuO4􀀀 with different transition temperatures (Tc) obtained through the oxygen annealing process.We find that spin excitations detected by neutron scattering have two distinct modes that evolve with Tc in a remarkably similar fashion to the low-energy electron tunnelling modes detected by STS. These results demonstrate that antiferromagnetism and superconductivity compete locally and coexist spatially on nanometre length scales, and the dominant electron–boson coupling at low energies originates from the electron-spin excitations.

2. Intense paramagnon excitations in a large family of high-temperature superconductors [Nphy 7:725(2011)]

In the search for the mechanism of high-temperature superconductivity, intense research has been focused on the evolution of the spin excitation spectrum on doping from the antiferromagnetic insulating to the superconducting state of the cuprates. Because of technical limitations, the experimental investigation of doped cuprates has been largely focused on low-energy excitations in a small range of momentum space. Here we use resonant inelastic X-ray scattering to show that a large family of superconductors, encompassing underdoped YBa2Cu4O8 and overdoped YBa2Cu3O7, exhibits damped spin excitations (paramagnons) with dispersions and spectral weights closely similar to those of magnons in undoped cuprates. The comprehensive experimental description of this surprisingly simple spectrum enables quantitative tests of magnetic Cooper pairing models. A numerical solution of the Eliashberg equations for the magnetic spectrum of YBa2Cu3O7 reproduces its superconducting transition temperature within a factor of two, a level of agreement comparable to that of Eliashberg theories of conventional superconductors.

New clue toward paramagnons as the glue

Certainly lots of doubts are over the magnetic fluctuations as the paring source of carriers in cuprate superconductors. A central issues concerns if there is sufficient paramagnons in the Sc region, since experiments have so far detected only a limited volume of such stuff. Now this gets changed due to this work [Nature Phys. 7, 725–730 (2011). ] reviewed below [http://www.nature.com/nphys/journal/v7/n9/full/nphys2077.html?WT.ec_id=NPHYS-201109]:

However, the observed excitations were restricted to a narrow window in both energy and momentum and furthermore carried relatively little spectral weight, posing a challenge to theoretical ideas about magnetic fluctuations being the source of Cooper pairing in these superconductors. Some researchers have suggested that the experimental limitations inherent in neutron scattering were partially responsible for this state of affairs — and only now has a breakthrough occurred.

In Nature Physics, Le Tacon and colleagues² report the application to various copper oxides of an alternative technique to map magnetic excitations: resonant inelastic X-ray scattering (RIXS)³. Here, an electron is transferred, by a high-energy photon, from a deep core level into an unoccupied low-energy state; subsequently, an electron from a different low-energy state fills the core hole and emits a high-energy photon. Thus, a net excitation is generated in a low-energy band, the energy and momentum of which can be measured by examining the scattered photon.

Among the advantages of RIXS, compared with neutron scattering, is the large cross-section for the scattering of photons (which eliminates the need for large samples) and the possibility to probe essentially the entire Brillouin zone. There are disadvantages as well: in contrast to neutron scattering, the cross-section is not simply related to a dynamic susceptibility, which complicates the data analysis, and the energy resolution is at present limited to about 100 meV (it's far below 1 meV in state-of-the-art neutron-scattering experiments). Despite these limitations, the past decade has seen exciting progress in RIXS³ such that investigations of elementary spin excitations have now become feasible.

Le Tacon et al.² have investigated magnetic excitations using RIXS in a family of copper-oxide materials, covering a range of hole dopings from the undoped insulator to the slightly overdoped superconductor. In all doped materials, they identified damped spin excitations with high intensity over a large part of momentum space. These excitations, in both their overall dispersion and their intensity, seem to show surprisingly little variation with doping.

These findings are important for a number of reasons. First, together with similar recent experiments^{3, 4, 5}, they establish RIXS as a powerful tool for the investigation of complex correlated-electron materials. Second, they show that previous neutron-scattering studies have indeed missed a significant part of the spectral weight of spin fluctuations in copper oxides. This implies that theories of electron pairing based on the exchange of magnetic fluctuations can be considered on safer ground. In fact, Le Tacon et al. provide a sample calculation of a superconducting critical temperature (T_c), in which they use the measured spin-fluctuation spectrum and electronic bands as input and obtain a T_c value comparable to the experimental one.

