Doping dependence of the $(\pi,\pi)$ shadow band in La-based cuprates studied by angle-resolved photoemission spectroscopy

Abstract

The $(\pi,\pi)$ shadow band (SB) in La-based cuprate family (La214) was
studied by angle-resolved photoemission spectroscopy (ARPES) over a wide doping
range from $x=0.01$ to $x=0.25$. Unlike the well-studied case of the Bi-based
cuprate family, an overall strong, monotonic doping dependence of the SB
intensity at the Fermi level ($E_F$) was observed. In contrast to a previous
report for the presence of the SB only close to $x=1/8$, we found it exists in
a wide doping range, associated with a doping-independent $(\pi,\pi)$ wave
vector but strongly doping-dependent intensity: It is the strongest at $x\sim
0.03$ and systematically diminishes as the doping increases until it becomes
negligible in the overdoped regime. This SB with the observed doping dependence
of intensity can in principle be caused by the antiferromagnetic fluctuations
or a particular form of low-temperature orthorhombic lattice distortion known
to persist up to $x\sim 0.21$ in the system, with both being weakened with
increasing doping. However, a detailed binding energy dependent analysis of the
SB at $x=0.07$ does not appear to support the former interpretation, leaving
the latter as a more plausible candidate, despite a challenge in quantitatively
linking the doping dependences of the SB intensity and the magnitude of the
lattice distortion. Our finding highlights the necessity of a careful and
global consideration of the inherent structural complications for correctly
understanding the cuprate Fermiology and its microscopic implication.

Full text

Page 1

arXiv:0911.2245v1 [cond-mat.supr-con] 11 Nov 2009
Doping dependence of the (π,π) shadow band in
La-based cuprates studied by angle-resolved
photoemission spectroscopy
R.-H. He1,2, X. J. Zhou1,3,4, M. Hashimoto1,2,3, T. Yoshida1,5, K.
Tanaka1,2,3,6, S.-K. Mo1,2,3, T. Sasagawa1,2,7, N. Mannella1,2,3,8,
W. Meevasana1,2‡, H. Yao1, E. Berg1, M. Fujita9, T. Adachi10,
S. Komiya11, S. Uchida5, Y. Ando12, F. Zhou4, Z. X. Zhao4, A.
Fujimori5, Y. Koike10, K. Yamada9, S. A. Kivelson1, Z.
Hussain3and Z.-X. Shen1,2
1Geballe Laboratory for Advanced Materials, Departments of Physics and Applied
Physics, Stanford University, Stanford, California 94305, USA
2Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator
Laboratory, Menlo Park, California 94025, USA
3Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley,
California 94720, USA
4National Laboratory for Superconductivity, Beijing National Laboratory for
Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences,
Beijing 100190, China
5Department of Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
6Department of Physics, Osaka University, Osaka 560-0043, Japan
7Materials and Structures Laboratory, Tokyo Institute of Technology, Kanagawa
226-8503, Japan
8Department of Physics and Astronomy, University of Tennessee, Knoxville,
Tennessee 37996, USA
9Institute of Materials Research and World-Premier-International Research Center
Initiative, Tohoku University, Sendai 980-8577, Japan
10Department of Physics and Applied Physics, Tohoku University, Sendai 980-8579,
Japan
11Central Research Institute of Electric Power Industry, Komae, Tokyo 201-8511,
Japan
12Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka
567-0047, Japan
E-mail: zxshen@stanford.edu
Abstract.
(La214) was studied by angle-resolved photoemission spectroscopy (ARPES) over a
wide doping range from x = 0.01 to x = 0.25. Unlike the well-studied case of Bi-
based cuprate family, a strong doping dependence of the SB intensity at the Fermi
level (EF) was observed at x < 1/8, which crosses over onto a moderate, if finite,
The existence of the (π,π) shadow band (SB) in La-based cuprate family
‡ Present address: School of Physics and Astronomy, University of St Andrews, St. Andrews, Fife
KY16 9SS, UK.

