High-Tc Superconductors Are Very Kinky - Update 2

A new update to my first essay on the kink feature in the ARPES spectra of high-Tc superconductors. This time, it could throw a major wrench into the analysis done previously on this high-energy kink feature that has been seen around 500 meV. The new paper[1] disputes the idea that this high energy kink is intrinsic to the band dispersion of the material. Rather, they argued that it is an artifact of the momentum distribution curve (MDC) method. Their analysis of the energy distribution cureve (EDC) does not show the same effect for that energy range.

It would be interesting to see if the previous authors who have done the analysis on this high energy kink would respond to this paper.

Zz.

[1] W. Zhang et al., Phys. Rev. lett. v.101, p.017002 (2008).

High-Tc Superconductors Are Very Kinky - Update 1

Since I last completed the essay on the "kink" that is observed in ARPES spectrum of high-Tc superconductors, I've made 2 updates on the list of references. There have been 2 preprints appearing on arXiv that argued for the phonon origin of this kink. It there does not seem to be any end to this issue in sight, at least for now.

I wonder how the ARPES spectrum for the FeAs-based superconductors are going to look at. I bet many people are scurrying to be the first to report on that, assuming of course that one has a sizable single-crystal sample that can be easily cleaved in vacuum.

Zz.

Death For Phonons In High-Tc Superconductors?

This is a highly interesting and certainly provocative result.

Remember I posted a while back on the "kink" observed in the angle-resolved photoemission spectra (ARPES) on high-Tc superconductors? There have been a continuing debate since the kink was observed on the origin of this observation. Two leading candidates are the coupling of the charge carrier to a spin fluctuation mode, and a coupling to the phonons.

Now two separate theoretical papers have calculated the coupling to the phonon modes and have arrived at the conclusion that such coupling cannot account for the strength of the kink observed in ARPES spectra.

In recent years, despite mounting experimental evidence against it, some physicists have clung on to this interpretation. But now teams from Germany and the US have performed calculations to suggest that lattice vibrations in cuprates can at best account for just a small fraction of the materials’ superconducting behaviour.
.
.
Manske’s team found that the theoretical energy–momentum relationship produced by these calculations did contain a kink — but about a three to five times smaller than the 2001 observations (Phys. Rev. Lett. 100 137001). This is bad news for physicists who have been hoping phonons can account for all of the behaviour of high-temperature superconductors. “It is embarrassing for people to admit they have worked on something for 20 years if it is not true,” jokes Manske.

Meanwhile, Steven Louie and colleagues at the Univerisity of California in Berkeley have come to a similar conclusion with the cuprate LaSrCuO4. From their calculations, the phonon contribution is almost an order of magnitude too small for the observed kink (Nature 452 975).

This could be rather devastating to the phonon picture. If this is true, the two new results still cannot account for the origin of superconductivity, but at least they have eliminated a red herring. Still, all this could be moot if an earlier report is true about the absence of any kind of "glue" in the mechanism for high-Tc superconductors.

So stay tune. The story is by no means over, and the fat lady hasn't even warmed her vocal cords yet.

High-Tc Superconductors Are Very Kinky

In trying to decipher the mysteries of the mechanism that causes superconductivity in high-Tc superconductors (HTS), we have to characterize and understand the many-body interactions that influence the behavior of the charge carriers in these material. In a standard Fermi Liquid theory, these charge carriers are called quasiparticles, and their behavior are described by what is known as the spectral function A(k,E) (i.e. the imaginary part of the single-particle Green's function). The interactions that influence the behavior of these quasiparticles are quantified in the spectral function via the complex self-energy term Σ. The real part of the Σ shows how these collective interactions influences the dispersion relations/band structure of the material (i.e. the E vs. k curves), while the imaginary part of Σ indicates the scattering rate or lifetime of the quasiparticles. For an idealized metal having a non-interacting free-electron gas, the self-energy term is zero. This means that there's no deviation from the non-interacting electronic band structure/dispersion (ReΣ=0) and it has zero scattering rate/infinite lifetime (ImΣ=0).

