of 6
August 2009
EPL,
87
(2009) 37005
www.epljournal.org
doi:
10.1209/0295-5075/87/37005
Scanning tunneling spectroscopic evidence
for magnetic-field–induced microscopic orders
in the high-T
c
superconductor YBa
2
Cu
3
O
7
δ
A. D. Beyer
1
,M.S.Grinolds
1
,M.L.Teague
1
,S.Tajima
2
and
N.-C. Yeh
1(a)
1
Department of Physics, California Institute of Technology - Pasadena, CA 91125, USA
2
Department of Physics, Osaka University - Osaka 560-0043, Japan
received 5 April 2009; accepted 23 July 2009
published online 26 August 2009
PACS
74.50.+r
– Tunneling phenomena; point contacts, weak links, Josephson effects
PACS
74.25.Op
– Mixed states, critical fields, and surface sheaths
PACS
74.72.Bk
– Y-based cuprates
Abstract
– We report spatially resolved tunneling spectroscopic evidence for field-induced
microscopic orders in the high-
T
c
superconductor YBa
2
Cu
3
O
7
δ
. The spectral characteristics
inside vortices reveal a pseudogap (
V
CO
) larger than the superconducting gap (∆
SC
) as well as a
subgap (∆

) smaller than ∆
SC
, and the spectral weight shifts steadily from ∆
SC
to
V
CO
and ∆

