# Monthly Archives: August 2015

## Lost in Translation

Like any good joke, there is a kernel (or a little more) of truth in the following one.

A dictionary of useful research phrases: what physics researchers say and what they mean by it

It has long been known: I didn’t look up the original reference.
A definite trend is evident: These data are practically meaningless.
Of great theoretical and practical importance: Interesting to me.
While it has not been possible to provide definite answers to these questions: An unsuccessful experiment, but I still hope to get it published.
Three of the samples were chosen for detailed study: The results of the others didn’t make any sense.
Typical results are shown: The best results are shown.
These results will be shown in a subsequent report: I might get around to this sometime if I’m pushed.
The most reliable results are those obtained by Jones: He was my graduate assistant.
It is believed that: I think.
It is generally believed that: A couple of other people think so too.
It is clear that much additional work will be required before a complete understanding of the phenomenon occurs: I don’t understand it.
Correct within an order of magnitude: Wrong.
It is hoped that this study will stimulate further investigation in this: This is a lousy paper, but so are all the others on this miserable topic.
A careful analysis of obtainable data: Three pages of notes were obliterated when I knocked over a glass of beer.

## The Prescience of Ginzburg

In 1977, before the discovery of high-temperature superconductivity, V. Ginzburg wrote:

“On the basis of general theoretical considerations, we believe at present
that the most reasonable estimate is Tc$\lesssim$300 K, this estimate being, of course, for materials and systems under more or less normal
conditions (equilibrium or quasi-equilibrium metallic systems in the absence
of pressure or under relatively low pressures, etc.). In this case, if we exclude
from consideration metallic hydrogen and, perhaps, organic metals, as well
as semimetals in states near the region of electronic phase transitions, then it is suggested that we should use the exciton [electronic] mechanism of attraction between the conduction electrons.

In this scheme, the most promising – from the point of view of the possibility of raising T$_c$-materials are, apparently, layered compounds and dielectric-metal-dielectric sandwiches. However, the state of the theory, let alone of experiment, is still far from being such as to allow us to regard as closed other possible directions, in particular, the use of filamentary compounds. Furthermore, for the present state of the problem of high-temperature superconductivity, the soundest and most fruitful approach will be one that is not preconceived, in which attempts are made to move forward in the most diverse directions.”

I took the quote out of this paper here, though many of the ideas are echoed from and better expressed in one of his previous papers, linked here. It is amusing that for at least 15 years prior to the discovery of the cuprates, Ginzburg stressed looking for high-temperature superconductors (with T$_c$s above the boiling point of liquid nitrogen) in layered, quasi-2D materials that could host superconductivity with an electronically driven Cooper pairing.

The papers linked above are very readable and he reached these conclusions on startlingly general grounds — by discussing the inverse dielectric function.

## Plasmons of a Luttinger Liquid

There’s a quite remarkable experiment in a paper by the Wang group at Berkeley that recently came out in Nature Photonics demonstrating the existence of peculiar plasmons in carbon nanotubes. These are significant because this may constitute the first observations of plasmons in a Luttinger liquid. To observe these plasmons, the group used scattering-scanning near-field optical microscopy (s-SNOM).

The plasmons are novel in that they appear to have a quantized propagation velocity that depends only on the number of conducting channels. Also, the ratios for the propagation velocities appear to be in the form $1:\sqrt{2}:\sqrt{3}:\sqrt{4}$ for one, two, three and four nanotubes respectively. (Each nanotube has one conducting channel).

The plasmons are extremely well-confined spatially ($\lambda_p/\lambda \sim 1/100$, where $\lambda_p$ and $\lambda$ are the plasmon wavelength and the wavelength of free-space light respectively) and also have a quality factor of $\sim$20. This means that there may be important applications in store for these kinds of plasmons as well, though I find the result from a more fundamental perspective quite intriguing.

## What DO We Know About High Tc?

Many papers on cuprate superconductors start out by saying that we don’t know much about them. About ten years ago, A.J. Leggett wrote down a laundry list of things we do know. Looking at this list, it seems like things are not as bleak as the introductions to papers on cuprates make them out to be! Here is his list of things we knew back in 2006:

1. Superconductivity in the cuprates is a result of Cooper pairing.
2. The main driver of superconductivity in the cuprates is the copper-oxide plane.
3. To a good approximation, Cooper pairs form independently on each layer (even in a multilayered compound) in the cuprates.
4. The net saving of energy in the transition to the superconducting state is not from ionic kinetic energy as in the classic BCS superconductors. (This surprising result in BCS superconductors was shown to be true in this paper.)
5. The spin state is a singlet.
6. The order parameter is of $d_{x^2-y^2}$ symmetry.
7. The size of Cooper pairs is somewhere between 10-30$\text{\AA}$.
8. The pairs are formed from time-reversed partners as in BCS theory.

There is one more aspect of this paper that I think is significant. Leggett stresses the importance of asking questions that are model-independent, such as, (1) What is the pairing symmetry? (2) Does the macroscopic Ginzburg-Landau theory work? and (3) Where is the energy saved in the transition to the superconducting state? Posing questions like these are the “tortoise” method versus developing microscopic theories, which are the “hare’s” method. With the existence of so many microscopic models, it seems to me that taking the “tortoise” path may yield fruit in the long term.

I have been told by a number of my peers that I apparently like lists, which is probably why this article sticks out in my mind. Between the time this article was written and the present, are there any additional items to add to the list? I’m not an expert in high-Tc, so I’m wondering if there is more we now know. Many experimental signatures spring to mind, but none that I would necessarily say that we know “for sure”.