So if one can actually measure this A(k,E), one can gain a lot of insight into the interactions that influence the behavior of the quasiparticles that are responsible for superconductivity in high-Tc superconductors. One of the ways to make a direct measurement of the spectral function (at least the occupied side of the band) is by using the angle-resolved photoemission spectroscopy (ARPES) technique. In an earlier post, I have highlighted a review of this powerful technique and how it can directly measure A(k,E). This technique has produced very clear signature of the various interactions in a typical metal such as Be[1] and Mo[2], showing very clearly the electron-electron interaction, the electron-phonon interaction, and electron-impurity interaction, all based on the self-energy obtained from ARPES measurement. The parameters obtained from the results, such as the electron-phonon coupling strength, all agree with existing theoretical predictions and previous measurements. So we know that such a technique works.

Because of that, ARPES has been extensively used in the study of HTS. This family of material is high suitable for this technique because of its layered, 2D structure. Furthermore, HTS compounds such as the BSCCO family are easily cleaved in situ along these 2D planes, exposing a pristine surface perfect for photoemission studies. A major progress in ARPES technique came in 1999 whereby not only the energy distribution curve (EDC) at a particular momentum are collected, but also the momentum distribution curve (MDC) at a particular energy can also be obtained simultaneously! This resulted in the collection of a 2D raw data of energy distribution and momentum distribution of the photoelectrons within an energy and momentum window[3]. What is essentially obtained is the dispersion curve. When this technique was done on the BSCCO family, a distinctive feature of a "kink" in the dispersion with an energy scale of around 50 meV was clearly observed[4]. This kink is the deviation of dispersion curve from the non-interacting dispersion, which signifies a coupling to some bosonic mode. By 2001, the race was on to analyze the nature of this kink to see if one can identify this "bosonic mode" that affects the electronic dispersion. This bosonic mode might be the "glue" that holds the Cooper pairs together in the formation of superconductivity.


[Figure shows the "kink", i.e. the deviation from the non-interacting dispersion (Campuzano et al. in The Physics of Superconductors, Vol. II, ed. K. H Bennemann and J. B. Ketterson (Springer, New York, 2004), p. 167-273., or at http://arxiv.org/abs/cond-mat/0209476]


There were three important papers that were published in 2001 that were the first to analyze the origin and nature of this kink[5,6,7]. Two different groups arrive at roughly the same conclusion - that the kink seems to indicate a coupling to a magnetic (spin) bosonic mode[5,6], while the Stanford group[7] proposed the phonon as the origin of the kink. There have been many publications since then arguing for various scenario for the origin of this kink and until today, there is no overwhelming consensus for either the magnetic, although my quick review of this matter seems to indicate that there are more publications related to ARPES experiment in favor of the magnetic channel [8,9]. Still, the phonon picture has many strong advocates and the issue isn't settled even to this date.

But that is not the end of the story. It appears that the high-Tc cuprate familyis even kinkier than first thought. There seems to be, in addition to the low energy kink (now regarded to be between 50 to 70 meV scale), a higher energy kink in the dispersion has been discovered. It was reported, in succession within the span of a couple of weeks, by 2 papers in Phys. Rev. Lett.[10,11]. This new kink occurs at an energy scale of around 340 meV, so it is considerably larger than the low energy kink. The latter concluded that this new high energy kink is consistent with coupling to the magnetic (spin excitation) mode.

Since then, there have been even more reports on high energy kink[12], and this one is even at a different energy scale (115 and 150 meV) and the authors are suggesting that these may be due to neither spin fluctuation nor phonon modes.

Moral of the story: the high-Tc family of material is very kinky, and that the study on the origin of these kinks could hold a vital clue on the mechanism of superconductivity in these materials. However, the issue is highly complicated, especially when new discoveries are continually being made as one tries to solve the old ones. Whether these kinks are due to coupling to the magnetic mode, phonon modes, or neither, remains to be seen. A lot more work is still to be done.

Zz.

Edit (04/10/08): A new preprint on arXiv[13] has appeared that studied the phonon mode in La doped Bi-cuprate compound. The result supports the electron-phonon coupling as the source of the kink in the cuprate superconductor.

Edit (06/10/08): A new preprint on arXiv[14] has studied the phonon dispersion in on of the Bi cuprate family using inelastic X-ray scattering. They found a significant phonon softening that's consistent with the same energy and momentum scale as the kink observed in the ARPES result. So this argues for the phonon origin of the kink.