Page 2

Doping dependence of the (π,π) shadow band in La214
2
doping dependence at x > 1/8. While the overall weakening of the SB intensity is
generally consistent with a decreasing strength of antiferromagnetic fluctuations in the
system, a binding energy dependence analysis of the SB at x < 1/8 does not appear
to support this interpretation in the weak-coupling picture. The crossover behavior
around x = 1/8 also raises a challenge for its direct relation with the particular form
of orthorhombic distortions in the system which persists up to x ∼ 0.21. This dilemma
in understanding the origin of the (π,π) SB in La214 calls for a more sophisticated
thinking, presumably by adding a potentially important strong-coupling perspective.

Page 3

Doping dependence of the (π,π) shadow band in La214
3
1. Introduction
The appearance of SBs in ARPES [1] indicates the existence of some form of super-
modulation in the crystal, which generally has a structural [2], electronic [3] or magnetic
[4] origin as demonstrated in various materials.
cuprates, consensus was finally reached after years of debate between scenarios for
its magnetic [5] or structural [6, 7] origin. The lack of additional renormalization in
the dispersion and lack of momentum broadening of the SB [8], the binding energy
independence and opposite [9] (if finite [10]) doping dependence in the underdoped
regime of the intensity ratio [8] of the SB vs.
the magnetic interpretation in the weak-coupling picture where the antiferromagnetic
correlations of this hole-doped system are believed not to be static. The structural
alternative was confirmed by a polarization dependence study of untwined samples where
the 4-fold symmetry breaking nature of the SB formation was uncovered due to a unique
form of bulk orthorhombic distortions of a tetragonal lattice structure, which is located
primarily in the BiO planes [11].
Such a structural interpretation specific for Bi-based cuprates apparently cannot
be directly applied to explain a similar existence of (π,π) SBs at various doping
levels of La214 in literature [12, 13, 14, 15, 16, 17]. However, in the low-temperature
orthorhombic (LTO) phase of La214 [18, 19] and also locally in the high-temperature
tetragonal (HTT) phase above [20], another form of (π,π) bulk orthorhombic distortions
exists which is caused by a staggered tilting of the CuO6 octahedra around the
Cu-O bond diagonal.While the contribution of this structural aspect might be
similarly expected to dominate the SB formation in La214, a recent report [17] of
an anomalous enhancement of the SB intensity at x = 1/8 argued for its intimate
connection with the coincident static spin and charge stripe orders although these orders
have incommensurate wave vectors different from (π,π) [21, 22, 23]. Considering a
considerable SB intensity reported at other doping levels [12, 13, 14, 15, 16], reliable
evaluation of a possible anomaly tied to x = 1/8 and its potential importance for our
understanding of the SB origin should be put in a wider context by means of a more
systematic doping dependence study in La214.
In this paper, we present ARPES data at doping levels ranging from x = 0.01 to
x = 0.25 in various members of La214. Our data suggest x = 1/8 might be special
but likely not in the form of an anomalous enhancement right at this doping. Unlike
the case of Bi-based cuprate family, a strong doping dependence of the SB intensity at
EF was surpringly observed at x < 1/8, which crosses over onto a moderate, if finite,
doping dependence at x > 1/8. While the overall weakening of the SB intensity appears
to be consistent with a decreasing strength of antiferromagnetic fluctuations in the
system, similar lack of additional renormalization in the SB dispersion and binding
energy dependence of the SB/MB intensity ratio is also found at x < 1/8, which
argues against the conventional magnetic interpretation based on the weak-coupling
spin-fluctuation approach [24, 8]. On the other hand, the crossover behavior around
About the (π,π) SB in Bi-based
the main band (MB) argue against