upon increasing magnetic field. Additionally, energy-independent conductance modulations at 3.6
and 7.1 lattice constants along the Cu-O bonding directions and at 9.5 lattice constants along the
nodal directions are manifested in the vortex state. These wave vectors differ fundamentally from
the strongly dispersive modes due to Bogoliubov quasiparticle scattering interferences and may
be associated with field-induced microscopic orders of pair-, charge- and spin-density waves.
Copyright
c
©
EPLA, 2009
Introduction. –
In conventional type-II supercon-
ductors, superconductivity is suppressed inside periodic
Abrikosov vortices [1], leading to continuous quasipar-
ticle bound states and a peak of local density of states
(LDOS) at zero energy [2–4]. In contrast, the effect
of magnetic field on high-
T
c
superconductors is much
more complicated than that on conventional type-II
superconductors. Macroscopically, high-
T
c
cuprates are
extreme type-II superconductors with strong thermal,
disorder and quantum fluctuations [5–8]. Microscopically,
neutron scattering experiments on hole-doped cuprate
La
1
.
84
Sr
0
.
16
CuO
4
reported an effective radius of vortices
substantially larger than the superconducting coherence
length
ξ
SC
[9]. Scanning tunneling spectroscopic (STS)
studiesofBi
2
Sr
2
CaCu
2
O
8+
x
(Bi-2212)foundnozero-bias
conductancepeaksinsidevortices[10,11].Furtherdetailed
spatially resolved STS studies of Bi-2212 in one magnetic
field
H
=5 T revealed a field-induced (4
a
0
×
4
a
0
) conduc-
tance modulation inside each vortex, where
a
0
=0
.
385nm
is the planar lattice constant of Bi-2212 [12]. The latter
finding has been attributed to the presence of a coex-
isting competing order (CO) such as pair-density waves
(a)
E-mail:
ncyeh@caltech.edu
(PDW) [13,14], pinned spin-density waves (SDW) [15,16],
or charge-density waves (CDW) [17–21] upon suppression
of SC inside the vortices. However, there have not
been high-resolution STS studies of the field-induced
collective modes on other high-
T
c
superconductors than
Bi-2212, neither has there been detailed investigation of
H
-dependent evolution of the collective modes, although
vortex images had been reported in Y-123 [22,23] and
effects of quasiparticle scattering by vortices have also
been investigated in Ca
2
x
Na
x
CaO
2
Cl
2
[24].
In this letter we report spatially resolved vortex-state
STSstudiesofY-123asfunctionsofmagneticfield,which
reveal two field-induced energy scales and three density-
wave modes with energy-independent wave vectors, in
addition to the effects associated with quasiparticle scat-
tering interferences [25,26]. These field-induced micro-
scopic orders differ fundamentally from the predictions
due to simple Bogoliubov quasiparticle scattering [25,26]
andaresuggestiveofsignificantinterplaybetweenSCand
competing orders upon increasing magnetic field.
Experimental. –
The synthesis and characterization
of the Y-123 untwinned single crystal with
T
c
=93K
studied here have been described elsewhere [27]. We
use chemical etching to prepare Y-123 surface for STS
37005-p1
A. D. Beyer
et al.
experiments because Y-123 is more difficult to handle
than Bi-2212 [23,28], and bromine chemical etching
techniques can reproducibly remove non-stoichiometric
surface layers to reveal quality surfaces, as manifested by
X-ray photoemission spectroscopy [28].
The spatially resolved tunnelling conductance (d
I/
d
V
)
vs
. energy (
ω
=
eV
) spectra for the quasiparticle LDOS
maps were obtained with our homemade cryogenic
scanning tunnelling microscope (STM). Our STM has a
base temperature of 6K, variable temperature range up
to room temperature, magnetic field range up to 7tesla,
andultra-highvacuumcapabilitydowntoabasepressure
<
10
9
torr at 6K. For each constant temperature (
T
)
and magnetic field (
H
), the experiments were conducted
by tunneling currents along the crystalline
c
-axis under
a range of bias voltages at a given location. The typical
junction resistance was
1GΩ. Current (
I
)
vs
. volt-
age (
V
) measurements were repeated pixel-by-pixel
over an extended area of the sample. To remove slight
variations in the tunnel junction resistance from pixel
to pixel, the differential conductance at each pixel is
normalized to its high-energy background [29].
Results and analysis. –
In fig. 1(a) we illustrate
the normalized zero-field
c
-axis tunneling conductance
spectra taken at
T
=6
,
77 and 102K. For
T
=6K, the
spectrum exhibits clear coherence peaks at energies
±
SC
∼±
20meV and shoulder-like satellite features
at
±
eff
∼±
38meV. At
T
=77K
<T
c
, only one set of
rounded features remains. Eventually for
T
=102K
>T
c
the peaks vanish within experimental resolution. The
long-rangehomogeneityofthezero-fieldtunnelingspectra
is exemplified by the (95
×
95)nm
2
spatial map of the
superconducting (SC) gap ∆
SC
in fig. 1(b) and by the
corresponding energy histogram (∆
SC
=20
.
0
±
1
.
0meV)
in fig. 1(c), which differs from the strong spatial vari-
ations in the quasiparticle spectra of Bi-2212 [25]. In
contrast, the satellite features at
±
eff
exhibit stronger
spatialinhomogeneity,asmanifestedbythe(95
×
95)nm
2
spatial map of ∆
eff
in fig. 1(e) and by the corresponding
histogram in fig. 1(f), showing ∆
eff
=37
.
8
±
2
.
0meV.
A possible interpretation for the zero-field spectra in
fig. 1(a) may be a scenario of coexisting CO and SC in
the ground state of the cuprates [19–21,26,30]. Following
the analysis briefly outlined in the Discussion section
and detailed elsewhere [19,20], we can account for the
zero-field spectra in fig. 1(a) by incorporating realistic
bandstructures for Y-123 and assuming either CDW or
disorder-pinned SDW as the CO with a wave vector
Q
CO
parallel to the Cu-O bonding directions. We find
that both CDW and disorder-pinned SDW yield equally
goodfittingexcept
|
Q
CDW
|
=2
|
Q
SDW
|
[16].At
T

