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.

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

Theory sometimes goes ahead of experiments

Imagination goes ahead of reality, from time to time.

Surely, a lot of theoretical scientists (e.g., Abrikosov) admit that they follow closely experiments. And they are mostly motivated by them. In numerous cases, little interest might be invested in a subject until some lab fellows could get their hands on it. Graphene offers a typical example of this kind. Before 2004, few body payed attention to this seemingly abstract material. The situation drastically changed due to Geim et al's fabrication. Often, only after the material becomes experimentally available and controllable will theorists come out to construct models and explain observations or make predictions. Efforts are primarily concentrated on such systems that already exist or at least, likely to exist. A great portion of work then surrounds the comparison between models and empirical data. This is especially true with particle physics or other arena where fundamental laws are sought. In these fields, the objects are created by GOD and already there and to be discovered.

But, in materials science or more generally, in condensed matter physics, one has to reset mind. Here, many things are invented rather than discovered. Experimentalists can be motivated by theorists, and model can advance data. Novel phases may not exist in any materials that are known currently, but in some models that are constructed merely by imagination. These models, although seem irrelevant to reality when they are born, could drive some workers to look for possibilities of realizing them in labs. On such occasions, it is not about qualifying or falsifying a theory. It is about how to put it into reality and into use. A nice example might be the spin liquid or Z2 gauge theory or string model. All these when born were nothing but brain products. But these thought products have been behind many many many wonderful experimental work.

In short, theory can go ahead. And it is not always about explanation and prediction. It can fostering new reality.

Noteworthy papers from latest issue of Science

1. Disorder-Enhanced Transport in Photonic Quasicrystals, 332:1541(2011);

Quasicrystals are aperiodic structures with rotational symmetries forbidden to conventional periodic crystals; examples of quasicrystals can be found in aluminum alloys, polymers, and even ancient Islamic art. Here, we present direct experimental observation of disorder-enhanced wave transport in quasicrystals, which contrasts directly with the characteristic suppression of transport by disorder. Our experiments are carried out in photonic quasicrystals, where we find that increasing disorder leads to enhanced expansion of the beam propagating through the medium. By further increasing the disorder, we observe that the beam progresses through a regime of diffusive-like transport until it finally transitions to Anderson localization and the suppression of transport. We study this fundamental phenomenon and elucidate its origins by relating it to the basic properties of quasicrystalline media in the presence of disorder.

2.Carbon-Based Supercapacitors Produced by Activation of Graphene, 332:1537(2011)

Supercapacitors, also called ultracapacitors or electrochemical capacitors, store electrical charge on high-surface-area conducting materials. Their widespread use is limited by their low energy storage density and relatively high effective series resistance. Using chemical activation of exfoliated graphite oxide, we synthesized a porous carbon with a Brunauer-Emmett-Teller surface area of up to 3100 square meters per gram, a high electrical conductivity, and a low oxygen and hydrogen content. This sp²-bonded carbon has a continuous three-dimensional network of highly curved, atom-thick walls that form primarily 0.6- to 5-nanometer-width pores. Two-electrode supercapacitor cells constructed with this carbon yielded high values of gravimetric capacitance and energy density with organic and ionic liquid electrolytes. The processes used to make this carbon are readily scalable to industrial levels.

3. The Limits of Ordinary Matter, 332:1513(2011)

All ordinary matter consists of protons and neutrons, collectively called nucleons, which are bound together in atomic nuclei, and electrons. The elementary constituents of protons and neutrons, the quarks, almost always remain confined inside nucleons (or any other particle made up of quarks, called hadrons). The fundamental force that binds quarks together—the strong, or “color” force—cannot be overcome unless extremely high-energy conditions are created, such as through heavy-particle collisions. Theoretical simulations based on quantum chromodynamics (QCD) predict that the transition temperature for the appearance of free quarks should occur at 2.0 × 10¹² K (an energy of 175 million eV) (1, 2). Since 2000, the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory has created the necessary conditions to form quark matter in particle collision, but determining the transition temperature under these conditions is challenging. On page 1525 of this issue, Gupta et al. (3) show that the relevant temperature and energy scales can be extracted from recent experimental studies and find that the transition temperature is in remarkable agreement with theory.

