Table Of ContentEvolution of Coherence and Superconductivity in Electron-Doped Cuprates
M. M. Qazilbash1,2, B. S. Dennis1, C. A. Kendziora3, Hamza Balci2, R. L. Greene2, and G. Blumberg1,†
1Bell Laboratories, Lucent Technologies, Murray Hill, NJ 07974
2Center for Superconductivity Research, Department of Physics,
University of Maryland, College Park, MD 20740
5 3United States Naval Research Laboratory, Code 6365, Washington D.C. 20375
0
(Dated: February 2, 2008)
0
2 The electron-doped cuprates were studied by electronic Raman spectroscopy across the entire
region of the superconducting (SC) phase diagram. We determined that the magnitude of the SC
n
a orderparametervariesbetween4.6and3.5kBTc,consistentwithweakcouplingBCStheory. Using
J a“Ramanconductivity”sumrule,wefoundthatdopedcarriersdivideintocoherentquasi-particles
(QPs) and carriers that remain incoherent. The coherent QPs mainly reside in the vicinity of
5
(±π/2a, ±π/2a) regions of the Brillouin zone. The carriers doped beyond optimal doping remain
1
incoherent. Only coherent QPs contribute tothe superfluid density in theSC state.
]
n PACSnumbers: 74.25.Gz, 74.72.Jt,78.30.-j
o
c
- Introduction.– In recentyears,there has been renewed imize the substrate contribution to the Raman signal.
r
p interest in the physical properties of electron n-doped The SC transitions were measured by ac susceptibility.
u high T superconducting (SC) cuprates. While there is The films provide an opportunity to study the extremes
c
s
. considerableevidence thatthe SC orderparameter(OP) oftheSCphasebecauseofbettercontrolofCedopingin
t
a oftheholep-dopedcuprateshasd-wavesymmetryinthe under-doped (UND) and highly over-doped(OVD) sam-
m entiredopingrangeoftheirSCphase[1,2],thesituation ples.
- for the n-doped compounds still remains controversial. Thesamplesweremountedinanopticalcontinuoushe-
d
EarlierRaman data for optimally-doped(OPT) samples lium flow cryostat. The spectra were taken in a pseudo-
n
implied a non-monotonic d-wave OP [3]. There is dis- backscattering geometry using linearly polarized excita-
o
c agreementamongthe few experiments that havestudied tions at 647 and 799 nm from a Kr+ laser. Incident
[ the doping dependence of the SC OP [4, 5, 6, 7]. Angle- laser powers between 0.5 and 4 mW were focused to a
1 resolved photoemission spectroscopy (ARPES) data at 50×100 µm spot on the sample surface. The spectra
v optimal doping indicates the presence of both well- were measured at temperatures between 4 and 30 K by
2 defined quasi-particles (QPs), as well as ill defined inco- a custom triple grating spectrometer and the data were
6 herent excitations [8]. There is current interest in exam- correctedforinstrumentalspectralresponse. Thesample
3
iningtherelationshipbetweenthecoherencepropertiesof temperaturesquotedinthisworkhavebeencorrectedfor
1
introduced carriers and development of the SC OP with laser heating.
0
5 doping. We report a systematic low energy electronic Ramanscatteringsymmetries.–Thepolarizationdirec-
0 Raman spectroscopy (ERS) study of Pr2−xCexCuO4−δ tions of the incident, ei, and scattered, es, photons are
t/ (PCCO) and Nd2−xCexCuO4−δ (NCCO) single crystals indicated by (eies) with x=[100], y=[010], x’=[110] and
a andfilmswithdifferentceriumdopingcoveringtheentire
y’=[110]. The presented data were taken in (xy), (x’y’)
m
SC region of the phase diagram and determine the mag-
and (xx) scattering geometries. For the tetragonal D
4h
d- nitude of the OP as a function of doping. By applying symmetryofthen-dopedcuprates,thesegeometriescor-
a ”Raman conductivity” sum rule [9, 10], we find that
n respondtoB +A ,B +A andA +B representa-
2g 2g 1g 2g 1g 1g
o carriersdopedbeyondoptimaldopingremainincoherent tions. Using circularly polarized light we confirmed that
c and do not contribute to the superfluid density.
thecontributiontotheA channelisveryweakforboth
: 2g
v PCCO and NCCO.