T
c
our
theoretical fitting (black solid curve) can account for the
sharp superconducting coherence peaks at
ω
=
±
SC
and
theshoulder-likesatellitefeaturesat
ω
=
±
eff
,wherethe
effective gap ∆
eff
is related to ∆
SC
and the CO energy
V
CO
via the relation ∆
2
eff
=[∆
2
SC
+
V
2
CO
] [19,20]. Thus,
Fig. 1: (Color online) Implication of CO from zero- and finite-
fieldSTSinY-123.(a)Normalizedzero-fieldtunnelingspectra
taken at
T
=6, 77 and 102K. The solid lines represent fittings
to the
T
=6, 77 and 102K spectra by assuming coexisting SC
and CO, following refs. [19,20]. For more details of the data
normalizationandtheoreticalfittingprocedures,seeDiscussion
andrefs.[19,20].(b)The∆
SC
mapovera(95
×
95)nm
2
areaat
T
=6Kand
H
=0.(c)Histogramof∆
SC
overthesameareaas
in(b),showing∆
SC
=(20
.
0
±
1
.
0)meV.(d)Spatiallyaveraged
intra-andinter-vortexspectrafor
T
=6Kand
H
=2T.(e)The
eff
map over a (95
×
95)nm
2
area at
T
=6K and
H
=0.
(f) Histogram of ∆
eff
in the same area as in (e), showing
eff
=37
.
8
±
2
.
0meV.
we obtain ∆
SC
=20meV,
V
CO
=32meV and
|
Q
CO
|
=
(0
.
25
±
0
.
03)
π
. For elevated temperatures below
T
c
, such
as
T
=77K, our fitting (red solid curve in fig. 1(a)) also
agrees with experimental data with rounded features at
±
eff
(
T
) [19,20].
An alternative way to verify the feasibility of the CO
scenario is to introduce vortices because the suppression
of SC inside vortices may unravel the spectroscopic
characteristics of the remaining CO. As exemplified in
fig. 1(d) for a set of intra- and inter-vortex spectra taken
at
H
=2T, the quasiparticle spectra near the center
of each vortex exhibit pseudogap (PG)-like features, in
contrast to theoretical predictions for a sharp zero-energy
peak around the center of the vortex core had supercon-
ductivity been the sole order in the ground state [2,3,31].
Interestingly, the PG energy inside vortices is comparable
to the CO energy
V
CO
32meV derived from our zero-
field fitting as well as the spin gap energy obtained from
neutron scattering studies of optimally doped Y-123 [32].
37005-p2
Magnetic-field–induced microscopic orders in YBa
2
Cu
3
O
7
δ
Fig. 2: (Color online) Vortex-state conductance maps at
T
=
6KinY-123.(a)Conductancepowerratio
r
G
mapovera(75
×
38)nm
2
area for
H
=2T, showing disordered vortices with an
average
a
B
=(33
.
2
±
9
.
0)nm. (b) The
r
G
map over a (75
×
40)nm
2
area for
H
=4
.
5T, showing
a
B
=(23
.
5
±
8
.
0)nm. (c)
Conductance spectra along the white line in (a), showing
SC peaks at
ω
=
±
SC
outside vortices and PG features at
ω
=
±
V
CO
inside vortices. (d) Conductance spectra along the
dashedlineindicatedin(b).Spatiallyaveragedintra-andinter-
vortex spectra for (e)
H
=2T,(f)
H
=4
.
5T and (g)
H
=6T.
To investigate how quasiparticle spectra evolve with
field, we performed spatially resolved spectroscopic stud-
ies at
H
=2, 4.5, 5 and 6T and for
T
=6K. In figs. 2(a)
and (b) we show exemplified spatial maps of the conduc-
tance power ratio
r
G
for
H
=2 and 4.5T, respectively.
Here
r
G
at every pixel is defined as the ratio of the
conductance power (d
I/
d
V
)
2
at
ω
=∆
SC
relative to that
at
ω
=0.Wefindthatthepresenceofvorticesisassociated
with the local minimum of
r
G
because of enhanced zero-
energy quasiparticle density of states inside the vortex
core. Moreover, the total flux is conserved within the
areastudieddespitetheappearanceofdisorderedvortices.
That is, the total number of vortices multiplied by the
flux quantum is equal to the magnetic induction multi-
plied by the area, within experimental errors. Thus, we
obtainaveragedvortexlatticeconstants
a
B
=33
.
2nmand
23.5nmfor
H
=2Tand4.5T,respectively,comparableto
thetheoreticalvaluesof
a
B
=35
.
0nmand23.3nm.Onthe
other hand, the mean “vortex halo” radius
ξ
halo
is much
longer than the SC coherence length
ξ
SC
, and the average
ξ
halo
decreaseswithfield.Wefind
ξ
halo
=(7
.
7
±
0
.
3)nmfor
H
=2T, (6
.
4
±
0
.
6)nm for
H
=4
.
5T,and(5
.
0
±
0
.
7)nm
for
H
=6T.
The spatial evolution of the vortex-state spectra
may be better manifested by following a line through
multiple vortices in the vortex maps of figs. 2(a) and (b).
Asshowninfigs.2(c)and(d)for
H
=2and4.5T,respec-
tively, the vortex-state spectral characteristics differ
from those of conventional type-II superconductors [4],
showing modulating gap-like features everywhere without
any zero-energy peaks. In figs. 2(e)–(g) we compare
representativespectratakeninsideandoutsideofvortices
for
H
=2,4.5and6T.Inaconstantfield,theinter-vortex
spectrum reveals a sharper set of peaks at
ω
=
±
SC
,
whereas the intra-vortex spectrum exhibits PG features
at
ω
=
±
V
CO
and
V
CO
>
SC
. Additional subgap features
at
ω
=
±