4 This paper is not published in Science, but highlighted in it: Nano Lett. 11, 10.1021/nl200928k (2011).

It has long been known from ex situ studies that metal nanoparticles can catalyze reaction of oxygen with graphite surfaces and create grooves or channels. Such reactions could be used for patterning graphene sheets. Booth et al. have studied the dynamics of silver nanoparticles on suspended monolayer and bilayer graphene sheets in a transmission electron microscope. They imaged these samples at temperatures from 600 to 850 K and partial pressures of oxygen over the sample from about 30 to 100 millitorr. The nanoparticles cut channels along <100> crystallographic directions, but some fluctuations of motion normal to the channel direction were also observed. The nanoparticles did not move at a constant speed. Instead, their velocity profile was erratic, and the start-stop motion was better described by a Poisson distribution.

LambdaDCM or MOND ?

Yesterday I encountered an article [http://physics.aps.org/articles/v4/23] and today I attended a public lecture, both on dark matter, which, if it exists, seems invisible to most of the forces known to us. But it does participate in gravitation and plausibly in weak interaction. Their nature is crying to be unveiled. In the article, the author explains the observed v-R curve in galaxies, which is the most direct motivation for dark matter, using the so-called MOND (Modified Newtonian Dynamics) and the dark matter is subsidiary. On the other hand, Harry Nelson, the today's lecturer, dismisses the MOND as unnecessary complications. He cited the "Bullet Cluster" [http://en.wikipedia.org/wiki/Bullet_Cluster] as evidences. All in all, I feel that, the MOND idea can hardly withstand this. The point is that, a good idea should explain not only the v-R curve but also many other relevant things, such as the "Bullet Cluster". On the other hand, what is dark matter ? This is regarded as one of the biggest questions in today's science.

Dark Matter Particles Remain Dark

Here is a controversy about dark matter particles, whose properties are definitely quite elusive. Most we know about them are just speculative. Bear in mind how a scientific conclusion has to go through scrutinies !

Inventing new physical systems

Particle physicists can hardly invent new physical systems but only to discover the already existing matter and energy world. Condensed matter physicists tend to create their own systems to meet fundamental intelligent challenges and practical ends. The as-created new physical systems are surely immense and the underlying physics are also diverse, but the mathematical models seem not so diverse: it is frequently the case that the model constructed for one system may be transplanted to describe another system, with proper interpretation of the symbols. In other words, there exists some kind of universality. This scenario offers opportunities for both theorists and experimentalists: (1) the theorists can make predictions about system A via the knowledge of system B if A and B are found sharing the same mathematical structure; while (2) the experimentalists can simulate system A by measuring system B. Such possibility drives the emergence of a host of artificial systems. The following is a list:
(1) p-n junction and transistors;
(2) 2DEG;
(3) Optical lattice and Ultra-cold atoms;
(4) Photonic crystals;
(5) Metamaterials;
(6) Circuit QED;
(7) Cavity QED;
(8) Trapped ions;
(9) Graphene, and CNTs;
(10) Topological insulators;
(11) ...

Wet dog shaking

This piece of study is something that should never be missed. It is perhaps one of the best examples exemplifying what science is all about: Just being curious and trying to find out how things actually happen. This work looks at how fast a wet dog wriggles its body to shake off the water sticking to its fur. These authors from Geogia Insttitute of Technology set up a model and compare the results out of this model to reality. They photographyed a range of animals and figure out the wriggling frequencies. Their model predicted the frequency should be proportional to the square root of the belly radius of the animals, close to the observations that yield an exponent of 0.75 rather than 0.5. [http://www.wired.co.uk/news/archive/2010-10/20/physicists-find-perfect-speed-for-wet-dogs-to-shake-at] In this link, there is a video that sumarizes their interesting and provoking work.

Failed theories of SC

In one of my previous entries, I mentioned the failed theories that were briefly reviewed in a preprint. Here in Nature Physics [Nature Physics, 6: 715, 2010], another one based on this review came out. I especially like this story about Laudau:

Yet it turns out that Landau first proposed these ideas in the context of superconductivity, thinking not of magnetization but of electrical current. He expanded the free energy F around the state of zero current, j = 0, and argued that as the direction of the current shouldn't affect F, the odd terms should vanish. This gives an equation of the form F(j) = F(0) + aj² + bj⁴. Assuming b > 0 and that a passes through zero at a critical temperature T_c, he showed that there could be an abrupt transition from zero to non-zero current below T_c.

