Gap symmetry and charge density excitations in high-Tc superconductors with extended saddle points in electron spectrum
It is shown that the strong anisotropy of the one-particle electron spectrum, due to the presence of extended saddle-point features (ESPF) close to the Fermi level in the hole-type cuprates YBCO and BSCCO, leads to the occurrence of a low-frequency peak in the spectral function of the charge dens...
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Інститут фізики конденсованих систем НАН України
1999
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| Назва видання: | Condensed Matter Physics |
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| Цитувати: | Gap symmetry and charge density excitations in high-Tc superconductors with extended saddle points in electron spectrum / E.A. Pashitskii, V.I. Pentegov, A.V. Semenov // Condensed Matter Physics. — 1999. — Т. 2, № 3(19). — С. 453-462. — Бібліогр.: 13 назв. — англ. |
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irk-123456789-1205262017-06-13T03:05:09Z Gap symmetry and charge density excitations in high-Tc superconductors with extended saddle points in electron spectrum Pashitskii, E.A. Pentegov, V.I. Semenov, A.V. It is shown that the strong anisotropy of the one-particle electron spectrum, due to the presence of extended saddle-point features (ESPF) close to the Fermi level in the hole-type cuprates YBCO and BSCCO, leads to the occurrence of a low-frequency peak in the spectral function of the charge density fluctuations due to the presence of acoustic plasmon branch in the collective electron spectrum. The retarded anisotropic electron-plasmon interaction leads to the suppression of the static screened Coulomb repulsion for small transferred momenta and, consequently, to the effective attraction between electrons in the dx²-y²-wave channel of the Cooper pairing of current carriers. Breaking of C₄v symmetry in YBCO crystals leads to a possibility of a change of dx²-y²-wave symmetry of the gap to a mixed s − d gap symmetry for singlet Cooper pairs or to a p-wave gap symmetry for triplet pairs. Показано, що сильна анізотропія одночасткового електронного спектру веде, завдяки наявності подовжених сідлових особливостей біля рівня Фермі у купратах YBCO та BSCCO, до появи низькочастотного піку у спектральній функції флуктуацій зарядової густини, що є наслідком присутності гілки акустичних плазмонів у колективному електронному спектрі. Електрон-плазмонна взаємодія веде до значного зменшення статичного кулонівського відштовхування в області малих переданих імпульсів та, як наслідок, до ефективного притягнення між електронами у dx²-y²-хвильовому каналі куперівського спарювання носіїв струму. Порушення C₄v симетрії у кристалах YBCO призводить до можливості заміни dx²-y²-хвильової симетрії надпровідної щілини на змішану s − d симертрію для сінглетних куперівських пар або на p -хвильову симетрію щілини для триплетних пар. 1999 Article Gap symmetry and charge density excitations in high-Tc superconductors with extended saddle points in electron spectrum / E.A. Pashitskii, V.I. Pentegov, A.V. Semenov // Condensed Matter Physics. — 1999. — Т. 2, № 3(19). — С. 453-462. — Бібліогр.: 13 назв. — англ. 1607-324X DOI:10.5488/CMP.2.3.453 PACS: 74.20.-z, 74.72.-h, 74.72.Hs http://dspace.nbuv.gov.ua/handle/123456789/120526 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
It is shown that the strong anisotropy of the one-particle electron spectrum,
due to the presence of extended saddle-point features (ESPF) close to the
Fermi level in the hole-type cuprates YBCO and BSCCO, leads to the occurrence of a low-frequency peak in the spectral function of the charge
density fluctuations due to the presence of acoustic plasmon branch in the
collective electron spectrum. The retarded anisotropic electron-plasmon interaction leads to the suppression of the static screened Coulomb repulsion
for small transferred momenta and, consequently, to the effective attraction
between electrons in the dx²-y²-wave channel of the Cooper pairing of
