Electrical resistivity and scattering processes in „Bi,Pb…
2
„Sr,La…
2
CuO
6+
studied
by angle-resolved photoemission spectroscopy
Takeshi Kondo,
1,2
Tsunehiro Takeuchi,
1,2
Syunsuke Tsuda,
3
and Shik Shin
3
1
Department of Crystalline Materials Science, Nagoya University, Nagoya 464-8603, Japan
2
EcoTopia Science Institute, Nagoya University, Nagoya 464-8603, Japan
3
Institute of Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan
Received 6 February 2006; revised manuscript received 16 June 2006; published 29 December 2006
The lifetime of the Bloch states at the Fermi level, the Fermi velocity, and the mean free path of the
conduction electrons in Bi,Pb
2
Sr,La
2
CuO
6+
Bi2201 superconductors are determined by angle-resolved
photoemission spectroscopy over a wide range of the hole concentration from heavily overdoped to lightly
underdoped conditions. The electrical resistivity in the CuO
2
plane is quantitatively reproduced by the calcu-
lation with the Boltzmann transport equation using the experimentally determined electronic structure. A
detailed investigation on the hole concentration and temperature dependence of the lifetime leads us to con-
clude that the scattering process of conduction electrons in the vicinity of ,0 is dominated by electron-
electron scattering, whereas around the node direction it is dominated by electron-phonon scattering.
DOI: 10.1103/PhysRevB.74.224511 PACS numbers: 74.72.Hs, 74.25.Fy, 74.25.Jb, 79.60.-i
I. INTRODUCTION
Temperature dependence of electrical resistivity along the
CuO
2
plane ab plane of the high-T
c
cuprates
ab
T is
widely known to possess strong hole-concentration p
dependence:
1–8
T
2
dependence in the overdoped samples, T
linear over a wide temperature range up to about 1000 K in
an optimally doped sample. In underdoped samples,
ab
T
shows nearly T-linear behavior at high temperature, but pos-
sesses a change in its temperature coefficient at a character-
istic temperature T
*
, which gradually increases with de-
creasing p. Since the superconductivity should be dominated
by the conduction electrons that determine electron-transport
properties, an investigation into the mechanism leading to
these characteristic behaviors in
ab
T should provide im-
portant information about the origin of high-T
c
superconduc-
tivity.
Because
ab
T possesses a positive temperature coeffi-
cient metallic behavior in the normal state of the high-T
c
cuprates, one may naturally expect a Boltzmann-type electri-
cal conduction,
ab
T=1/
ab
T, that is given by
ab
T =
e
2
8
3
lk -
f
dS
d . 1
Here, l represents the mean free path, and has a relation of
lk =
tr
kvk with the transport relaxation time
tr
and the group velocity v. Fermi-Dirac distribution func-
tion is expressed as f , and dS
represents a small fraction
of equienergy surface at . Notably, all factors except for
tr
in Eq. 1 can be obtained from the energy-momentum
- k dispersion.
The angle-resolved photoemission spectroscopy ARPES
is widely known as a powerful experimental technique ca-
pable of directly determining the - k dispersion. The life-
time of the Bloch states, which is closely related to
tr
, can
also be estimated from the peak width energy width of the
energy distribution curves EDC’s in the ARPES spectra.
9–17
We stress, therefore, that all factors in Eq. 1 are quantita-
tively determined solely by the ARPES measurements.
On the basis of ARPES measurements on the high-T
c
cuprates, especially on Bi
2
Sr
2
CaCu
2
O
8+
Bi2212, charac-
teristics in the electronic structure and scattering events of
the conduction electrons have been intensively investigated,
and the behaviors of
ab
T have been discussed.
14,16,18,19
These studies, however, provided only qualitative informa-
tion, and thus the mechanism of electron conduction has
been regarded as one of the controversial issues in the field
of the high-T
c
cuprates. We believe that quantitative analysis
with properly considering the contributions from all Bloch
states
k’s to
ab
T can clarify the mechanism of the characteris-
tic behaviors of
ab
T, and it provides us important informa-
tion about the origin of the high-T
c
superconductivity.
In this work, by employing ARPES measurements, we
determined the Fermi velocity v
F
, the lifetime of the Bloch
states at the Fermi level
F
, and the mean free path of
conduction electrons at the Fermi level l
F
as a function of
the Fermi wave vector k
F
for a Bi,Pb
2
Sr,La
2
CuO
6+
Bi2201 superconductor with various hole concentrations
p’s. The p dependence of
ab
200 K was quantitatively
evaluated by using the Boltzmann transport equation with
the experimentally determined parameters. We demonstrate
reliability of the present analysis by showing extremely good
consistency between the measured
ab
200 K and the calcu-
lated one, and discuss the scattering mechanism of conduc-
tion electrons in Bi2201.
II. EXPERIMENTAL PROCEDURE
Bi,Pb
2
Sr,La
2
CuO
6+
Bi2201 single crystals were
grown by the conventional floating-zone FZ technique.
Single crystals were typically cut to 1–3 3 0.05 mm in
dimension both for the ARPES and electrical resistivity mea-
surements. We partially substituted Pb of a larger ion radius
for Bi in all samples to remove the lattice modulation along
PHYSICAL REVIEW B 74, 224511 2006
1098-0121/2006/7422/2245119 ©2006 The American Physical Society 224511-1