Abrikosov and the path to understanding high-Tc superconductivity
An early attempt to try to understand the high superconducting transition temperatures in the cuprate super-conductors was Abrikosov's theory of extended Van Hove singularities. It was based on our early experimental data on the YBa₂Cu₃O₆.₉ and YBa₂Cu₄O₈ compounds which showed an extended saddl...
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Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2018
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| Цитувати: | Abrikosov and the path to understanding high-Tc superconductivity / Juan Carlos Campuzano // Физика низких температур. — 2018. — Т. 44, № 6. — С. 658-662. — Бібліогр.: 16 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859733020955639808 |
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| author | Juan Carlos Campuzano |
| author_facet | Juan Carlos Campuzano |
| citation_txt | Abrikosov and the path to understanding high-Tc superconductivity / Juan Carlos Campuzano // Физика низких температур. — 2018. — Т. 44, № 6. — С. 658-662. — Бібліогр.: 16 назв. — англ. |
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| container_title | Физика низких температур |
| description | An early attempt to try to understand the high superconducting transition temperatures in the cuprate super-conductors was Abrikosov's theory of extended Van Hove singularities. It was based on our early experimental data on the YBa₂Cu₃O₆.₉ and YBa₂Cu₄O₈ compounds which showed an extended saddle point singularity in the dispersion of the electronic excitations. This appeared to lead to a Van Hove singularity in the density of states with a divergence stronger than the known logarithmic one observed in conventional materials. The consequent high density of states of the extended singularity was thought to lead to high Tc's in a conventional BCS mechanism. Unfortunately, it was soon realized that the very incoherent nature of the electronic excitations in these materials did not provide the expected high density of states. Here we summarize the many unusual characteristics of the electronic excitations in the cuprates, and what they imply for a possible theoretical description of hight-temperature superconductivity.
|
| first_indexed | 2025-12-01T14:01:10Z |
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Low Temperature Physics/Fizika Nizkikh Temperatur, 2018, v. 44, No. 6, pp. 658–662
Abrikosov and the path to understanding high-Tc
superconductivity
Juan Carlos Campuzano
Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607, USA
E-mail: jcc@uic.edu
Received January 5, 2018, published online April 25, 2018
An early attempt to try to understand the high superconducting transition temperatures in the cuprate super-
conductors was Abrikosov's theory of extended Van Hove singularities. It was based on our early experimental
data on the YBa2Cu3O6.9 and YBa2Cu4O8 compounds which showed an extended saddle point singularity in the
dispersion of the electronic excitations. This appeared to lead to a Van Hove singularity in the density of states
with a divergence stronger than the known logarithmic one observed in conventional materials. The consequent
high density of states of the extended singularity was thought to lead to high Tc's in a conventional BCS mecha-
nism. Unfortunately, it was soon realized that the very incoherent nature of the electronic excitations in these
materials did not provide the expected high density of states. Here we summarize the many unusual characteris-
tics of the electronic excitations in the cuprates, and what they imply for a possible theoretical description of
hight-temperature superconductivity.
PACS: 74.72.–h Cuprate superconductors;
74.25.Jb Electronic structure.
Keywords: cuprates, normal state, ARPES.
1. Introduction
When high-temperature superconductivity burst into the
scene in 1986, many mechanisms were proposed to explain
this remarkable phenomena, including the presence of a Van
Hove singularity near the Fermi energy [1–4]. With this
motivation, we examined the electronic structure in the two
cuprate superconductors YBa2Cu3O6.9 and YBa2Cu4O8 by
angle-resolved photoemission, and found an “extended”
saddle point singularity in the energy spectrum in the neigh-
borhood of the (0, )π point [5]. This singularity occurs in
the band derived from the CuO2 planes at a binding energy
of less than 30 meV [6].
Figure 1(a) shows the observed experimental band
structure obtained along the (0,0) (0,2 )→ π symmetry
line for the YBa2Cu3O6.9 and YBa2Cu4O8. It can be seen
that a band disperses towards the Fermi energy, but does
not cross it, remaining instead at a very small binding
energy of ≈ 30 meV, as determined from the position of
the highest intensity in the peak. The peak width is very
narrow, being limited entirely by the instrumental resolu-
tion available at the time, again indicating that at these
values of , ,x yk k the band bottom is close to EF, as
shown in Fig. 1(b). We found that there is no observable
dispersion along zk [7] for optimally doped samples, as
shown in Fig. 2. This peak had been observed before by
Manzke et al. [8] and Tobin et al. [9], although the nature
of the singularity had not been appreciated [6]. A sche-
matic representation of the experimental band structure is
shown in Fig. 1(c).