current carriers. Breaking of C₄v symmetry in YBCO crystals leads to a
possibility of a change of dx²-y²-wave symmetry of the gap to a mixed
s − d gap symmetry for singlet Cooper pairs or to a p-wave gap symmetry
for triplet pairs. |
| format |
Article |
| author |
Pashitskii, E.A. Pentegov, V.I. Semenov, A.V. |
| spellingShingle |
Pashitskii, E.A. Pentegov, V.I. Semenov, A.V. Gap symmetry and charge density excitations in high-Tc superconductors with extended saddle points in electron spectrum Condensed Matter Physics |
| author_facet |
Pashitskii, E.A. Pentegov, V.I. Semenov, A.V. |
| author_sort |
Pashitskii, E.A. |
| title |
Gap symmetry and charge density excitations in high-Tc superconductors with extended saddle points in electron spectrum |
| title_short |
Gap symmetry and charge density excitations in high-Tc superconductors with extended saddle points in electron spectrum |
| title_full |
Gap symmetry and charge density excitations in high-Tc superconductors with extended saddle points in electron spectrum |
| title_fullStr |
Gap symmetry and charge density excitations in high-Tc superconductors with extended saddle points in electron spectrum |
| title_full_unstemmed |
Gap symmetry and charge density excitations in high-Tc superconductors with extended saddle points in electron spectrum |
| title_sort |
gap symmetry and charge density excitations in high-tc superconductors with extended saddle points in electron spectrum |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
1999 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120526 |
| citation_txt |
Gap symmetry and charge density excitations in high-Tc superconductors with extended saddle points in electron spectrum / E.A. Pashitskii, V.I. Pentegov, A.V. Semenov // Condensed Matter Physics. — 1999. — Т. 2, № 3(19). — С. 453-462. — Бібліогр.: 13 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT pashitskiiea gapsymmetryandchargedensityexcitationsinhightcsuperconductorswithextendedsaddlepointsinelectronspectrum AT pentegovvi gapsymmetryandchargedensityexcitationsinhightcsuperconductorswithextendedsaddlepointsinelectronspectrum AT semenovav gapsymmetryandchargedensityexcitationsinhightcsuperconductorswithextendedsaddlepointsinelectronspectrum |
| first_indexed |
2025-07-08T18:01:45Z |
| last_indexed |
2025-07-08T18:01:45Z |
| _version_ |
1837102748594601984 |
| fulltext |
Condensed Matter Physics, 1999, Vol. 2, No. 3(19), pp. 453–462
Gap symmetry and charge density
excitations in high-Tc superconductors
with extended saddle points in electron
spectrum
E.A.Pashitskii, V.I.Pentegov, A.V.Semenov
Institute of Physics, National Academy of Sciences of Ukraine,
252650, Kiev, Ukraine
Received June 25, 1998
It is shown that the strong anisotropy of the one-particle electron spectrum,
due to the presence of extended saddle-point features (ESPF) close to the
Fermi level in the hole-type cuprates YBCO and BSCCO, leads to the oc-
currence of a low-frequency peak in the spectral function of the charge
density fluctuations due to the presence of acoustic plasmon branch in the
collective electron spectrum. The retarded anisotropic electron-plasmon in-
teraction leads to the suppression of the static screened Coulomb repulsion
for small transferred momenta and, consequently, to the effective attraction
between electrons in the dx2
−y2 -wave channel of the Cooper pairing of
current carriers. Breaking of C4v symmetry in YBCO crystals leads to a
possibility of a change of dx2
−y2 -wave symmetry of the gap to a mixed
s− d gap symmetry for singlet Cooper pairs or to a p -wave gap symmetry
for triplet pairs.
Key words: extended saddle point, acoustic plasmon, d -wave pairing
PACS: 74.20.-z, 74.72.-h, 74.72.Hs
1. Introduction
Any theoretical model intended for adequately describing the nature of the HTS
in cuprates, should account for the d-wave superconducting gap symmetry, mani-
fested by spontaneous Josephson currents [1], by generating the half-integer quanta
of the magnetic flux [2,3], as well as by a strong anisotropy of the gap in the plane
of CuO2 layers [4].