=
±
(7–10)meV are found inside vortices,
which become more pronounced with increasing
H
.The
physical origin of ∆

is still unknown.
Next, we perform Fourier transformation (FT) of
the vortex-state spectra and compare the results with
the FT zero-field spectra taken in the same area. We
define the FT-LDOS taken under a magnetic field
H
and at a constant energy
ω
by the quantity
F
(
k
,ω,H
).
In figs. 3(a)–(c), we illustrate field-induced FT-LDOS
|
̃
F
(
k
,ω,H
)
|≡|
F
(
k
,ω,H
)
F
(
k
,ω,
0)
|
at
H
=5T and
integrated over different ranges of energies, where
̃
F
(
k
,ω,H
)
i
e
i
k
·
R
i
[
d
I
d
V
(
R
i
,ω,H
)
d
I
d
V
(
R
i
,ω,
0)
]
.
(1)
Here
R
i
denotes the coordinate of the
i
-th pixel, and
the sum is taken over all pixels of each two-dimensional
map. Systematic analysis of the energy dependence
of the FT-LDOS [33] reveals two types of diffraction
spots. One type of spots are strongly dispersive and
may be attributed to elastic quasiparticle scattering
interferences as seen in the zero-field FT-LDOS [25,26].
The other type of spots are nearly energy-independent,
as manifested in figs. 3(a) and (b) for FT-LDOS at
two different energies
ω
=
10meV and
20meV,
respectively, and in fig. 3(c) for normalized FT-LDOS
integrated from
ω
=
1meV and
30meV. In addition
to the reciprocal lattice vectors, we find two sets of nearly
energy-independent wave vectors along (
π,
0)
/
(0
)and
one set along (
π,π
):
Q
PDW
=[
±
(0
.
56
±
0
.
06)
π/a
1
,
0] and
[0
,
±
(0
.
56
±
0
.
06)
π/a
2
],
Q
CDW
=[
±
(0
.
28
±
0
.
02)
π/a
1
,
0]
and [0
,
±
(0
.
28
±
0
.
02)
π/a
2
], and
Q
SDW
=[
±
(0
.
15
±
0
.
01)
π/a
1
,
±
(0
.
15
±
0
.
01)
π/a
2
]. Here
a
1
=0
.
383nm and
a
2
=0
.
388nm.Forclarity,weillustrate
|
̃
F
(
k
)
|
fordiffer-
ent energies along
k