This early theory conflicted with observations — it erroneously predicted j ~ (T_c − T)^1/2 just below the critical temperature — and Landau went back to the drawing board. Yet here already were the seeds of the later Ginzburg–Landau theory of phase transitions. And Landau's introduction of the notion of an 'order parameter' as a convenient handle on order and how it changes has influenced physics ever since, even if it did appear in a failed theory.

This idea is crazy: when one expands free energy in current, one has in his mind that he is dealing with an equilibrium state. However, current usually exists in a non-equilibrium state. This gives a glimpse of the aberration of superconductivity !

... Thus consciousness becomes the source of what we call scientific reality. The entire creation of the universe(s) is a product of expanding human mind.

This is not true. Because science, as a creation of minds, cannot replace the objects it reflects on. Not only scientists, but also every human look at things in their own way. Despite various reflections upon it, the reality is one. Reflections, however many and ingenious they are, can by no means be called reality. Science is reflections of this kind that are scrutinized by reasoning.

I would like to forward this interesting blog here:

First we have the issue of the debate about the differences between Economics and Econophysics. Then there's an argument on why Economics will never be like Physics. Now comes an argument on why Econophysics will never work!

The markets are not physical systems. They are systems based on creating an informational advantage, on gaming, on action and strategic reaction, in a space that is not structured with defined rules and possibilities. There is feedback to undo whatever is put in place, to neutralize whatever information comes in.

The natural reply of the physicist to this observation is, “Not to worry. I will build a physics-based model that includes feedback. I do that all the time”. The problem is that the feedback in the markets is designed specifically not to fit into a model, to be obscure, stealthy, coming from a direction where no one is looking. That is, the Knightian uncertainty is endogenous. You can’t build in a feedback or reactive model, because you don’t know what to model. And if you do know – by the time you know – the odds are the market has changed. That is the whole point of what makes a trader successful – he can see things in ways most others do not, anticipate in ways others cannot, and then change his behavior when he starts to see others catching on.

It will be interesting to see if the writer has actually read Christophe Schinckus AJP's paper (my guess is he hasn't), and if Schinckus has a response to this.

The question whether something works or is valid in field of studies such as economics, social science, politics, etc. is rather interesting. In the physical sciences, there's usually no ambiguity because we can either test it out, or go look for it. Something works when what it predicts can be observed and reproducible. So how does one determines if the various principles and models in economics, social science, politics, etc. are valid and do work? Simply based on previous data and observation that somehow fit into the model? But as this writer has stated, there's no model to fit because the model keeps changing due to such model-changing feedback. It appears that the whole field is more based on "intuition" than on any rational reasoning.

If that's the case, then it truly isn't a science but more of an art. So why do people who graduate with a degree in economics, social "science", or politics, sometime get a "Bachelor of Science" degree?

Zz.

Resource Letter PTG-1: Precision Tests of Gravity

A package of current research topics on experimental gravity.

This resource letter provides an introduction to some of the main current topics in experimental tests of general relativity as well as to some of the historical literature. It is intended to serve as a guide to the field for upper-division undergraduate and graduate students, both theoretical andexperimental, and for workers in other fields of physics who wish learn about experimental gravity. The topics covered include alternative theories of gravity, tests of the principle of equivalence, solar-system and binary-pulsar tests, searches for new physics in gravitational arenas, and tests of gravity in new regimes, involving astrophysics and gravitational radiation.

Through the years leading to the discovery of BCS theory

Almost half a century passed between the discovery of superconductivity by Kammerlingh Onnes and the theoretical explanation of the phenomenon by Bardeen, Cooper and Schrieffer. During the intervening years the brightest minds in theoretical physics tried and failed to develop a microscopic understanding of the effect. A summary of some of those unsuccessful attempts to understand superconductivity not only demonstrates the extraordinary achievement made by formulating the BCS theory, but also illustrates that mistakes are a natural and healthy part of the scientific discourse, and that inapplicable, even incorrect theories can turn out to be interesting and inspiring.

http://arxiv.org/ftp/arxiv/papers/1008/1008.0447.pdf

How do you interpret your results ?