2. Extended Van Hove model, and why it does not work
The experiment thus shows that is a saddle point singu-
larity at the zone edge. The idea [5] was that the Van Hove
singularity arising from such a saddle point increases the
density of states, and therefore cT . Van Hove singularities
had been considered before (see, for example, Refs. 1–4),
although the consequences of an extended singularity had
not been considered. Another characteristic of the cuprate
superconductors that needed to be accounted for was the
suppression of the isotope effect, due to the fact that the
integration limits in this case are determined not by the
Debye frequency, but by the limits of the singularity, i.e.,
by some electronic energy scale. Even at the time of the
publication of the Abrikosov paper [5], we pointed out that
we were aware of the unusual nature of the normal state,
which we intended to examine in a subsequent paper.
© Juan Carlos Campuzano, 2018
Abrikosov and the path to understanding high-Tc superconductivity
However, that paper was not published. We later realized
that the extended Van Hove singularity scenario did not in
fact lead to a high cT .
The reason for this, pictured in Fig. 3, is that the peaks
near the Fermi energy are quite broad above cT , of order
200 meV FWHM. The overlap of the particle and hole
wavefunctions does not therefore lead to a high density of
states. Here we find the first problem with the normal
state of the cuprates, in that a BCS model cannot lead to
superconductivity.
3. Properties of the normal state of the HTSCs
There are many other properties of the electronic exci-
tations in the normal state of the cuprates which are most
unusual and difficult to understand. Moreover, there is no
know path to a change in the nature of the electronic exci-
tations going from the normal to the superconducting state.
We will now summarize the properties of the elementary
excitations of the normal state using symmetryzed angle
resolved photoemission (ARPES) data, obtained as follows
[11]: The ARPES intensity ( , )I k ω is proportional to
( ) ( , ),f A kω ω where A is the spectral function, and f is
the Fermi function [10]. The effect of f can be eliminated
from the ARPES data using the assumption of particle-hole
symmetry ( , ) = ( , )k kA A−ε −ω ε ω for small | |ω . Within
the small k-window centered at Fk , one can show that the
symmetrized intensity ( ) ( )I Iω + −ω at Fk is simply the
Fig. 1. (Сolor online) Dispersion of the single band important in the HTSC problem: (a) from the Brillouin zone center to the zone edge; (b)
along the zone edge; and (c) a schematic representation of the dispersion.
Fig. 2. (Сolor online) Dispersion along the direction perpendicular to the CuO2 planes for (Bi,Pb)2(Sr,La)2CuO6+δ samples vs. photon
energy for the values of Tc's indicated. The small dispersion of 10 meV along the kz direction observed in an OD 0 K sample disappears
with decreasing hole concentration. Note the very flat saddle point dispersion for the optimally doped sample. From Ref. 7.
Low Temperature Physics/Fizika Nizkikh Temperatur, 2018, v. 44, No. 6 659
Juan Carlos Campuzano
spectral function (convolved with the resolution). Results
obtained from symmetrized data agree with those obtained
from the leading edge of the raw data [11].
The varied and unusual properties of the electronic exci-
tations around the phase diagram are summarized in Fig. 4
[13]. Figure 4(a) shows the temperature-doping phase dia-
gram of BISCO. The points correspond to some of the data
shown here. Unless stated otherwise, the data shown here
were obtained at the antinode, where in the superconducting
state the gap is maximum.
In Fig. 4(b) we show the electron spectral function in the
region shaded pale red, dubbed the “strange metal” region,
where the spectral function does not depend on temperature
or doping. They can all be described by the same Lorentzian
function, modulo an amplitude factor. This behavior is quite
unusual, since normally doping strongly alters the charge
screening radius, which in turn alters the lineshape. Since
these spectra are much wider than temperature, perhaps it is
not surprising neither doping nor temperature play a role in
determining the lineshape. These facts lead us to think that
the spectral functions do not correspond to usual quasi-
particle excitations, but rather to collective excitations,
whose nature still remains to be determined.
While the spectral function is invariant in the strange
metal region, as the temperature is lowered, it evolves into
spectral functions of quite different nature at different dop-
ing values. For example, the excitations which are to the left
of optimal doping acquire a “pseudogap” at a crossover
temperature *,T as shown in Fig. 4(b) [12]. The pseudogap
Fig. 3. (Color online) Effective umklapp is not favored by very
incoherent excitations.
Fig. 4. (Color online) Electronic excitation spectra at the point of maximum gap along the Fermi surface.
660 Low Temperature Physics/Fizika Nizkikh Temperatur, 2018, v. 44, No. 6
Abrikosov and the path to understanding high-Tc superconductivity
becomes more pronounced as either the doping decreases or
the temperature is lowered. Once the superconducting phase
transition takes place, the pseudogap turns into the super-
conducting gap at cT .
On the other hand, strange metal excitations on the right
of optimal doping evolve into Fermi-liquid quasiparticle
excitations at a temperature coh ,T as shown in Fig. 4(c).
Not surprisingly, the onset of Fermi-liquid behavior occurs
at progressively higher coherence temperatures as the dop-
ing increases and charge screening also increases.