(
π,
0) in the upper of fig. 3(d) and
along (
π,π
) in the lower panel, where the
ω
-independent
peaks correspond to
|
Q
XDW
|
(X=P,C,S)andthe
reciprocal lattice vector (2
π/a
1
,
2
). These wave vectors
are nearly energy independent, as shown in fig. 3(e). For
comparison, a dispersive wave vector due to quasiparticle
scattering interferences [25,26] along (
π,π
), which is
denoted as
q
7
in ref. [25], is also shown in the lower panel
of fig. 3(e). We note that the dispersion relation for the
mode
q
7
along the nodal direction is in good agreement
with both the experimental results found in Bi-2212 [25]
37005-p3
A. D. Beyer
et al.
Fig. 3: (Color online) FT studies of the vortex-state conductance maps in the two-dimensional reciprocal space and at
H
=5T.
(a) FT-LDOS
|
̃
F
(
k
)
|
for
ω
=
10meV. (b) FT-LDOS
|
̃
F
(
k
)
|
for
ω
=
20meV. (c) Normalized FT-LDOS obtained by
integrating
|
̃
F
(
k
)
|
from
1meVto
30meV. Comparing (a)–(c), we find three sets of energy-independent spots in addition
tothereciprocallatticeconstantsandthe(
π,π
)resonance:
Q
PDW
and
Q
CDW
alongthe(
π,
0)
/
(0
)directionsand
Q
SDW
along
(
π,π
), which are circled for clarity. (d)
|
̃
F
(
k
)
|
for different energies are plotted against
k

(
π,
0) and (
π,π
) in the upper and
lower panels, respectively, showing peaks at energy-independent
Q
PDW
,
Q
CDW
and the reciprocal lattice constants at (2
π/a
1
)
along (
π,
0), and at
Q
SDW
along (
π,π
). Additionally, dispersive wave vectors due to quasiparticle scattering interferences are
found, as exemplified in the lower panel. (e) Momentum (
|
q
|
)
vs
.energy(
ω
)for
|
Q
PDW
|
,
|
Q
CDW
|
and
|
Q
SDW
|
. One dispersive
wave vector along (
π,π
), denoted as
q
7
[25], is also shown in the lower panel for comparison. (f) The symmetric and anti-
symmetric components of Re[
̃
F
(
k
)] for
k
=
Q
PDW
,
Q
CDW
and
Q
SDW
are shown as functions of
ω
in the upper and lower
panels, respectively.
andthetheoreticalpredictionsforquasiparticlescattering
interferences [25,26].
Interestingly,wefindthat
Q
PDW
and
Q
CDW
correspond
to charge modulations at wavelengths of (3
.
6
±
0
.
4)
a
1
,
2
and(7
.
1
±
0
.
6)
a
1
,
2
alongtheCu-Obondingdirections.The
former is comparable to the checkerboard modulations
reported in the vortex state of Bi-2212 [12], whereas
the latter is consistent with the Fermi surface-nested
CDW wave vector derived from our zero-field analysis.
On the other hand, the nodal wave vectors
Q
SDW
may be
associatedwithSDWbecauseofthefield-inducedunequal
populations of spin-up and spin-down quasiparticles. In
thiscontext,wenotethatintensespotsassociatedwiththe
(
π,π
)spinresonance[32]arealsomanifestedfor
ω<
SC
,
as exemplified in fig. 3(a) for
ω
=
10meV. These field-
induced collective modes along the nodal direction are
suggestive of important interplay between SC and spin
excitations in the cuprates.
To better understand the nature of these field-induced
wave vectors, we consider the symmetry of the complex
quantity Re[
̃
F
(
k
)] relative to energy (
ω
)at
k
=
Q
XDW
in fig. 3(f), with the symmetric and anti-symmetric
components of Re[
̃
F
]at
k
=
Q
XDW
shown in the upper
and lower panels, respectively. We find that
̃
F
is predom-
inantly symmetric at
Q
PDW
and primarily antisymmetric
at
Q
SDW
. On the other hand,
̃
F
appears to have compa-
rable symmetric and anti-symmetric components at
Q
CDW
. The antisymmetric
̃
F
is consistent with the SDW
scenariofor
k