Edit (07/02/08): This is getting to be quite interesting. A new PRL paper[15] has just been published, arguing that the high energy kink is more of an artifact of the MDC analysis, and that the EDC spectra provides a more accurate information about the band dispersion in high-Tc superconductors. So this certainly calls into question the conclusion made in previous papers on this high-energy kink.

Zz.

[1] S. LaShell et al. Phys. Rev. Lett. v.61, p.2371 (2000).
[2] T. Valla et al., Phys. Rev. Lett. v.83,p.2085 (1999).
[3] T. Valla et al., Science v.285, p.2110 (1999).
[4] P.V. Bogdanov et al., Phys. Rev. Lett. v.85, p.2581 (2000).
[5] P.D. Johnson et al., Phys. Rev. Lett. v.87, p.177007 (2001).
[6] A. Kaminski et al., Phys. Rev. Lett. v.86, p.1070 (2001).
[7] A. Lanzara et al., Nature v.412, p.510 (2001).
[8] A.A. Kordyuk et al., Phys. Rev. Lett. v.92, p.257006 (2004); A.A. Kordyuk et al., Phys. Rev. Lett. v.97, p.017002 (2006).
[9] A. Macridin et al., Phys. Rev. Lett. v.99, p.237001 (2007).
[10] B.P. Xie et al., Phys. Rev. Lett. v.98, p.147001 (2007).
[11] T. Valla et al., Phys. Rev. Lett. v.98, p.167003 (2007).
[12] http://arxiv.org/abs/0711.1706.
[13] http://arxiv.org/abs/0804.1372
[14] http://arxiv.org/abs/0804.1372
[15] W. Zhang et al., Phys. Rev. lett. v.101, p.017002 (2008).

"Violating" Einstein's Photoelectric Effect

One of the most spectacular theoretical description that Einstein had ever produced is the corpuscular nature of light that he used in his 1905 photoelectric effect paper. In fact, there have been arguments put forth that of all of his 1905 papers, the one proposing this model for light is what is truly most revolutionary, even more than his special relativity theory.

In case you need a refresher, the photoelectric effect experiment is where you shine light onto a surface of a material (typically a metal). If the light has a sufficient "energy", then photoelectrons are emitted. What was puzzling before the 1900s was that light, as understood as a wave via the Maxwell Equations, seemed to not be behaving the way it should within this photoelectric effect experiment. The energy of the light wave was tied to its intensity - the larger the intensity, the larger the energy. Yet, in the photoelectric effect experiment, there were two puzzling observations:

1. As one increases the intensity, the energy distribution of the emitted photoelectrons does not change. Electrons are not emitted with more energy. Rather, increasing the intensity simply increases the number of electrons being emitted. The energy distribution remains the same as before.

2. If the frequency of the light is below some value, then no matter how intense the light is, no electrons is emitted.

Einstein took those two puzzling observations and reformulated the light description, tying the frequency, not the intensity, to the energy of light. Not only that, he proposed that light's energy comes in discrete quantum (photon). He then proposed a simple description of the photoelectric effect experiment:

KE = hf - F

where KE is the kinetic energy of the emitted photoelectrons, hf is the energy of each photon (f is the frequency of light and h is the Planck constant), while F is what is known as the work function of the material. When the photoelectric effect is defined this way, then a natural explanation for both #1 and #2 is obtained. Since light's energy only depends on the frequency, increasing the intensity does nothing to the energy of each photon. The intensity only affects the rate of photons being emitted, thus that explains why we obtain more photoelectrons, but with the same energy distribution. And if the frequency of light is less than the work function F, then no matter how intensity it is, it is still less than F and therefore unable to produce any photoelectrons.

This photoelectric effect description was soon experimentally verified by Millikan (who initially was very skeptical of Einstein's description, but later on admitted that all of the experiments seemed to point to its validity). Since then, Einstein's formulation of what light is has certainly been verified and accepted many times over, and is the only description of light being used in many advanced application such as photoemission spectroscopy.