i Experimental.– Raman scattering was performed from
X TheelectronicRamanresponsefunction,χ′′(is)(ω),for
natural ab surfaces of single crystals and films of PCCO
a given polarization geometry (e e ) is proportional to
r and single crystals of NCCO. Crystals with different Ce i s
a the sum over the density of states at the Fermi surface
concentrations were grown using a flux method as de-
(FS) weighted by the square of the momentum k depen-
scribedin [11]. Aftergrowth,thecrystalswereannealed
in an Ar-rich atmosphere to induce superconductivity. dentRamanvertexγk(is) [13,14,15]. Becausethescatter-
ing geometries selectively discriminate between different
The SC transitions were measured by a SQUID magne-
regions of the FS, ERS provides information about both
tometer. The Ce concentration of the crystals was mea-
sured with wavelength dispersion spectroscopy. c-axis themagnitudeandthekdependenceoftheSCOP.Inthe
oriented PCCO films were grown on strontium titanate effective mass approximationγkB1g ∝t(coskxa−coskya)
substrates using pulsed laser deposition [12]. The films and γB2g ∝ 4t′(sink asink a) where t and t′ are near-
k x y
were grown to a thickness of about 0.8 to 1 µm to min- est and next-nearest neighbor hopping integrals in the
2
Pr CeCuO Nd CeCuO crystals
2-x x 4-d 2-x x 4-d
UND OPT OVD OVD OVD OVD x OPT OVD
x 0.135 + 0.003 0.147 + 0.003 0.165 + 0.005 0.17 + 0.005 0.17 + 0.002 0.18 + 0.002 x 0.15 + 0.005 0.16 + 0.005
Tc(K) 16.5 + 1 23.5 + 1.5 15 + 2 13 + 2 13 + 0.5 10 + 0.5 T(K) 22 + 1 14 + 2
film crystal crystal crystal film film c
2205 B2g x 0.5 nits)30 B2g B2g 30
el. units) 11055 nse (rel. u1200 1200
se (r 40 B1g espo 06 B1g B1g 60
n R
po 3 n 4 4
s a
e 2 m
R a 2 2
n 1 R
ma 0 0 0
Ra 24 A1g X 0.2 0 Ra5m0an S0hift 5(0cm 1-10)0
18
X 0.4
12
FIG.2: AcomparisonoftheRamanresponseintheSCstate
6
for OPT (first column) and OVD (second column) NCCO
0
0 50 0 50 0 50 0 50 0 50 0 50 100 crystals. The first and second rows show spectra for B2g
Raman Shift (cm-1) and B1g channels respectively. The violet (light) and orange
(dark) curves are data taken with red laser excitation (λL =
FIG. 1: Doping dependence of the low energy electronic Ra- 647nm)andnear-IRexcitation(λL=799nm). TheB2g and
manresponseofPCCOsingle crystalsandfilmsfor B2g,B1g B1g dataforλL =647nmhasbeenshiftedupby5unitsand
and A1g channels obtained with 647 nm excitation. The 1 unit respectively. All spectra are taken at T ≈ 4 K. The
columns are arranged from left to right in order of increas- dashedverticallinesshowthepositions ofthe2∆ peaks. For
ing cerium doping. The light (red) curves are thedata taken the OPT crystal a low-frequency ω3 power law is shown in
justabovetherespectiveTc ofthesamples. Thenormalstate theB1g panel for comparison (light-bluedotted line).
responseintheB2g andB1g channelsisdecomposedintoaco-
herentDrudecontribution in aquasi-elastic form (green dot-
ted line) and an incoherent continuum (yellow dotted line).
The dark (blue) curves show the data taken in the SC state polarizations in the OVD samples and are significantly
atT≈4K.Thedashedverticallinesindicatepositionsofthe stronger in the UND and OPT samples. This lack of
2∆ peak. FortheOPTcrystalalow-frequency ω3 powerlaw screening is not understood within the framework of ex-
is shown in the B1g panel for comparison (light-blue dotted isting theoretical models.
line). OVDcrystalsandfilmsshowsimilar behavior,indicat-
Pair breaking excitations out of the SC condensate.–
ing thegood quality of thefilms.
In the B and A channels, the pair-breaking 2∆ co-
2g 1g
herencepeaksappearfor alldoping concentrationswhile
in the B channel the 2∆ peaks are negligibly weak in
1g
tight-binding model. For the B channel the Raman
2g the UND and the most OVD films. For the OPT crystal
vertex is maximum around (π/2a, π/2a) and equivalent
(T = 23.5 K) the coherence peak energy is larger for
c
regionsofthe Brillouinzone (BZ) andvanishes along(0,
the B channel compared with that in B and for all
0)→(π/a, 0) and equivalent lines. For the B channel 2g 1g
1g channels it is larger than the scattering rate Γ obtained
nodal (0, 0)→(π/a, π/a) diagonals do not contribute to
fromthe spectrainthe normalstatediscussedinthe fol-
theintensitythatmainlyintegratesfromtheregionsnear
lowing section. The intensity below the coherence peaks
intersections of the FS and the BZ boundary.