(
π,π
)[15,16],whereasfor
k

(
π,
0)
/
(0
),
symmetric and anti-symmetric
̃
F
may be attributed
respectively to PDW [13,14] and CDW [17–21].
In fig. 4(a) we illustrate the energy histograms of
the SC and PG (or CO) features for
H
=0, 2, 4.5
and 6T. A strong spectral shift from SC at
ω
=∆
SC
to PG at
ω
=
V
CO
is seen with increasing
H
, together
with the appearance of a third subgap (SG) feature
at
ω
=∆

<
SC
. For comparison, schematic histograms
for conventional type-II superconductors are shown in
fig. 4(b), which exhibit spectral shifts from an initial
ω
=
SC
to a continuous energy distribution
ω<
SC
, with
an additional peak appearing at
ω
=0 in the
H

H
c
2
and
T

T
c
limit. The fraction of the spectral downshift
is approximately given by (
πξ
2
SC
/
2)
/
(
3
a
2
B
/
4), which
is linear in
H
. The predictions in fig. 4(b) apparently
37005-p4
Magnetic-field–induced microscopic orders in YBa
2
Cu
3
O
7
δ
Fig. 4: (Color online) Field-dependent spectral evolution at
T
=6K in Y-123. (a) Energy histograms derived from STS
data for
H
=0, 2, 4.5, and 6T, showing a spectral shift from
SC
to
V
CO
and ∆

with increasing
H
. (b) Schematic of
the histograms for a conventional type-II superconductor in
the limit of
T

T
c
and
H

H
c
2
. (c) Gaussian fitting to the
histogramsin(a)revealsnearlyfield-independent∆
SC
and
V
CO
(left), decreasing SC and increasing CO spectral weight with
increasing
H
(center), and increasing SC and CO line widths
with increasing
H
(right).
differ from our empirical findings in fig. 4(a). In fig. 4(c)
we summarize the Gaussian fitting parameters to the
histograms in fig. 4(a). We find that the values of both
SC
and
V
CO
remain invariant with
H
, whereas the CO
spectralweightandlinewidthincreasewithincreasing
H
.
Discussion. –
The occurrence of two energy scales
V
CO
(
>
SC
) and ∆