Third, and perhaps most importantly, their data indicate that key features of the spin fluctuations in doped copper oxides are strikingly similar to that of their undoped counterparts (Fig. 1): at the elevated energies probed by RIXS, the only significant effect of doping is an energy broadening of the excitations, probably arising from damping due to electron-hole excitations. (One should note that the present energy resolution of RIXS is insufficient to resolve fine structures on scales below 100 meV; therefore the similarity of doped and undoped spectra refers to gross features, and the details may well differ.)

Another simple and universal role in high Tc ?

These authors presented a very simple rule that seems validated by their analysis of experimental data [J. Phys.: Condens. Matter 23 (2011) 295701 (17pp)]. In this rule, the Tc of optimal compounds is essentially set by two length scales and the electron charge, i.e., Tc~e^2/l\times l'. What is striking is that, this rue was argued to cover a wide range of materials, including cuprates, pnictides and ruthenates. They proposed a paring mechanism via Compton scattering: e.g., the holes in the conducting layer is scattered by the electrons in the charge reservoir layer. Instead of forming excitons, superfluid forms. The following is a brief sojourn over this work [http://iopscience.iop.org/0953-8984/labtalk-article/46706]:

High-T_C superconductors have layered crystal structures, where T_C depends on bond lengths, ionic valences, and Coulomb coupling between electronic bands in adjacent, spatially separated layers. Analysis of 31 high-T_C materials—cuprates, ruthenates, rutheno-cuprates, iron pnictides and organics—has revealed that the optimal transition temperature T_CO is given by the universal expression k_B^-1e²Λ / ℓζ. Here, ℓ is the spacing between interacting charges within the layers, ζ is the distance between interacting layers, Λ is a universal constant, equal to about twice the reduced electron Compton wavelength, k_B is Boltzmann's constant and e is the elementary charge. Non-optimum compounds in which sample degradation is evident typically exhibit T_C below T_CO. Figure 1 shows T_CO versus (ση/A)^1/2/ζ—a theoretical expression determining 1 / ℓζ, where σ is the charge fraction, η is the layer number count and A is the formulaic area. The diagonal black line represents the theoretical T_CO. Coloured data points falling within ± 1.4 K of the line constitute validation of the theory.

Figure 1. Experimental test of theory.

Figure 2. Proposed pairing interaction.

The elemental building block of high-T_C superconductors comprises two adjacent and spatially separated charge layers. The factor e² / ℓζ, determining T_CO arises from Coulomb forces between them. Remarkably an explicit dependence on phonons, plasmons, magnetism, spins, band structure, effective masses, Fermi-surface topologies and pairing-state symmetries in high-T_C materials is absent. The magnitude of Λ suggests a universal role of Compton scattering in high-T_C superconductivity, as illustrated in figure 2 that considers pairing of carriers (h) mediated by electronic excitation (e) via virtual photons (ν). Several other important predictions are given. A conducting charge sheet is non-superconducting without a second mediating charge layer next to it, and a charge structure representing a room-temperature superconductor yet to be discovered is presented.

Pseudogap does not twin with Superconducting gap: another evidence

I only have time to quickly graze over this interesting paper for the moment.

In underdoped cuprate superconductors, phase stiffness is low
and long-range superconducting order is destroyed readily by
thermally generated vortices (and anti-vortices), giving rise to
a broad temperature regime above the zero-resistive state in
which the superconducting phase is incoherent1–4. It has often
been suggested that these vortex-like excitations are related to
the normal-state pseudogap or some interaction between the
pseudogap state and the superconducting state5–10. However,
to elucidate the precise relationship between the pseudogap
and superconductivity, it is important to establish whether
this broad phase-fluctuation regime vanishes, along with the
pseudogap11, in the slightly overdoped region of the phase
diagram where the superfluid pair density and correlation
energy are both maximal12. Here we show, by tracking
the restoration of the normal-state magnetoresistance in
overdoped La2􀀀xSrxCuO4, that the phase-fluctuation regime
remains broad across the entire superconducting composition
range. The universal low phase stiffness is shown to be
correlated with a low superfluid density1, a characteristic of
both underdoped and overdoped cuprates12–14. The formation
of the pseudogap, by inference, is therefore both independent
of and distinct from superconductivity.