vanishes smoothly without a threshold to the lowest fre-
Figure 1 exhibits the evolutionwith doping of the Ra- quency measured. The absence of a threshold that has
man response function above T and at 4 K, deep in beenobservedins-wavesuperconductorsprecludesinter-
c
the SC state, for all three observable symmetry chan- pretation in terms of a fully gapped Fermi surface [13].
nels: B , B and A . The total intensity is signifi- The smooth decrease in the Raman response below the
2g 1g 1g
cantlystrongerintheB thanintheB channelforall 2∆peakisconsistentwithnodesinthegap. Wecompare
2g 1g
doping concentrations. This underlines the importance the low-frequency tail in the B response (Fig. 1) to an
1g
of the next-nearest neighbor hopping t′ for the n-doped ω3 power law that is expected for a dx2−y2-wave super-
cuprates and is in contrastwith p-doped cuprates where conductorinthecleanlimit[17]. Theobserveddeviation
the response inthe B channelis generallyweakerthan from cubic to a linear response at the lowest frequen-
2g
in B [16]. Although Coulomb screening should lead to ciesisanindicationoflow-energyQPscattering[18,20].
1g
a much weaker Raman response in the fully symmetric ThedataforOPTPCCOisverysimilartothatforOPT
channel, we find that the intensities in the A channel NCCO (see Fig. 2) which was interpreted in terms of a
1g
are of the same order of magnitude as those in crossed non-monotonicd-waveorderparameterwithnodesalong
3
the (0, 0)→(π/a, π/a) diagonal and the maximum gap Tunneling
10
a
being closer to this diagonal than to the BZ boundaries
[3]. 8 B2g
Interestingly, in the OVD PCCO samples (Fig. 1) and V) B1g
me 6
OVD NCCO crystal (Fig. 2), the 2∆ peak positions are
( A
at the same energies for both the B2g and B1g chan- D2 4 1g
40
nels. The 2∆ peak positions and intensities decrease in T
the OVD regime compared to the OPT samples. More- 2 Tc 20c (K
over, 2∆ ∼ Γ indicates that superconductivity is ap- )
0 0
proaching the dirty or disordered limit [20]. The Ra-
B2g b
manresponsebelowthe2∆-peaksvanishessmoothlyand
c 4
no well-defined threshold is observed. The data for the TB B1g
799 nm excitation is measured down to 4.5 cm−1 and /k
D2 2 A1g
shows no obvious sub-gap threshold. The peak posi-
tions and the sub-gap Raman response in the NCCO
crystals are almost independent of the laser excitation 0
40
energies (Fig. 2). A similar symmetry independent pair wd B
breaking peak energy with continuously decreasing Ra- /w) 30 2g
man scattering intensity down to the lowest frequencies EP20
Q
" c
measured has been observed in the Raman spectra in (c 10
∫
OVD samples of p-doped Bi-2212[21]. The Raman data 0
presented in Figs. 1-2 for OVD n-doped samples is simi-
lartotheRamandataforOVDBi-2212. Thecoincidence wd30 30 l
/w) -2
of the coherence peak energies in the B1g and B2g chan- " D220 20(mm
nels is probably caused by enhanced QP scattering [20]. (c∫10 B2g d 10)-2
Nevertheless, the continuously decreasing Raman inten-
sity below the coherence peak is not inconsistent with a 0 0
0.13 0.15 0.17
nodal gap structure.
x (Ce)
Figure 3(a) summarizes the energy of the 2∆ coher-
ence peak as a function of doping for all three scattering FIG. 3: The phase diagram of PCCO (filled symbols) and
channels. The coherence peak energy has a pronounced NCCO (open symbols) superconductors explored by ERS.
maximum at optimal doping. The 2∆ features in the Panelsshow: (a)Tc and2∆peakpositions(gapmagnitudes)
A channel occur at lower energies compared to those forB1g,B2g andA1g channelsaswellasthedistancebetween
1g coherence peaks from point contact tunneling spectroscopy
in the B and B channels. For comparison, we in-
2g 1g [22]; (b) The magnitude of the reduced gap (2∆/kBTc) for
clude the value of twice the SC gap energy obtained
three Raman channels; (c) The integrated QP (Drude) re-
from point contact tunneling spectroscopy [22]. While sponse just above Tc; (d) The integrated intensity in the SC
for OPT and OVD samples the maximum value of the coherence peak at 4 K. For comparison, we plot 1/λ(0)2 val-
Raman 2∆ peak positions are very similar to the single ues from refs. [5] (×) and [7] (open crosses). Error bars
particle spectroscopy gap values, this is not the case for on the cerium concentrations are shown only on the Tc data
points to preserve clarity of the figure. Solid lines are guides
theUNDsampleswherethetunnelingspectroscopydata
to theeye.