One of the Cooper pairing mechanisms, producing the d-wave symmetry of the
superconducting gap in high-Tc superconductors, is described by the model of the
electron-magnon interaction in an almost antiferromagnetic quasi-2D Fermi liquid
[5,6]. This model leads to an anisotropic repulsion between electrons (or holes) in the
c© E.A.Pashitskii, V.I.Pentegov, A.V.Semenov 453
E.A.Pashitskii, V.I.Pentegov, A.V.Semenov
entire 2D momentum space with peaks in the corners of the Brillouin zone (BZ).
Such an interaction results in an effective attraction responsible for dx2−y2-wave
singlet Cooper pairing. However, the main question regarding the sufficiently large
value of the coupling constant of electron-magnon interaction for obtaining a high
value (∼ 100 K) of the critical temperature remains open.
New and important information about the structure of the electronic spectrum of
high-Tc superconductors was recently obtained using the angle-resolved photoemis-
sion spectroscopy with high energy resolution [7,8]. These experiments exhibited the
presence of extended saddle point features (ESPF) near the Fermi level in cuprates
with hole-type conductivity. According to [9,10], the ESPF in the band spectrum
can be the result of a strong hybridization of the overlapping broad and narrow 2D
bands in the layered cuprate crystals.
In this paper we present results of our theoretical and numerical investigations of
the effect of the ESPF in the band spectrum on the HTS mechanisms in the layered
crystals of cuprates. We consider the ESPF effects on the spectrum of the collective
charge-density excitations, on the screened Coulomb interaction as well as on the
superconducting gap symmetry.
In §2 it is shown that the strong anisotropy of the one-particle electron spectrum
in the CuO2 layers due to the presence of ESPF leads to the occurrence of the
low frequency branch with an acoustic dispersion in the collective spectrum of the
electron density excitations. These excitations are similar to acoustic plasmons (AP)
in metals having a multiply-connected Fermi surface (FS) with essentially different
effective masses of the current carriers in different extrema of the band spectra
[11,12]. The spectral function of the charge-density excitations is strongly anisotropic
in this case and is peaked at frequencies corresponding to the AP branch. Due
to the Kramers-Kronig relations for the reciprocal dielectric function, the static
screened Coulomb interaction has got an anisotropic structure with the pronounced
minimum in the region of small transferred momenta |q| ≪ π/a (where a is the
lattice constant). This suppression of the Coulomb repulsion is caused by a retarded
interaction between electrons due to the exchange of virtual AP.
In §3 we argue that the deep minimum of the screened Coulomb repulsion due to
the electron-plasmon interaction leads to the effective attraction between electrons in
the dx2−y2-wave channel of the singlet Cooper pairing with the gap ∆d (ϕ) ∝ cos 2ϕ .
This mechanism of the d-wave pairing differs from those proposed by the authors of
[5,6], who accentuated the important role of the sharp repulsion peak at q = (π, π)
and believed the peculiarities of the interaction at small q to be irrelevant.
Breaking of the C4v symmetry occurs in Y BCO crystals as well due to the
existence of ordered 1D CuO chains along the b-axis, leading to the mixed s+dx2−y2
or s + dxy symmetry of the gap parameter for singlet Cooper pairing, as well as to
the possibility of the p-wave gap symmetry with ∆p(ϕ) ∝ sinϕ or ∆p(ϕ) ∝ cosϕ in
the triplet pairing channel.
454
Gap symmetry and charge density excitations in high-Tc superconductors
2. Acoustic plasmons and screened Coulomb interaction in
crystals with ESPF
�
�
�
�
π
−π
�
−π
π
(�
N��
�H9
N[D
N\D
Figure 1. The conductivity band
E (kx, ky) of the 2D electron hybrid
spectrum, calculated in [9].