Still, does this mean that we do not have any evidence that this description can be "violated"? I'm putting "violated" in quotes because, as I'll explain later on, it turns out that, as is the case in many areas of physics, the photoelectric effect description of Einstein is only the simplest, most naive description of a "single-photon" emission. What this implies is that we have several situation where the Einstein's photoelectric effect equation can be "violated".

There are two different types of experiments where this can be done.

A. The Schottky effect type experiment.

This type of experiment was done[1] even way back in the 20th century, even by giants in physics such Ernest Lawrence[2]. This is where the same photoelectric effect experiment was done, but in a rather high external accelerating electric field. This field is applied usually perpendicular to the metal's surface in the direction that will accelerate the emitted electrons away from the metal's surface. What is observed here is that one can in fact observe emission of electrons even when the energy of the photons are LESS than the work function (violation of #2 above). What is going on here is that the applied electric field acts in such a way that it lowers the effective work function of the metal. The photons with a lower energy can start to emit electrons even below the metal's bulk work function.

B. Multiphoton photoemission.

This discovery occurs especially after lasers were invented, and high intensity monochromatic light sources become easily available. What is observed in these experiments is that, even without applying any high fields to the metal (i.e. no lowering of the effective work function), one can still get photoelectrons even using photons with energy lower than the work function, especially when one increases the intensity of the light source by a lot. This again violates #2. A very simple explanation for this is that, with highly intense light source such as those coming from a laser, one can induce a multiphoton photoemission process.[3,4] This is where the first photon excites an electron in the metal's conduction band to an intermediate state. Normally, its lifetime in the femtosecond range would cause it to decay back down. But with a highly intense light source, the probability of another photon being absorbed by that excited electron before it decays becomes significant. Thus, if you have a light source with photon energy just slightly more than half of the work function, there is a non-negligible probability that you can now have an emission of electron due to the absorption of 2 photons. One can easily imagine this being done for 3, 4, etc.. photons. Of course, the probability of emission with higher number of photons is significantly lower.

So here, I've just described two different ways of violating Einstein's photoelectric effect description[5]. So does this mean that we should try to get the Nobel committee to revoke Einstein's prize? Does this mean that the photoelectric effect description is no longer valid?

NO!

The most significant consequence of Einstein's photoelectric effect description - the photon - is STILL valid and very much alive. In fact, the multiphoton experiments could not be easily explained without using the concept of photons. What we know now is that the Einstein's description is valid only for the simplest case - an emission of electron using single photons only, i.e. single-photon photoemission and under a revised definition of the work function being the EFFECTIVE work function, rather than the original bulk work function. As with other aspects of physics, we make progress in the study of an area, and now we know more of what we didn't know then. Einstein's work opened the pathways to viewing light in a different way. Without such insight, most of what we know now in this area would not have been possible. Just as Newtonian mechanics became more of an approximation (albeit a valid one at our normal scales), the Einstein's equation also became more of a special case valid for the simplest situation.

Zz.

[1] E. Guth and C.J. Mullin, Phys. Rev. v.59, p.867 (1941).
[2] E.O. Lawrence and L.b. Linford, Phys. Rev. v.36, p.482 (1930).
[3] K. Giesen et al., Phys. Rev. Lett. v.55, p.300 (1985).
[4] W.S. Fann et al., Phys. Rev. B v.44, p.10980 (1991).
[5] There is actually another way, via heating the metal. See, for example, R.H. Fowler, Phys. Rev. v.38, p.45 (1931).

Modern Theory and Applications of Photocathodes

I wrote a while back on the legacy of Bill Spicer, a name that you may not have heard, but whose influence probably have affected your life in some way. One of such ways is the scenario where there are just some papers, no matter how old they are, that continue to be used, cited, and scrutinized. These papers continue to be highly relevant even today.

One such paper is this one, published in 1993, and written by Spicer and Herrera-Gomez. It deals with the physics of photocathodes. For those of us in the accelerator physics field, this paper continues to be cited and studied when we deal with photocathodes for particle accelerators. Other than Sommer's Photoemissive Material text, this paper is a tour de force in almost everyone one needs to know about basic photoemission (not angle-resolved or resonant etc.) processes that are relevant in a photoinjector.