Smectic Coexisting with nematic in cuprate

In the pseudogap phase of cuprate superconductors, incredibly rich and exotic things have been observed, among which are the checkerboard pattern that breaks the C4v symmetry within an unit cell and the stripes that break an additional translational symmetry. These are called electronic nematic and smectic phases, respectively. According to this study, there should be an interesting interplay between the two on cuprates, due to topological defects. The authors formalize the coupling in a gauge invariant way.

Coupling to the smectic fields can then occur either through phase or amplitude fluctuations of the smectic. Here, we focus on the former, which means that couples to local shifts of the wave vectors and . Replacing the gradient in the x direction by a covariant-derivative-like coupling gives(4)and similarly for the gradient in the y direction, to yield a GL term coupling the nematic to smectic states. The vector represents by how much the wave vector, , is shifted for a given fluctuation. Hence, we propose a GL functional (for modulations along ) based on symmetry principles and and being small:(5)where … refers to terms we can neglect for the present purpose (SOM d). If we were to replace by where is the electromagnetic vector potential, Eq. 5 becomes the GL free energy of a superconductor; its minimization in the long-distance limit yields and thus quantization of its associated magnetic flux (22, 23). Analogously, minimization of Eq. 5 implies surrounding each topological defect (SOM e). Here, the vector is proportional to and lies along the line where = 0. The resulting key prediction is that will vanish along the line in the direction of that passes through the core of the topological defect, with becoming greater on one side and less on the other (Fig. 4B). Additional coupling to the smectic amplitude can shift the location of the topological defect away from the line of = 0 (SOM e).

No concensus

A glance at how fierce the quarrels over the working mechanism of high Tc superconductors are !

No one is predicting a full understanding of high-temperature superconductivity any time soon — not least because such an account would have to make sense of the huge number of papers. “A rich enough theory should explain everything and not just cherry pick,” says David Pines, a physicist from the University of Illinois at Urbana-Champaign.
But it’s not always clear exactly what needs to be explained. Roughly 15 years ago, for example, researchers discovered that some high-temperature superconductors allow electron pairs to form above the transition temperature. In this ‘pseudogap’ regime, the material
spontaneously organizes itself into stripes: linear regions that act like rivers and carry electron pairs through the insulating landscape where electrons remain stuck in place. “It’s a precursor state to the superconducting state and is therefore fundamental to understanding this problem,” says Ali Yazdani, a physicist at Princeton University. Not so, says Pines, who thinks the pseudogap state “interferes with superconductivity but is not responsible for it”.
Much as physicists had to wait for highly developed quantum-mechanical tools to unlock the secret behind traditional superconductivity, researchers today may require future ideas to complete their task.
If nothing else, the field’s early quarrels have ensured that only the most determined researchers have stayed. Those remaining are perhaps humbled by their experiences. “I think our biggest problem has been human fallibility,” says Anderson. And perhaps these initial difficulties have helped to forge theories that can stand the test of time. “In the end, it’s your competitor that makes you strong,” says Shen

Nesting not so holy in pnictides

This [Phys. Rev. B 83, 220504 (2011)] might be call theories solely based on nesting into question !

Despite intense study, researchers have not yet uncovered the secrets behind the peculiar properties of iron-based (pnictide) superconductors. Many theories that try to explain the driving mechanism of superconductivity in these materials suggest it is tied to so-called nesting of the electron and hole Fermi surfaces. This geometric feature of the Fermi surface, where one portion of the surface maps to another if it is translated by a suitable reciprocal-lattice vector, is common to the structure of many families of pnictides. Nesting often implies the existence of collective electron behavior, so if it is present in the host materials of the pnictides, it would have significant implications for their properties.