(
<
SC
) inside vortices and the
field-induced energy-independent wave vectors
Q
PDW
,
Q
CDW
and
Q
SDW
strongly suggest that the vortex-state
quasiparticle tunneling spectra in Y-123 cannot be
explained by simple Bogoliubov quasiparticle scattering
interferences alone [24–26]. On the other hand, these
findings may be compared with the scenario of coexisting
CO’s and SC [13–21]. In particular, we find that the
energy scale
V
CO
and the wave vector
Q
CDW
manifested
in the vortex-state spectra are consistent with the CO
parameters derived from our Green’s function analysis of
the zero-field data. That is, we assume that the ground
state of Y-123 consists of coexisting SC and CO so that
the corresponding mean-field Hamiltonian is given by the
following expression [19,20]:
H
MF
=
H
SC
+
H
CO
=
k
ξ
k
c
k
c
k
k
SC
(
k
)(
c
k
,
c
k
,
+
c
k
,
c
k
,
)
+
k
V
CO
(
k
)(
c
k
+
Q
c
k
+
c
k
c
k
+
Q
)
.
(2)
Here ∆
SC
(
k
)=∆
SC
(cos2
θ
k
)for
d
x
2
y
2
-wave pairing,
k
denotes the quasiparticle momentum,
θ
k
tan
1
(
k
y
/k
x
),
ξ
k
is the normal-state eigenenergy relative to the Fermi
level,
c
and
c
are the particle creation and annihilation
operators, and
α
=
,
refers to the spin states. We
incorporate realistic bandstructures into
ξ
k
for direct
comparison with experiments [19,20]. By assuming a
Fermi surface-nested CDW along (
π,
0)
/
(0
)asthe
relevant CO, we diagonalize
H
MF
and obtain the bare
Green’s function
G
0
(
k
). The effect of quantum fluc-
tuations may be further included by solving the Dyson’s
equation for the full Green’s function
G
(
k
) [19,20].
Thus,thequasiparticleDOSmaybederivedfrom
G
(
k
)
as detailed in refs. [19,20]. For finite temperatures, we
employ the temperature Green’s function [19,20].
Following the approach outlined above and detailed
in refs. [19,20], we can account for the zero-field tunnel-
ing spectra shown in fig. 1(a) by the following fitting
parameters: ∆
SC
=(20
±
1)meV,
V
CO
=(32
±
1)meV,
and
Q
CO
=(0
.
25
π,
0)
/
(0
,
0
.
25
π
) for the CDW. We note
that the energy scale
V
CO
=(32
±
1)meV accounts for
the shoulder-like features at
ω
=
±
eff
≈±
38meV in the
tunneling spectra, where ∆
eff
[∆
2
SC
+
V
2
CO
]
1
/
2
[19,20].
Moreover, the magnitude of
V
CO
=(32
±
1)meV agrees
with that of the spin gap observed in neutron scattering
data of optimally doped Y-123 [32] and the PG energy
seen inside the vortex cores, as shown in figs. 2(e)–(g).
On the other hand, the corresponding wave vector
Q
CO
is along the Cu-O bonding direction, which remains in
the vortex-state and is identified as the mode
Q
CDW
in
the FT-LDOS.
As an interesting comparison, we note that our recent
vortex-state STS studies on an electron-type optimally
dopedcuprateLa
0
.
1
Sr
0
.
9
CuO
2
(La-112)alsorevealedPG-
like features inside vortices [34], except that the PG
energy in La-112 is
smaller
than ∆
SC
. This finding
may also be interpreted as a CO being revealed upon
the suppression of SC. Furthermore, the smaller energy
associated with the PG-like features inside vortices of
La-112 is consistent with the
absence
of PG above
T
c
in
electron-typecupratesuperconductors[34].Thesefindings
from the vortex-state quasiparticle spectra of La-112 are
in contrast to those of Y-123 and the differences may be
attributed to the different magnitude of
V
CO
relative to
SC
[34].
Conclusion. –
Ourspatiallyresolvedscanningtunnel-
ingspectroscopicstudiesofY-123inthevortexstatehave
revealed various novel spectral characteristics, includ-
ing two energy scales (
V
CO
and ∆

) other than the SC
gap ∆
CO
inside vortices and three accompanying energy-
independent wave vectors
Q
PDW
,
Q
CDW
and
Q
SDW
.
These results cannot be reconciled with theories assum-
ing a pure SC order in the ground state [35]. Rather, they
areconsistentwiththeCOscenarioandsuggestimportant
interplay between SC and various collective excitations in
high-
T
c
superconductors.
37005-p5
A. D. Beyer
et al.
∗∗∗
This work was jointly supported by the Moore Foun-
dation and the Kavli Foundation through the Kavli
Nanoscience Institute at Caltech, and the NSF Grant
DMR-0405088. The authors thank Dr.
A. I. Rykov
for growing the single crystal used in this work and
Profs.
S. A. Kivelson
and
S.-C. Zhang
for useful
discussions. ADB acknowledges the support of Intel
Graduate Fellowship.
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