ΓΓ������ 0��π���
;��π�π�
Figure 2. Cross section of the Fermi sur-
face in the original and shifted Brillouin
zones.
It is known [11,12] that a low-
frequency AP branch in the collec-
tive electron spectrum can occur in
multi-band (multi-valley) crystals hav-
ing a multiply-connected FS and sev-
eral groups of current carriers (electrons,
holes) with significantly different effec-
tive masses. We show that a similar
collective electron branch with acous-
tic dispersion relation can occur in lay-
ered crystals having a singly-connected
FS but strong anisotropy in the electron
density of states (DOS) and the Fermi
velocity due to the presence of the ESPF
[7,8]. The experimental values of the
Fermi energy and Fermi momentum for
the quasi-1D spectrum near the bottom
of ESPF are respectively µ1 ≈ 20meV
and kF1 ≈ 0.15Å−1. In the parabolic
spectrum approximation µ1 = k2
F1/2m
∗
1
we obtain an effective electronic mass
m∗
1 ≈ 4.3m0 (where m0 is the bare elec-
tron mass).
In the present paper when choosing
parameters for the hybridized conduc-
tivity band we use the results of the
multiple band calculations of [9]. This
conductivity band E(kx, ky) is shown in
figure 1. When the Fermi level lies above
the bottom of the ESPF, it is convenient
to use a shifted BZ centered in (π, π)
point, in order to obtain a closed hole-
type FS (figure 2).
We proceed to show that the strong
anisotropy of the DOS on the FS (and
hence the anisotropy of the Fermi ve-
locity of the quasi-particles) leads to
the occurrence of the low frequency AP
branch in the collective electron spec-
trum, despite the fact that the FS is
singly connected.
455
E.A.Pashitskii, V.I.Pentegov, A.V.Semenov
� � � � �
��
��
�
�
�
�
�
Π
(ω
�T __),
D�X
�
ω�Y�T
ω,�H9
��� ��� ��� ��� ��� ���
9 F�T __��6
SO�T __�ω �
�D �
���H
9
���
���
� � � �
Figure 3. The real (solid curve) and
imaginary (dashed curve) parts of the
polarization operator in the long wave
limit (q → 0), when q is parallel to one
of the main crystallographic axes, in a
function of ω
v1q‖
for the case of strong
anisotropy of the Fermi velocity.
Figure 4. The frequency depen-
dence of the spectral function of
the electronic charge density fluctua-
tions Spl (q, ω) multiplied by the bare
Coulomb matrix element Vc (q) for
q⊥ = 0 and for several values of q‖
along the BZ diagonal: 1 – q‖ =
√
2π
16a
,
2 – q‖ =
√
2π
8a
, 3 – q‖ = 3
√
2π
16a
, 4 –
q‖ =
√
2π
4a
.
The dispersion relation ωpl(q) of the AP branch is determined by zero of the real
part of the longitudinal complex dielectric function
ε (q, ω) = 1 + Vc (q) Π
(
q‖, ω
)
, (1)
where Vc is the matrix element of the Coulomb interaction in the layered crystals,
Vc (q) =
2πe2
q‖
·
sinh q‖d
cosh q‖d− cos q⊥d
(2)
and Π is the polarization operator, corresponding to the 2D band E(k‖), which is
crossed by the Fermi level. Here q‖ and k‖ are the longitudinal momenta in the a−b
plane, q⊥ is the transverse momentum along the c-axis, d is the distance between
layers.
In figure 3 the real and imaginary parts of the polarization operator are shown
as functions of ω/q‖ for q‖ → 0.