In a Rapid Communication appearing in Physical Review B, Brendan Arnold at the University of Bristol, UK, and colleagues use the de Haas-van Alphen effect, where electrons and holes orbit the extrema of the Fermi surface in response to a magnetic field, to map out the electron and hole Fermi surface sheets of BaFe₂P₂, the parent material of an important family of pnictide materials. Besides providing highly detailed information about the geometry of the Fermi surfaces, they find, rather surprisingly, that the nesting present in the superconducting doped compounds BaFe₂(As_1-xP_x)₂ persists in BaFe₂P₂, which is not superconducting. This finding agrees with a growing list of experiments that conclude nesting does not play a dominant role in the development of superconductivity, at least in one family of pnictide compounds. – Alex Klironomos

Delocalization of Cooper pairs by doping ?

This is definitely a very wonderful step forward. Have not read it yet, but eager to tomorrow.
http://www.nature.com/nature/journal/v472/n7344/pdf/nature09998.pdf

Where enter the doped holes in cuprates？

Years have elapsed without a consensus on the full microscopic understanding of the physics involved in cuprate superconductors. One problem central to experimentalists is the residence of doped holes. Although widely held that at low concentrations of dopants, most holes go to Zhang-Rice orbital, whose character is essentially of planar O p orbital, what happens in the overdoped case is still not clear. In this Science report [1], the workers used high resolution Compton scattering to resolve this issue. They claimed that, doped holes are mostly of Cu d character in the OD case. Their results resonate with a two-orbital model [2] that takes into account both dz^2 and dx^2-y^2 orbital. In ref.[2], the energy difference between these orbital, Delta, is the key parameter in determining Tc. Larger Delta gives larger Tc. What is implied in [1], is perhaps that, such Delta should depend on doping x. As x increases, Delta decreases. This might explain the fact that, the SC dome has a small collapse at its up right corner.

Is there a sharp transition ?

[1]Science, 332:698(2011)
[2]PRL, 105:057003(2010)

I would like to mention another paper, which measures orbital current in CuO[Science, 332:696(2011)].

Manifesto for higher Tc

A perspective by A.V.Chubukov, who is an enthusiast of spin-fluctuation type gluon. He compared the iron-based and the copper-based superconductors and surmise a higher Tc, observing
(1)Kexp/KLDA for existing high Tc SCs is around 0.5;
(2)superfluid density ~ dc conductivity x Tc.
Point (1) indicates that, high Tc is likely with a mixture of mobility and localization [Nature Physics, 7:272(2011)].

More on the pseudogap in cuprate

This article [http://www.nature.com/nphys/journal/v7/n4/full/nphys1921.html?WT.ec_id=NPHYS-201104#/affil-auth] definitely refreshes one's mind in thinking about the nature of the pseudogap of cuprates. The review is here [http://www.nature.com/nphys/journal/v7/n4/full/nphys1973.html?WT.ec_id=NPHYS-201104]. The authors measured the specific heat of UD YBCO under magnetic field. Oscillations were found above H* ~27T. But not only that, there is a background scaling as the square root of H.
What does this imply ?

SC fluctuations not so strong as previously thought

Here is a wonderful Letter [Nature Physics, 7:298(2011)] which, in a sense, denies the pseudogap as precursor of SC in cuprate. These authors probes LSCO, a very typical p-type high Tc, by Terahertz spectroscopy. They found that, such SC fluctuations persist up to 16 K above Tc, much weaker than former speculations. This is actually quite consistent with a latest work with ARPES [see my yesterday's entry].