What is not expected however, is that the *T and cohT
lines cross, defining a region of the phase diagram where
the pseudogap and coherent excitations coexist, as exem-
plified by the spectra shown in Fig. 4(e). Sharp peaks cor-
responding to coherent excitations appear at the edges of
the pseudogap. The crossing of the *T and cohT lines is
unlike many sketches in the literature, where the two lines
do not cross. Also, in our phase diagram the *T line is
tangent to the cT dome.
An additional property of the pseudogap is that at its on-
set, it exists over a region of the Fermi surface near the anti-
nodes of the superconducting gap, as shown in Fig. 5
[15,14]. The rest of the Fermi surface forms arcs, unex-
pected because in metals, the Fermi surface is continuous.
These arcs contract as the temperature is lowered, and turn
into the point nodes of the superconducting state (Fig. 5(a)).
The Fermi arcs scale, becoming smaller as the doping de-
creases [15].
Once the doping is sufficiently low, such that = 0,cT
the material becomes a nodal metal [16], a most unusual
state, where the entire Fermi surface is gapped, except for
the four protected point nodes, as shown in Fig. 4(f).
From the brief descriptions of the excitations in the
normal state of the cuprate superconductors, it is clear
that the formulation of a theory that accounts for all the
amazing phenomena described above will be a monu-
mental task.
The work summarized here could not have possibly
come to fruition without each one of the experimental
collaborators over nearly three decades, each having
played crucial roles in the study of the cuprate supercon-
ductors. However, I would like to particularly thank theo-
reticians Alexei Abrikosov, Mohit Randeria and Michael
Norman, who had the most impact in helping us experi-
mentalists understand the significance of our results.
________
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Fig. 5. (Color online) Electronic excitations around the Fermi
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Juan Carlos Campuzano
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662 Low Temperature Physics/Fizika Nizkikh Temperatur, 2018, v. 44, No. 6
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1. Introduction
2. Extended Van Hove model, and why it does not work
3. Properties of the normal state of the HTSCs
|
| id | nasplib_isofts_kiev_ua-123456789-176149 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 0132-6414 |
| language | English |
| last_indexed | 2025-12-01T14:01:10Z |
| publishDate | 2018 |
| publisher | Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України |
| record_format | dspace |
| spelling | Juan Carlos Campuzano 2021-02-03T19:03:20Z 2021-02-03T19:03:20Z 2018 Abrikosov and the path to understanding high-Tc superconductivity / Juan Carlos Campuzano // Физика низких температур. — 2018. — Т. 44, № 6. — С. 658-662. — Бібліогр.: 16 назв. — англ. 0132-6414 PACS: 74.72.–h, 74.25.Jb https://nasplib.isofts.kiev.ua/handle/123456789/176149 An early attempt to try to understand the high superconducting transition temperatures in the cuprate super-conductors was Abrikosov's theory of extended Van Hove singularities. It was based on our early experimental data on the YBa₂Cu₃O₆.₉ and YBa₂Cu₄O₈ compounds which showed an extended saddle point singularity in the dispersion of the electronic excitations. This appeared to lead to a Van Hove singularity in the density of states with a divergence stronger than the known logarithmic one observed in conventional materials. The consequent high density of states of the extended singularity was thought to lead to high Tc's in a conventional BCS mechanism. Unfortunately, it was soon realized that the very incoherent nature of the electronic excitations in these materials did not provide the expected high density of states. Here we summarize the many unusual characteristics of the electronic excitations in the cuprates, and what they imply for a possible theoretical description of hight-temperature superconductivity. The work summarized here could not have possibly come to fruition without each one of the experimental collaborators over nearly three decades, each having played crucial roles in the study of the cuprate superconductors. However, I would like to particularly thank theoreticians Alexei Abrikosov, Mohit Randeria and Michael Norman, who had the most impact in helping us experimentalists understand the significance of our results. en Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України Физика низких температур Специальный выпуск К 90-летию со дня рождения A.A. Абрикосова Abrikosov and the path to understanding high-Tc superconductivity Article published earlier |
| spellingShingle | Abrikosov and the path to understanding high-Tc superconductivity Juan Carlos Campuzano Специальный выпуск К 90-летию со дня рождения A.A. Абрикосова |
| title | Abrikosov and the path to understanding high-Tc superconductivity |
| title_full | Abrikosov and the path to understanding high-Tc superconductivity |
| title_fullStr | Abrikosov and the path to understanding high-Tc superconductivity |
| title_full_unstemmed | Abrikosov and the path to understanding high-Tc superconductivity |
| title_short | Abrikosov and the path to understanding high-Tc superconductivity |
| title_sort | abrikosov and the path to understanding high-tc superconductivity |
| topic | Специальный выпуск К 90-летию со дня рождения A.A. Абрикосова |
| topic_facet | Специальный выпуск К 90-летию со дня рождения A.A. Абрикосова |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/176149 |
| work_keys_str_mv | AT juancarloscampuzano abrikosovandthepathtounderstandinghightcsuperconductivity |