The spectral function of the electronic charge density fluctuations (virtual plas-
mons) given by
Spl (q, ω) = −
1
π
Im ε−1 (q, ω) =
1
π
Im ε (q, ω)
[Re ε (q, ω)]2 + [Im ε (q, ω)]2
(3)
456
Gap symmetry and charge density excitations in high-Tc superconductors
���
���
���
���
���
�
π
�
π
9 F��T __��D
����
H9
T[D
T\D
a
Figure 5. The plot of the static screened Coulomb repulsion Ṽc
(
q‖
)
calculated
for the electron spectrum of figure 1.
and calculated with the electron spectrum of figure 1, is plotted in figure 4 for several
q‖ 6= 0 along one of the two BZ diagonals and for q⊥ = 0. The function Spl(q, ω)
has got a maximum at the frequency ωpl(q) of the AP since Re ε(q, ωpl) = 0, while
for ω → 0 according to (3) Spl(q, ω) ∼ ω since Im ε (q, ω) ∼ ω.
By virtue of the Kramers-Kronig relation for the reciprocal dielectric function
ε−1 (q, ω) the matrix element of the static (for ω = 0) screened Coulomb repulsion
between electrons can be written as
Ṽc (q) ≡
Vc (q)
ε (q, 0)
= Vc (q)
1− 2
∞∫
0
dω′
ω′ Spl (q, ω
′)
. (4)
The plot of Ṽc
(
q‖
)
calculated for the band of figure 1 is presented in figure 5. As
we see, Ṽc (q) has got a deep minimum in the region of small transferred momenta q ‖
due to the low frequency maximum of the charge density spectral function S(q, ω)
in the region of the AP branch presence. Such a suppression of the static Coulomb
repulsion is caused by the effective electron-electron attraction through the exchange
of the virtual AP.
In the general case of C4v symmetry of the electron spectrum the Fourier series
expansion of the screened Coulomb matrix element Ṽc
(
k‖ − k′
‖
)
with respect to the
angles ϕ and ϕ′
Ṽc(ϕ, ϕ
′) =
∑
n,m
Vnme
inϕ+imϕ′
. (5)
will contain harmonics Vnm with indices satisfying the condition n+m = 4l, where
l is an integer.
457
E.A.Pashitskii, V.I.Pentegov, A.V.Semenov
3. The effect of the electron spectrum anisotropy on the gap
symmetry
In what follows, we show that the marked momentum dependence of the screened
Coulomb interaction (4), connected to the low frequency peak of the plasmon spec-
tral function (3), determines the symmetry of the superconducting gap.
We will use the Eliashberg equations [13] for the gap in superconductors with
strong coupling, taking into account the retarded interaction between electrons due
to the exchange of virtual phonons and acoustic plasmons, as well as the screened
Coulomb repulsion. Near the critical temperature, T → Tc, the linearized equation
for the anisotropic gap ∆(k‖, ω) on the FS, given the quasi-2D character of the
electron spectrum, using the static Kramers-Kronig relation (4), can be written on
the FS (|k‖| = kF) as
(1 + λ) ∆ (ϕ, 0) = 1
2
2π∫
0
dϕ′
2π
Ω̃∫
−Ω̃
dω
ω
∆(ϕ′, ω) ν (ϕ′, ω)
×
[
Wph θ
(
Ω̃ph − |ω|
)
− Ṽc (ϕ, ϕ
′)
]
tanh ω
2Tc
,
(6)
where λ is the renormalization constant, connected to the normal self-energy, θ (x)
is the unit step function, the electron-phonon interaction Wph is taken to be quasi
isotropic, Ω̃ is a cut-off energy of the Coulomb interaction (Ω̃ ≈ EF), and ν (ϕ′, ω)
is the anisotropic DOS.