The nature of the underdoped pseudogap regime of the high-temperature copper oxide superconductors has been a matter of long-term debate^{1, 2, 3}. On quite general grounds, we expect that, owing to their low superfluid densities and short correlation lengths, superconducting fluctuations will be significant for transport and thermodynamic properties in this part of the phase diagram^{4, 5}. Although there is ample experimental evidence for such correlations, there has been disagreement about how high in temperature they may persist, their role in the phenomenology of the pseudogap and their significance for understanding high-temperature superconductivity^{6, 7, 8, 9, 10}. Here we use THz time-domain spectroscopy to probe the temporal fluctuations of superconductivity above the critical temperature (T_c) in La_2−xSr_xCuO₄ (LSCO) thin films over a doping range that spans almost the entire superconducting dome (x=0.09–0.25). Signatures of the fluctuations persist in the conductivity in a comparatively narrow temperature range, at most 16 K above T_c. Our measurements show that superconducting correlations do not make an appreciable contribution to the charge-transport anomalies of the pseudogap in LSCO at temperatures well above T_c.

Two Consecutive Thermal phase transitons make a High Tc supercoductor !

This is claimed in this wonderful article [Science, 331:1579(2011)], which I have already mentioned in my yesterday's entry.

In cuprate superconductors, people observe not only one d-wave SC gap but an additional gap, which opens up at the zone boundary and at a temperature T* far above Tc. A natural question is how these two gaps are connected. Two proposed scenarios are common in the market: one takes both originating from the same source while the other associates them with respective orders. Clarifying this question paves the way to the ultimate theory of high Tc copper oxides.

Now this article provides convincing evidence, combining ARPES, Polor Ker Effect and Time Resolved Reflectivity, that, T* signals a true but somewhat rounded thermal phase transition into a non-Sc phase. Actually, their work revealed three temperatures: Tc, T* and Tg. Here the Tg is a bit higher than Tc but far below T*, indicating the pairing fluctuations. Their mean-field calculations some candidate orders suggest that the paring energy and the pseudogap energy are of the same order, raising the question if they are connected in a deeper manner.

The current

I think I have missed some very funny things these days. I would like to pile their links below and I'll come back to them as I get time.
1. Physics, 4:26 (2011), by I.I.Mazin. This is a review on the puzzles and surprised conferred by the iron-based superconductors, which shows quasi-3D structure rather than a 2D one, quite different from their cuprate counter-parts.
2. Physics, 4:25 (2011), by P.Recher et al. This is an analog of spin Hall effect. It reviews a work that shows how a line defect could be utilized to filter valley-featured carriers in graphene.
3. Science, 331: 1579 (2011), by R.-H. He et al. This is a sequel to an earlier article by these authors. They have previously argued that, two gaps of distinct origins should exist in cuprates instead of one. Here they further explore their work and show the opening of the pseudogap might be related to a phase transition.

Celebrating 100 years of superconductivity

This year marks the 100th anniversary since superconductivity was discovered in Leiden, The Netherlands, by Heike Kamerlingh Onnes and co-workers on 8 April 1911. Yielding no less than seven Nobel Prizes, the study of superconductors remains more active than ever in terms of forming a fundamental understanding of their underlying mechanism, and in seeking new and novel applications that already extend to digital electronics, sensors, medicine and metrology.

In recognition of this centennial year we are pleased to present a collection of superconductivity-themed review articles published in Reports on Progress in Physics over the last 10 years. Reflecting the wide-reaching impact of superconductors across many areas of physics, each article will be free to read until the end of 2011.

Tim Smith
Senior Publisher

More oscillations in cuprate superconductors

http://www.nature.com/nphys/journal/v7/n3/full/nphys1930.html?WT.ec_id=NPHYS-201103