As I've said before, this is roughly what Spicer started with when he delved into photoemission physics. It is fitting that, to this day, his work still has relevance in that field of study.

Zz.

Phonons and High-Tc Superconductors

There seems to be a rather interesting development in this issue during this past week. But first, a little bit of a very, very short history on this.

The whole "holy grail" of superconductivity (and condensed matter physics, in general) is finding the "glue" that causes pairing in the high-Tc superconductor family. This glue will be the direct mechanism that causes this phenomenon in these material, very much like phonon being the pairing glue of conventional superconductors.

Currently, there are two competing scenarios for the possible candidates for this glue: phonons and magnetic interactions. While these two scenarios have been floating around for a while as the possible mechanism for high-Tc superconductors, they both came to a head-on clash with the publications of 3 papers in the same year. The papers by Kaminsky et al.[1] and Johnson et al.[2] support the idea that the magnetic channel is responsible for the electronic properties in these superconductors and thus, is the responsible mechanism for superconductivity. On the other hand, the paper by Lanzara et al.[3] argued for the phonon mechanism in the same material. What is interesting here is that all three papers essentially are looking at the same type of experimental results! All of them are studies using angle-resolved photoemission spectroscopy (ARPES), and all of them are looking in particular at the "kink" feature along the nodal direction of the reciprocal space of the material, with varying doping! So what you have here is the same type of experimental results, with 2 different interpretations.

While there have been many papers arguing for both phonons and magnetic interactions since then, two recent papers have appeared in Nature that made definite claims for the phonons being the responsible glue. The first one, published in 2004, was a new ARPES study of the isotope effect in the bismuth cuprate superconductor.[4] Now, while the isotope effect has been found to influence the value of the critical temperature Tc in conventional superconductors, such an observation isn't found in high-Tc superconductors, which was the initial impetus for many to drop the phonon mechanism in these material. However, this paper showed that there is a large effect on the electronic structure seen in the ARPES result when an isotope substitution was made (i.e. changing O16 to O18). This was seen in the high energy broad "hump" in the spectrum.

A new rebuttal of that paper was just published this week that repeated the same measurement (and more), and found no such effect.[5] While they do not claim to dispute the phonon picture, they certainly threw doubt into the experimental results of the earlier paper.

The second paper that also originally supported the phonon mechanism was based on results from scanning tunneling microscopy (STM).[6] Here, again, the energy scale of the "dip-hump" feature that is common in tunneling results was examined as a function of substitution between O16 and O18 isotopes. The authors argue that the "mode frequency" changes dramatically with such substitution, and such dependence argues for the phonons as the source that this mode.

This interpretation too is disputed. A new paper has argued that the tunneling results that was seen was primarily due to the inelastic tunneling effect.[7] It is argued that the paper was probing the excitation of the apical oxygen that resides in the insulating later, and not the conducting Cu-O plane where superconductivity is believed to occur.

Moral of the story: the phonon picture is far from having any convincing results that would make this as the pairing glue.

Zz.

[1] Kaminsky et al., PRL 86, 1070 (2001).
[2] Johnson et al., PRL 87, 177007 (2001).
[3] Lanzara et al., Nature 412, 510 (2001).
[4] Gweon et al., Nature 430, 187 (2004).
[5] Douglas et al., Nature 446, E5 (2007).
[6] Lee et al., Nautre 442, 546 (2006).
[7] Hwang et al., Nature 446, E3 (2007).

Mottness

Phillip Phillips has a very good review of the normal state of the cuprate superconductors. One may wonder on why we care about the normal state behavior when what we want is what is causing it to be superconducting. Well, as with the conventional superconductor, the normal state tends to give us a lot of clues on what exactly is going on as one approach the superconducting regime. By looking at various parameters in the normal states, we can see how they evolve and maybe give us hints on the cause of the onset of superconductivity in these materials.

One of the interesting aspect of the normal state is the resistivity behavior. The linear resistivity as a function of temperature is seen almost over the whole doping range. While such a thing is predicted within the phenomenological model of a Marginal Fermi Liquid, it actually provides a strong argument for quantum criticality in the phase diagram of this material. This is illustrated in Fig. 1 of the article.