3.1. Unbroken C4v symmetry
For the layered crystals, having the unbroken C4v symmetry of the electron spec-
trum (for instance, BiSrCaCuO, TlBaCaCuO, HgBaCaCuO), the anisotropic DOS
can be approximated by
ν (ϕ, ω) = ν+ (ω) + ν− (ω) cos 4ϕ, (7)
where
ν± (ω) =
1
2
[
ν1Re
√
µ1
µ1+ω
± ν2
]
. (8)
At the same time it is possible to retain in the Fourier expansion (5) only the
main terms, corresponding to the A1 and B1 representations of the C4v group:
Ṽc (ϕ, ϕ
′) ≈ V00 + V22 (cos 2ϕ cos 2ϕ′ − sin 2ϕ sin 2ϕ′)
+ V44 (cos 4ϕ cos 4ϕ′ − sin 4ϕ sin 4ϕ′) ,
(9)
where the isotropic part of the Coulomb repulsion V00 > 0, while V22 and V44,
containing the anisotropic contribution of the electron-plasmon interaction, may be
either positive or negative (see below). Substituting (7) and (9) in equation (6) we
conclude that the singlet Cooper pairing is possible either in d- or s-channels. For
the s-wave pairing with the anisotropic gap
∆s (ϕ) = ∆0 +∆4 cos (4ϕ) (10)
458
Gap symmetry and charge density excitations in high-Tc superconductors
we obtain the following coupled equations determining the critical temperature T s
c
(1 + λ)∆0 =
Wph − V ∗
00
2
Ω̃ph∫
−Ω̃ph
dω
ω
[
ν+ (ω)∆0 +
ν− (ω)∆4
2
]
tanh
ω
2T s
c
(11)
(1 + λ)∆4 = −
1
4
V44
Ω̃∫
−Ω̃
dω
ω
[ν+ (ω)∆4 + ν− (ω)∆0] tanh
ω
2T s
c
, (12)
where
V ∗
00 =
V00
1 + ν2V00 ln(EF/Ω̃ph)
. (13)
For the d-wave pairing the critical temperature T d
c is given by equation
(1 + λ) ·∆d (ϕ) = −
V22
2
2π∫
0
dϕ′
2π
Ω̃∫
−Ω̃
dω
ω
ν (ϕ′, ω)∆d (ϕ
′)
× (cos 2ϕ cos 2ϕ′ − sin 2ϕ sin 2ϕ′) tanh
ω
2T d
c
(14)
The sign of the coefficient V22 determines the type of d-wave symmetry of the
gap. For the negative value of V22 the gap has dx2−y2 symmetry, ∆d (ϕ) = ∆2 cos 2ϕ,
and the equation (14) is reduced to
(1 + λ) =
|V22|
4
Ω̃∫
−Ω̃
dω
ω
(
ν+(ω) +
1
2
ν−(ω)
)
tanh
ω
2T d
c
. (15)
For the positive value of V22 from (14) the solution of the form ∆d (ϕ) = ∆2 sin 2ϕ
follows, corresponding to the dxy-wave gap symmetry.
3.2. YBCO-type crystals with CuO chains
For the YBa2Cu3O7 and YBa2Cu4O8 crystals, where C4v symmetry is broken
due to the presence of the ordered 1D chains CuO, the anisotropic DOS has got
approximately the following angular dependence
ν (ϕ, ω) = ν̃0 (ω)−
ν̃c
2
cos 2ϕ+ ν− (ω) cos 4ϕ, (16)
where ν̃0(ω) = ν+(ω) + ν̃c/2, and ν̃c is the electron DOS in the 1D chains.
The asymmetric terms in the electron-electron interaction in this case are
U (ϕ, ϕ′) = Ũ11 (1 + cosϕ cosϕ′ − sinϕ · sinϕ′) . (17)
Substitution of (16) and (17) in (6) leads, for the singlet Cooper pairing, to the
system of coupled gap equations
(1 + λ)∆0 =
Wph − Ũ11 − V ∗
00
2
Ω̃ph∫
−Ω̃ph
dω
ω
[
∆0ν̃0 (ω) +
∆2ν̃c
2
]
tanh
ω
2Tc
, (18)
459
E.A.Pashitskii, V.I.Pentegov, A.V.Semenov
(1 + λ)∆2 =
|V22|
4
Ω̃∫
−Ω̃
dω
ω
{
∆0ν̃c +∆2
[
ν̃0 (ω) +
ν− (ω)
2
]}
tanh
ω
2Tc
(19)
for s- and d-wave components of the anisotropic superconducting gap which is given
by,
∆sd (ϕ) =
{
∆0 +∆2 cos 2ϕ if V22 < 0,
∆0 +∆2 sin 2ϕ if V22 > 0.