Page 4

Doping dependence of the (π,π) shadow band in La214
4
x = 1/8 cannot be easily reconciled with the structural interpretation because the major
form of orthorhombic distortions in the system remains strong at low temperature above
x = 1/8 and can persist up to a much higher doping. A more sophisticated scenario
seems to be necessary in understanding the origin of the (π,π) SB in La214 than in
Bi-based family, for which a strong-coupling version of the magnetic scenario could be
a reasonable starting point.
2. Experimental
ARPES measurements were carried out on beam line 10.0.1 at Advanced Light Source
(ALS) using different versions of Scienta electron energy analyzer, SES-200, SES-2002
and SES-R4000, across the years (1999 - present). The photon energies (hν) used are
55, 55.5 & 59.5 eV and the polarization of light was fixed in plane and orthogonal
to the zone diagonal (nodal) direction during each experiment by virtue of a sample-
fixed analyzer-rotating capability. The typical energy resolution was ∼20 meV and
angular resolution was 0.25◦(0.015˚ A−1in momentum). Single crystals grown by the
traveling solvent floating zone method were studied for different members of La214
family, La2−xSrxCuO4(LSCO or LS, grown by groups in Tokyo Institute of Technology
[25, 26], University of Tokyo [27], Electric Power Industry [28], Chinese Academy of
Sciences [29]), La2−xBaxCuO4 (LBCO or LB, grown by groups in Tohoku University
[22, 30, 31]) and 1% Fe-doped LSCO (Fe-LSCO or FeLS, grown by the group in Tohoku
University [32]). Superconducting transition temperature (Tc) vs. doping relations are
similar to the published results (of LSCO [18], LBCO [31], Fe-LSCO [34]) but varies
sightly for growth by different groups. Samples were cleaved in vacuum with a typical
base pressure better than 5x10−11Torr and measured at temperatures ∼20 K.
3. Results and Discussion
3.1. Existence of the (π,π) shadow band at x = 0.07
Fig. 1a shows an example for the typical Fermi surface (FS) mapping geometry of
this study. The spectral intensity in the nodal region of 2nd Brillouin zone (BZ) is
relatively enhanced compared to the one in 1st BZ due to the matrix element effects
[35, 12]. Despite the suppression of overall intensity and quasi-particle spectral weight
(Fig. 1e), the spectra along the nodal cut in 1st BZ of LSCO x = 0.07 show two counter-
dispersing bands which have comparable spectral weight (Fig. 1c). Their momemta are
approximately symmetric about the (π,π) BZ boundary (Fig. 1d). We denote hereafter
the ones marked in blue and in green are the MB and its (π,π) SB, respectively. In
contrast, the spectra taken at the nodal cut in 2nd BZ is dominated by a single dispersing
band with barely noticeable intensity on its corresponding SB feature (Fig. 1b & d).
The inequivalence of the intensity ratio of SB vs. MB (SB/MB) at equivalent in-plane
momenta indicates the SB and MB have different matrix element effects, suggesting
that the SB is unlikely a trivial replica of the MB due to the final-state photoelectron

Page 5

Doping dependence of the (π,π) shadow band in La214
5
Figure 1. a, FS map of LSCO x = 0.07 measured by SES-2002 across 3 BZs (Z’-Γ-Z)
taken with cuts parallel to the bond diagonal (nodal) direction. hν=55 eV. Intensity
integration window, EF±5 meV. Blue dashed line is the (π,π) BZ boundary, whose
crossing with a given cut is denoted as kAF hereafter. b & c, ARPES intensity as
a function of binding energy and parallel momentum along Cuts 1 & 2, the nodal
direction in 2nd and 1st BZ, respectively. The momentum direction and range as
indicated by the red and green arrows correspond to those in a. d, Intensity line
profiles of Cuts 1 & 2 in a shown in corresponding colors. Red, blue and green markers
point out the Fermi crossings (kF) of main band (MB) in 2nd BZ, MB and shadow
band (SB) in 1st BZ, respectively, which correspond to those in b & c. e, Energy
distribution curves (EDCs) at kF marked by the same colors in b & c.