Since its discovery almost 25 years ago, high-temperature superconductivity has led to a wealth of new theoretical ideas and deepened our understanding of complex condensed-matter systems. At the same time, the study of cuprates has been the driving force for tremendous innovations in the experimental methodology of condensed-matter physics, with methods ranging from photoemission, scanning microscopy, optics and neutron scattering to, in the past few years, quantum oscillations. As reported in Nature Physics¹, measurements by Brad Ramshaw et al. of quantum oscillations in the underdoped high-temperature superconductor YBa₂Cu₃O_6.59 typifies these advances in a number of striking ways. First, the samples studied are the result of two decades of intensive development leading to unique levels of purity that would previously have been unimaginable in such complex oxides. Second, the measurements take place in pulsed magnetic fields that reach both a magnitude of field and a quality of signal-to-noise ratio far beyond what could formerly be achieved. And third, the latest innovation of 'genetic algorithms' allows consistent parameters to be extracted from a large data set of quantum oscillations as a function of field direction and temperature. The authors obtain, among other things, a value of the g-factor of the charge carriers near 2, showing that they are surprisingly like free electrons. This result has profound implications for the nature of the ground state that gives rise to these oscillations.

Anderson and Scalapino talk on Science

This is not a latest news but still interesting for those who are working with cuprate superconductors, which are widely thought to be a central problem faced with by contemporary physicists. The two argue about the possibility of a paring glue. [http://www.sciencemag.org/content/316/5832/1705/reply]

[Anderson]:

I do not, however, accept that Scalapino’s calculations, refined as they are, come near to settling the question he has raised. The numerical analysis of Scalapino’s reference 7, and the analysis of experiments in his references 8 and 9, all have, logically, two pieces. To take ref 7 for definiteness, Scalapino’s group does two computations. The first, while difficult, is logically unimpeachable: It is a carefully designed simulation of the properties of the Hubbard model which we both agree is by far the main Hamiltonian candidate. Sure enough, they find d-wave superconductivity and other physical properties that agree with experiments—and also with much simpler mean field theories (1).

In step 2, they attempt to derive from the measured quantities a number of theoretical constructs, such as the "pairing interaction vertex," assuming that the underlying theory is the conventional Feynman-Dyson diagram theory as adapted for condensed matter problems in the 1960s. Thus, the procedure, far from being a purely direct computational result, is a theoretical construct with a very relevant input of unproven assumptions. The interaction vertex which is derived does not look at all like the J term in the Hamiltonian; it is much smaller than it should be, at high energies, growing to its full strength only at the lowest energies.

This is an unlikely result. It says that somehow all the low-frequency spin fluctuations have killed this giant interaction at the high-frequency end, but left it intact at low frequency to do its work on the pairing gap. It amounts to replacing my "elephant" J with almost nothing but its indirect consequences. It also contradicts the simplest mean field theory of the t-J model (ref 1, called because of its simplicity the "Plain Vanilla" theory).

If I found a result which so blatantly did not make physical sense, I might have questioned the method rather than attacking those of us who seem to have found the right answers by doing things otherwise. It is very attractive to abandon these particular methodological assumptions, because the same set of assumptions, applied in the normal state of the same materials, have had zero success in describing its unique and very anomalous properties.

[Scalapino]:

While there is a growing consensus that superconductivity in the high T_c cuprates arises from strong short-range Coulomb interactions between electrons rather than the traditional electron-phonon interaction, the precise nature of the pairing interaction remains controversial (1). This is the case even among those who agree that the essential physics of the cuprates is contained in the Hubbard model (Perspectives, "Is there glue in cuprate superconductors?", by P. W. Anderson, 22 June 2007, p. 1705). For example, both Anderson’s resonating-valence-based (RVB) theory (2) and the spin-fluctuation exchange theory (3, 4) lead to a short-range interaction which forms d _x²−y² pairs. However, the dynamics of the two interactions differ.

In the RVB picture, the superconducting phase is envisioned as arising out of a Mott-liquid of fluctuating singlet pairs. These pairs are bound by a superexchange interaction J which is proportional to t²/U. Here t is the effective hopping matrix element between adjacent sites and U is an onsite Coulomb interaction. J is determined by the virtual hopping of an electron of a given spin to an adjacent site containing an electron with an opposite spin (5). Thus the dynamics of J involves virtual excitations above the Mott gap which is set by U, and the pairing interaction is essentially instantaneous. In this case, as Anderson recently discussed (6), one would not speak of a pairing glue.