(20)
In other words, the presence of the 1D chains of CuO in YBCO should bring about
the mixed s-d symmetry of the gap.
Furthermore, a sufficiently strong interaction Ũ11 in (17), violating the C4v sym-
metry, could give rise to triplet Cooper pairing of electrons in 1D chains with p-type
order parameter symmetry
∆p (ϕ) =
{
∆1 cosϕ if Ũ11 < 0
∆1 sinϕ if Ũ11 > 0
. (21)
In this case, the critical temperature T p
c will be defined by the equation
(1 + λ) =
1
4
|Ũ11|
Ω̃∫
−Ω̃
dω
ω
ν̃0 (ω) tanh
ω
2T p
c
. (22)
Notice that the negative value of Ũ11 can result from the strong electron-phonon
interaction in the CuO chains.
4. Conclusions
We have shown that strong anisotropy of the one-particle electron spectrum,
associated, in particular, with the presence of the ESPF near the Fermi level, may
lead to the occurrence of the acoustic plasmon branch in the collective electron
spectrum. These electronic excitations cause the low frequency peak in the spectral
function of the charge density fluctuations Spl (q, ω) = − 1
π
Im ε−1 (q, ω) and, through
the Kramers-Kronig relation for the reciprocal dielectric function ε−1 (q, ω), lead to
the deep minimum in the static screened Coulomb repulsion for the small transferred
momenta q. Such a suppression of the Coulomb repulsion, which is the result of the
effective electron-electron attraction due to the exchange of the virtual acoustic
plasmons, favours the dx2−y2-wave Cooper pairing of the current carriers with the
superconducting gap structure ∆d (ϕ) ∼ cos 2ϕ in the layered crystals of the cuprate
metal-oxide compounds, having C4v symmetry of the CuO2 layers. Breaking of C4v
symmetry leads to the mixed s − d wave singlet Cooper pairing, or to the p-wave
triplet pairing of current carriers.
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Gap symmetry and charge density excitations in high-Tc superconductors
References
1. Wollman D.A., Van Harlingen D.J., Lee W.C., Ginsberg D.M., Leggett A.J. Experi-
mental determination of the superconducting pairing state in YBCO from the phase
coherence of YBCO-Pb dc SQUIDs. // Phys. Rev. Lett., 1993, vol. 71, p. 2134.
2. Tsuei S.S., Kirtley J.R., Chi C.C., Yu-Jahnes L.S., Gupta A., Shaw T., Sem J.Z.,
Ketchen M.B. Pairing symmetry and flux quantization in a tricrystal superconducting
ring of YBa2Cu3O7−δ. // Phys. Rev. Lett., 1994, vol. 73, p. 593.
3. Kirtley J.R., Tsuei S.S., Rupp M., Sun J.Z., Yu-Jahnes L.S., Gupta A., Ketchen M.B.,
Moler K.A., Bhushan M. Direct imaging of integer and half-integer Josephson vortices
in high-Tc grain boundaries. // Phys. Rev. Lett., 1996, vol. 76, p. 1336.
4. Ding H., Norman M.R., Campuzano J.C., Rnaderia M., Bellman A.F., Yokoya T.,
Takahashi T., Mochiku T., Kadowaki K. Angle-resolved photoemission spectroscopy
study of the superconducting gap anisotropy in Bi2Sr2CaCu2O8+x. // Phys. Rev. B,
1996, vol. 54, p. R9678.
5. Millis A.J., Monien H., Pines D. Phenomenological model of nuclear relaxation in the
normal state of YBa2Cu3O7. // Phys. Rev. B, 1990, vol. 42, p. 167.
