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.

The role of phase

This demonstration (you can watch a video there) comes from Harvard Natural Sciences Lecture Demonstrations

What it shows: Fifteen uncoupled simple pendulums of monotonically increasing lengths dance together to produce visual traveling waves, standing waves, beating, and random motion. One might call this kinetic art and the choreography of the dance of the pendulums is stunning! Aliasing and quantum revival can also be shown.

How it works: The period of one complete cycle of the dance is 60 seconds. The length of the longest pendulum has been adjusted so that it executes 51 oscillations in this 60 second period. The length of each successive shorter pendulum is carefully adjusted so that it executes one additional oscillation in this period. Thus, the 15th pendulum (shortest) undergoes 65 oscillations. When all 15 pendulums are started together, they quickly fall out of sync—their relative phases continuously change because of their different periods of oscillation. However, after 60 seconds they will all have executed an integral number of oscillations and be back in sync again at that instant, ready to repeat the dance.

So you know ?

Sometimes I met students majoring in theoretical physics who has no clear idea about the following important fact of quantum mechanics at the introductory level based on non-relativistic Schrodinger equation:
1. The single-valuedness and finiteness everywhere of physical wave functions are derived solely from the Born interpretation;
2. The matching conditions (or say interface conditions) used for example in textbook problems such as a particle tunneling through a square potential barrier are derived solely from Schrodinger equation and vary from case to case;
3. The sign of energy, E, determines whether a state is localized or extended : localized for E<0 while extended for E>0, because the notion of 'localized' and 'extended' actually refers to what happens on the boundary at infinity and henceforth, in the infinity, negative energy leads to imaginary wave number while positive to real. One just needs check the asymptotic behaviors of Schrodinger equation.
4. The boundary conditions for localized states: wave functions vanishing in the infinity; while that for extended: wave functions finite everywhere. Therefore, 'localized' or 'extended' are simply states of distinct boundary conditions.
5. Localized states form discrete spectrum (whose values can not be experimentally prepared in arbitrary fasion); while extended ones (whose values can be experimentally prepared in arbitrary fasion) form a continua. A simple illustration: to get localized states one just imagines a particle in a very large box, while to get extended ones one just makes use of free particle states (plane waves). Scattering states are typical extended states.

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.

Cool Water Fountain

Here is a show of a very cute water fountain in Japan.

Think about the physics in it !

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).

New upper limit on the electron dipole moment

This experiment sets a new limit on the possible electron dipole moment, and thus put stringent constraints on candidate extensions, such as supersymmetric models, over the Standard Model, hoping for new physics.

The electron is predicted to be slightly aspheric¹, with a distortion characterized by the electric dipole moment (EDM), d_e. No experiment has ever detected this deviation. The standard model of particle physics predicts that d_e is far too small to detect², being some eleven orders of magnitude smaller than the current experimental sensitivity. However, many extensions to the standard model naturally predict much larger values of d_e that should be detectable³. This makes the search for the electron EDM a powerful way to search for new physics and constrain the possible extensions. In particular, the popular idea that new supersymmetric particles may exist at masses of a few hundred GeV/c² (where c is the speed of light) is difficult to reconcile with the absence of an electron EDM at the present limit of sensitivity^{2, 4}. The size of the EDM is also intimately related to the question of why the Universe has so little antimatter. If the reason is that some undiscovered particle interaction⁵ breaks the symmetry between matter and antimatter, this should result in a measurable EDM in most models of particle physics². Here we use cold polar molecules to measure the electron EDM at the highest level of precision reported so far, providing a constraint on any possible new interactions. We obtain d_e = (−2.4 ± 5.7_stat ± 1.5_syst) × 10⁻²⁸e cm, where e is the charge on the electron, which sets a new upper limit of |d_e| < 10.5 × 10⁻²⁸e cm with 90 per cent confidence. This result, consistent with zero, indicates that the electron is spherical at this improved level of precision. Our measurement of atto-electronvolt energy shifts in a molecule probes new physics at the tera-electronvolt energy scale².