In the spin-fluctuation exchange picture, the pairing is viewed as arising from the exchange of particle-hole spin 1 fluctuations whose dynamics reflect the frequency spectrum seen in inelastic magnetic neutron scattering. This spectrum covers an energy range which is small compared with U or the bare bandwidth 8t. In this case, the pairing interaction is retarded and in analogy to the traditional phonon mediated pairing, one says that the spin-fluctuations provide the pairing glue.

Thus, the question of whether there is pairing glue in the cuprates is a question about the dynamics of the pairing interaction. It offers a way of distinguishing different theories. For the Hubbard model, recent numerical calculations (7) have shown that the strongest pairing occurs for U of order the bandwidth 8t. This is also thought to be the parameter regime appropriate to the cuprates. In this regime, these calculations find that the dynamic dependence of the pairing interaction is the same as that of the dynamic spin susceptibility. Thus, there is pairing glue in the Hubbard model.

Of course, the ultimate question is: What does the experiment tell us about the dynamics of the pairing interaction? Just as the spatial structure of the pairing interaction can be determined from the k-dependence of the superconducting gap, the dynamics of the interaction is reflected in the frequency dependence of the gap. In addition, if the interaction is retarded, that is delayed for a time of order ћ/(2J), the gap will have both a real and an imaginary component. This frequency structure of the gap is reflected in a variety of experiments and analysis of structure in the angular resolved photoemission spectrum (8), and the infrared conductivity (9) have suggested that the dynamics is indeed determined by spin-fluctuations. However, as opposed to the Hubbard model, real materials have phonons and alternative explanations have also been proposed (10). Thus, while there is pairing glue in the Hubbard model, more experimental work is needed to settle the question of whether there is glue in the cuprate superconductors.

Competing gaps scenario for underdoped cuprates

The normal state properties are definitely more exotic than the superconducting properties of the engimatic quasi-2D d-wave cuprate superconductors. Under special inspection is the psudogap state, which is signalled with a loss in quasi-particle spectral weight above a typical temperature T*, which is much higher than Tc, the SC critical temperature. A basic question concerns the nature of this gap opening. One idea precasts that the pseudogap senses the preformed cooper pairs, which will condense into a coherent superfluid at Tc. Another idea relates this gap to a different order, which might compete with the SC order. Up to now, evidences regarding these two ideas are elusive. This terrific work [Nature Physics, 7: 21–25 (2011) doi:10.1038/nphys1851] comes to give a real boost. They study Bi2212 with various dopings. They focus on the temperature dependence of the weight loss associated with the antinodal point in the 1BZ. As the sample is cooled across T*, a linear tempeature dependence was spotted around T*, but a very fast deviation sets in at lower temperatures, T**>Tc. This deviation motivates the authors to conceive a two-gap scenario: the proper pseudogap opens at T*, but the cooper pair forms at T**, and SC coherence comes at Tc. According to this proposition, the pseudogap has a separate origin that should be concerned with a different order. They are able to find out a remarkably accurate scaling behaviors regarding the dependence of the cooper paring spectral weight loss on the T**. This scaling law holds for all samples they prepared. Read this paper !! Very inspiring !!

Light-Induced Superconductivity in a Stripe-Ordered Cuprate

This is a funny study, which shows how light mobilizes carriers in gapped states to become superconducting temporarily. [http://www.sciencemag.org/content/331/6014/189.full.pdf]. What does all these imply for the microscopic theory of cuprates, anyway?

One of the most intriguing features of some high-temperature cuprate superconductors is the interplay between one-dimensional “striped” spin order and charge order, and superconductivity. We used mid-infrared femtosecond pulses to transform one such stripe-ordered compound, nonsuperconducting La1.675Eu0.2Sr0.125CuO4, into a transient three-dimensional superconductor.
The emergence of coherent interlayer transport was evidenced by the prompt appearance of a Josephson plasma resonance in the c-axis optical properties. An upper limit for the time scale needed to form the superconducting phase is estimated to be 1 to 2 picoseconds, which is significantly faster than expected. This places stringent new constraints on our understanding of stripe order and its relation to superconductivity.