6. Pines D. dx2−y2 pairing and spin fluctuations in the cuprate superconductors: experi-
ment meets theory. // Physica C, 1994, vol. 235–240, p. 113;
Nearly antiferromagnetic Fermi liquids: a progress report. // Zeit. Phys. B, 1997,
vol. 103, p. 129.
7. King D.M., Shen Z.-X., Dessau D.S., Marshall D.S., Park C.H., Spicer W.E.,
Peng J.L., Li Z.Y., Greene R.L. Observation of a saddle-point singularity in
Bi2(Sr0.97Pr0.03)2CuO6+d and its implications for normal and superconducting state
properties. // Phys. Rev. Lett., 1994, vol. 73, p. 3298.
8. Gofron K., Campuzano J.C., Abrikosov A.A., Lindroos M., Bansil A., Ding H.,
Koelling D., Dabrowski B. Observation of an “extended” Van Hove singularity in
YBa2Cu3O8 by ultrahigh energy resolution angle-resolved photoemission. // Phys.
Rev. Lett., 1994, vol. 73, p. 3302.
9. Andersen O.K., Jepsen O., Liechtenstein A.I., Mazin I.I. Plane dimpling and saddle-
point bifurcation in the band structures of optimally doped high-temperature super-
conductors: A tight-binding model. // Phys. Rev. B, 1994, vol. 49, p. 4145.
10. Pashitskii E.A., Pentegov V.I. On the nature of the anisotropic gap structure in high-
temperature superconductors: competition between s- and d-symmetry types. // Zh.
Eksp. Teor. Fiz., 1997, vol. 111, p. 298 [JETP, 1997, vol. 84, p. 164].
11. Pines D. Electron interaction in solids. // Canad. J. Phys., 1956, vol. 34, 1379.
12. Ruvalds J. Are there acoustic plasmons? // Adv. Phys., 1981, vol. 30, p. 677.
13. Eliashberg G.M. Interaction between electrons and lattice vibrations in a supercon-
ductor. // Zh. Exsp. Teor. Fiz., 1960, vol. 38. p. 966 [Sov. Phys. JETP, 1960, vol. 11,
p. 696];
Temperature Green’s functions for electrons in superconductors. // Zh. Exsp. Teor.
Fiz., 1960, vol. 39, p. 1437 [Sov. Phys. JETP, 1961, vol. 12, p. 1000].
461
E.A.Pashitskii, V.I.Pentegov, A.V.Semenov
Cиметрiя надпровiдної щiлини та збудження
зарядової густини у високотемпературних
надпровiдниках з подовженими сiдловими
особливостями в електронному спектрi
Е.А.Пашицький, В.I.Пентегов, О.В.Семенов.
Iнститут Фiзики НАН України, 252650, Київ
Отримано 25 червня 1998 р.
Показано, що сильна анізотропія одночасткового електронного
спектру веде, завдяки наявності подовжених сідлових особливостей
біля рівня Фермі у купратах YBCO та BSCCO, до появи низькочастот-
ного піку у спектральній функції флуктуацій зарядової густини, що
є наслідком присутності гілки акустичних плазмонів у колективному
електронному спектрі. Електрон-плазмонна взаємодія веде до знач-
ного зменшення статичного кулонівського відштовхування в облас-
ті малих переданих імпульсів та, як наслідок, до ефективного при-
тягнення між електронами у dx2
−y2 -хвильовому каналі куперівсько-
го спарювання носіїв струму. Порушення C4v симетрії у кристалах
YBCO призводить до можливості заміни dx2
−y2 -хвильової симетрії
надпровідної щілини на змішану s − d симертрію для сінглетних ку-
перівських пар або на p -хвильову симетрію щілини для триплетних
пар.
Ключові слова: подовжені сідлові точки, акустичний плазмон,
d -хвильове спарювання
PACS: 74.20.-z, 74.72.-h, 74.72.Hs
462
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