exhibits a gap that is larger than the Raman coherence
peaks. For UND samples the twoQPs excited outof the
SC condensate by Ramanprocessescontinue to interact,
the B channel and is even lower for the A channel,
binding into a collective excitonic state that costs less 1g 1g
particularly for the UND sample. The reduced energies
energy than excitation of two independent QPs. Similar
for all the channels are significantly lower than for p-
observations were made previously for p-doped cuprates
doped materials [16, 23, 27] suggesting a BCS weak cou-
[16,23]. Theimportanceofthefinalstateinteractionsin
pling limit for the n-doped cuprates.
the formation of a collective mode in UND cuprates has
been demonstrated in Refs. [24, 25]. Evolution with carrier doping in the normal state.– In
Reduced energies of the coherence peaks, 2∆/k T , the normal state the Raman response can be decom-
B c
are plotted in Fig. 3b as a function of doping. For the posed into a featureless continuum and a defined low-
channel that exhibits the highest ratio, B2g, the values frequency quasi-elastic scattering peak (QEP): χ′N′(ω)=
fall between 4.6 for the UND and OPT samples and 3.5 χ′Q′EP(ω)+χ′M′ FL(ω). The QEP response χ′Q′EP(ω) =
for the most OVD samples, within the prediction of the a(is) Γω is described in a Drude model as a well de-
ω2+Γ2
mean-field BSC values for d-wave superconductors [26]. fined QP contribution from doped carriers [10, 28] while
The coherence peak energy remains below 4.2k T for the featureless continuum χ′′ (ω) = b(is)tanh(ω/ω )
B c MFL c
4
represents a collective incoherent response [29]. Symme- channel decrease monotonically from 4.6 for the UND
trydependenta(is) andb(is) parameterscontrolthespec- sample to 3.5 for OVD samples. Using the “Ramancon-
tralweightinthesecoherentandincoherentchannels,ω ductivity” sum rule, we find that carriers doped beyond
c
is a cut-off frequency of order k T [29] and the QEP optimal doping remain incoherentand do not contribute
B
position Γ is the Drude scattering rate that at low tem- totheDrudeconductivityandsuperfluiddensity. There-
peratures remains between 2 and 2.5 meV for the entire duced ratio of coherent on the background of incoherent
studied doping range. This deconvolution of the Raman carrierspossiblyexplainsthe fragilityofsuperconductiv-
response into two components presented here is consis- ity in the OVD n-doped cuprates.
tent with the ARPES data that simultaneously displays
defined QPs in the vicinity of the (π/2a, π/2a) point The authors thank A. Koitzsch, A. Gozar, Y. Dagan,
and ill defined excitations in the other parts of the FS C. P. Hill and M. Barr for assistance, B. Liang for WDS
[8]. One can observe from the deconvolution that the measurements, V. N. Kulkarni for Rutherford Backscat-
Raman response in the B channel is dominated by the tering on PCCO films, and Z. Y. Li for crystal growth.
2g
QP (Drude) response while in the B channel by the This work was supported in part by NSF Grant No.
1g
incoherent continuum [28, 30]. This confirms that the DMR 01-02350.
defined QP states reside in the vicinity of the (±π/2a,
±π/2a) regions of the BZ.
Figure 3(c) displays the evolution of the integrated
QP spectral weight of the “Raman conductivity” [10] [†] E-mail: [email protected]
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s
[18] OpticalconductivitydataalsoindicatesthatOPTPCCO
frompenetrationdepth(λ)measurements[5,7]areplot-
films are between theclean and dirty limits [19].
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N SC
equality implies that not all doped electrons but only [20] T.P.Devereauxet al.,Phys.Rev.Lett.74,4313(1995).
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contribute to the superfluid stiffness [31].
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(1961).
gapsmeasuredbyERSareinagreementwiththosemea-
[25] A.V. Chubukov, D.K. Morr and G. Blumberg, Solid St.
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smaller gapimplying strongfinal state interactions. The [27] C. Kendziora and A. Rosenberg, Phys. Rev. B 52, 9867
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5
[28] A.Koitzsch et al., Phys.Rev.B 67, 184522, (2003). with doping in the relevant doping range (0.13 < x <
[29] C. M. Varma, Phys. Rev.Lett. 63, 1996 (1989). 0.18).Indeed,thereisonlyaweakchangeinopticalcon-
[30] Thefeaturelesscontinuumisstrongerforthefilmsamples ductivityabove0.8eVwithdopingintherelevantdoping
compared to the single crystals. This is an indication of range [32].
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[31] Theaboveanalysisassumesthattheresonantproperties et al.,Phys.Rev. B 69, 024504 (2004).
of the Raman vertex, i.e. the optical conductivity near
the laser excitation of 647 nm (1.9 eV), do not change