However, I don't believe that there has been a clear evidence of, say a highly overdoped cuprate that goes from the superconducting state into a Fermi Liquid State, and then into a Strange Metal state as one raises its temperature. I think there have been a few evidence that there might be 2 different gap scales in the underdoped cuprates, so this certainly matches that part of the phase diagram. But the overdoped part isn't clear. In angle-resolved photoemission on the overdoped cuprates, the coherent peak, representing the presence of well-defined quasiparticle states, survives till very high temperatures (150K or so). I don't think there's any evidence yet that the peak disappears abruptly as it crosses from the Fermi Liquid regime into the Strange Metal regime. We expect this to occur because for optimally doped cuprates, its normal state is the Strange Metal. As soon as the material goes above Tc, the quasiparticle peak disappears promptly.

The mystery continues...

Zz.

Completing the Circle

Recently, one of the giants of condensed matter physics, Bill Spicer, passed away.

Again, this is one of those names that most people have never heard of (like Bardeen), and yet, his contribution to the advancement of knowledge is so immense, the results of his effort are being used by practically everyone! Best known for his development of the photoemission spectroscopy (especially angle-resolved photoemission) that is now one of the most important technique in condensed matter physics - the 3-step model of photoemission has always been known as the Spicer 3-step model. He left a huge legacy at Stanford where he has established not just a world-renown photoemission center, but his students have continued to expand the field and carried on his work.

I'm bringing this up because of a rather interesting coincidence. Bill Spicer, when he first started out developing the photoemission technique, studied photocathodes used to produce electrons for accelerators, synchrotrons, etc. One of his very last Ph.D students at Stanford before he retired became my postdoctoral supervisor. So after working in doing photoemission work for 2 1/2 years, when I informed my postdoc boss that I will be leaving to take a job at an accelerator facility to study and make photocathodes, he looked surprised and said "Well, that has gone full circle now, hasn't it?"

We both knew what he meant. What started with Spicer working with photocathodes, then evolved into a powerful technique to study a wide range of materials, came into its full potential with the discovery of high-Tc superconductors, then having the Spicer's legacy and pedigree passed down to his students, and indirectly, I acquired his influence through one of his students, and now I'm bringing it back to where it all started.

Being a physicist, I am constantly aware of all the great people who have made the progress I've seen and taken for granted. These are not the names that most people recognize, yet they have contributed to a tremendous amount of advancement in knowledge. In some small part of me, I know I'm carrying the legacy of Bill Spicer even though I've never met him. To know that I am going to use what he has help developed in going back to work in an area he started with is very humbling. I can only hope that I do justice to what he has left behind.

Zz.

Photoemission Spectroscopy

Sometime, when a phenomenon is so well-known and well-understood, we often use it to study other things. X-ray diffraction is one example. Another is photoemission/photoelectric effect.

Photoemission is the extension of our understanding of the photon picture of light. Ever since Hertz's discovery of the photoelectric effect phenomena, Einstein's theoretical photon model, and Millikan's subsequent verification of the Einstein's photon model, this effect has been so well-tested and understood that today, we use it to study other things. In particular, photoemission, in its various forms, is used to study the electronic properties of solids, such as metals, semiconductors, superconductors, etc. In fact, the clearest verification of the validity of the band structure of solids came from photoemission spectroscopy.

The progress in this experimental technique evolved rather spectacularly after the discovery of the high-Tc superconductors. Having the 2D layers of copper-oxide planes where most of the superconducting effects are thought to occur, these made them a natural candidate to be studied by photoemission, especially using a technique called angle-resolved photoemission.

It is imperative to point out that ALL of the theory of photoemission, including those applied in the study of materials that we are now using in modern electronics, make use of ONLY the photon picture of light. There has been NO other alternative formulation of light to account for the experimental observations of photoemission spectroscopies. NONE.

There are two very good reviews of the usage of the photoemission technique on superconductors. The identical technique is also used on other materials.

http://arxiv.org/abs/cond-mat/0209476 (exact reference: The Physics of Superconductors, Vol. II, ed. K. H Bennemann and J. B. Ketterson (Springer, New York, 2004), p. 167-273.)

http://arxiv.org/abs/cond-mat/0208504

Zz.