Scientists should take caution when they explain their findings to journalists. Here is an example on how misleading claims can be made. The article headline claims 'innate correlation between various power law phenomena', which however lacks justifications in their original work. In their work, the authors study the relation between donation and wealth, which was found following Zipf's power law. This law was originally used to describe the distribution of words in language. Now that these two distant phenomena share the same mathematical structure, they claimed their work demonstrates an innate correlation between these two phenomena, which is however quite inappropriate. It is obvious that, sharing the same mathematical structure does equal having innate relation. By 'innate relation', we mean 'a phenomenon is a logical corollary of another'. In this sense, one cannot see any innate relation between 'wealth-donation' and 'words-language'. They just share the same math curve, which may be a coincidence. One can find many similar examples in physics and other fields. For example, physicists have found that, the gauge theory, which was originally designed for descriptions of particle behaviors, also emerges in condensed matter, but one cannot say one can be deduced from the other.

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Researchers Find Innate Correlations Among Different Power Law Phenomena

November 17, 2009 By Lisa Zyga

Enlarge

The Zipf plot of wealth and donation are innately connected. The upper part of the donation distribution follows Zipf’s law, and the Zipf exponent is equal to that of the corresponding wealth distribution. Image credit: Q. Chen, et al.

(PhysOrg.com) -- Studying the patterns that emerge in natural and social phenomena is a popular area of research, although usually individual phenomena are studied separately from each other. In a recent study, researchers have found innate correlations among some of these phenomena, showing that the amount of money that individuals in a society donate to a charity can be used to determine the distribution of personal wealth in that society. The connection between these two topics can also be used for exploring the complexity of a society's economic system.

“The greatest significance of this work is showing that power law phenomena in different references may correlate with each other innately,” Yougui Wang of Beijing Normal University told PhysOrg.com. “Thus, this implies that some power law phenomena should be the derivatives of other basic ones.”

The key to using patterns from one data set to infer the patterns of a different set of data is realizing that both sets share a mathematical principle called Zipf’s law, explained Wang, along with coauthors Qinghua Chen and Chao Wang of Beijing Normal University. Although Zipf’s law was originally proposed in the field of linguistics to explain the distribution of words in a language, it has attracted much more attention because it also describes a wide variety of natural and social phenomena. Zipf’s law quantitatively describes how the most common entities of a set (such as the common word “the”) appear with a high frequency that logarithmically tapers off as entities become less common. The same power law holds true for the distribution of population sizes, Internet traffic, and other phenomena. As researchers have previously found, in some cases the law stems from a competition among individuals for a constraint resource.

In the current study, the scientists show that collective donations follow a particular pattern: the upper part (made of the larger monetary donations) follows Zipf’s law, while the lower part (made of smaller donations) exhibits a uniform distribution. The data comes from donations by Chinese to the Chinese Red Cross Foundation after an earthquake of magnitude 8.0 struck Sichuan province in southwest China in May 2008. The data includes more than 230,000 personal donations, with the donation amount ranging from 0.01 RMB to 2.79 million RMB. Significantly, 205,000 donations (87.5%) of the total sample were 100 RMB or more. This part of the data approximately followed Zipf’s law, while the distribution of donations of less than 100 RMB was basically uniform.

So far, the analysis is yet another phenomenon of human behavior that follows the regularity of Zipf’s law. But the researchers also developed a model to explain this pattern, taking into account the previous finding that wealth distribution has also been known to follow Zipf’s law. Their model shows that only a portion of the individuals in a society have a desire to donate, and of these, each individual donates a portion of his or her overall wealth that is random but uniformly distributed. Even though only a small sample of the donators in the case of the Sichuan earthquake was collected and analyzed, the researchers’ model could generate the distribution of personal wealth throughout China, which is consistent with what has been obtained from the data of the richest 500 individuals in China.

As the researchers explain, donation and wealth, like other power law phenomena, seem to coexist in complex systems. By showing that power law phenomena can be related to one another, the researchers’ work could be valuable for exploring the correlations among natural patterns in systems.

“Based on the results of our study, the distribution of wealth could be derived from that of donation,” said Qinghua Chen. “Once the link between two variables involved in a complex system is just like the relation between donation and wealth in our case, we can infer the distribution of one variable from the other.”

More information: Q. Chen, C. Wang, and Y. Wang. “Deformed Zipf’s law in personal donation.” Europhysics Letters, 88 (2009) 38001. doi: 10.1209/0295-5075/88/38001

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