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.

Edit (12/22/08): A new theoretical analysis using parameters from the inelastic neutron scattering experiment has produced a model that can explain all the ARPES results[16]. It points to the incommensurate spin excitation as the dominant scattering mechanism.

Edit (02/26/09): A new manuscript has just appeared that compares the high energy kinks between the electron-doped cuprate with the hole-doped cuprates[17].

Edit (04/14/09): A manuscript has appeared that discussed the possibility that the high energy kink in the Bi-cuprates might be due to an artifact of the matrix element. The calculation produced showed that it isn't, and that this kink points to the coupling of the quasiparticles to the electronic mode [18].

Edit (06/16/09): A manuscript appeared today calculating the phonon contribution to the kink[19]. They concluded that phonons only contribute ~10% to the kink, while non-phonon sources contribute to the other 90%.

Edit (08/05/09): A PRL paper on ARPES measurement of single layer, bilayer, and trilayer Tl-family of high-Tc cuprate[20] shows that the kink has a momentum dependence as one changes the number of CuO planes per unit cell. The authors claim that this is not consistent with magnetic coupling scenario, and thus, seems to point to the electron-phonon coupling as the origin of the band renormalization (i.e. the kink).

Edit (02/02/10): A preprint on arXiv has reported a high-resolution, laser-based ARPES measurement on heavily overdoped (Bi,Pb)2Sr2CuO6. The report claims that the 70 meV kink along the nodal direction is due to coupling to multiple phonon modes[21].

Edit (02/15/10): 2 new reports on a new kink in the band dispersion of Bi2212. This kink is ~8 meV below the gap energy and may be tied to the optical phonon mode[22,23]

Edit (05/24/10): A new theoretical analysis of the low and high energy kink in the cuprates have revealed that these kinks can be reproduced by phonons using the extended Eliasberg theory [24]

Edit (01/10/11): An analysis of the low energy kink has attributed it to an in-plane acoustic phonon branch[25].

Zz.

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[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).
[16] T. Dahm et al., http://arxiv.org/abs/0812.3860.
[17] M. Ikeda et al., http://arxiv.org/abs/0902.4280
[18] S. Basak et al., http://arxiv.org/abs/0904.1749
[19] E. Schachinger et al., http://arxiv.org/abs/0906.2627.
[20] W.S. Lee, Phys. Rev. Lett. v.103, p.067003 (2009).
[21] L. Zhao et al. http://arxiv.org/abs/1002.0120
[22] J.D. Rameau et al. Phys. Rev. B v.80, p.184513 (2009) http://arxiv.org/abs/1002.1990
[23] I.M. Vishik et al., Phys. Rev. Lett. v.104, p.207002 (2010) http://arxiv.org/abs/1002.2630
[24] E.A. Mazur http://arxiv.org/abs/1005.3930
[25] S. Johnston et al., http://arxiv.org/abs/1101.1302