Nonmonotonic d_{x^2-y^2} Superconducting Order Parameter in Nd_{2-x}Ce_xCuO_4

4 Pages·0.2 MB·

by  G. Blumberg

Nonmonotonic d Superconducting Order Parameter in Nd Ce CuO
x2−y2 2−x x 4
G. Blumberg1,†, A. Koitzsch1, A. Gozar1, B.S. Dennis1, C.A. Kendziora2, P. Fournier3,¶, and R.L. Greene3
1Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey 07974
2United States Naval Research Laboratory, Code 6333, Washington, D.C. 20375
3Center for Superconductivity Research and Department of Physics, University of Maryland, College Park, MD 20742
2
(June15, 2001; accepted for PRL)
0
0 Low energy polarized electronic Raman scattering of the electron doped superconductor
2 Nd2−xCexCuO4 (x=0.15, Tc =22 K)has revealed anonmonotonic dx2−y2 superconducting order

n parameter. Ithasamaximumgapof4.4kBTc atFermisurfaceintersectionswith antiferromagnetic
a Brillouin zone (the “hot spots”) and a smaller gap of 3.3kBTc at fermionic Brillouin zone bound-
J aries. The gap enhancement in thevicinity of the “hot spots” emphasizes role of antiferromagnetic

9 fluctuationsandsimilarity intheorigin ofsuperconductivityforelectron- andhole-dopedcuprates.
2
PACS numbers: 74.25.Gz, 74.72.Jt, 78.30.-j

]
n Introduction.–Nd2−xCexCuO4(NCCO)isoneofafew to the doping dependence of Tc are discussed.
o
electron doped cuprate superconductors [1]. The physi- Experimental.– The Raman experiments were per-
c
- cal properties of the electron doped cuprates are differ- formed from a natural ab surface of a plate-like single
r ent from the hole-doped. Structurally, NCCO does not crystalgrownasdescribedinRef.[12]. Aftergrowth,the
p
u have apical oxygen atoms. It is commonly believed that crystal was annealed in an oxygen-reduced atmosphere
s the charge carriers in NCCO are electrons rather than to induce the doping level for optimal T . SC transition
c
.
t holes asin other cuprate families [1,2]. In optimally hole measuredbySQUIDwasabout22Kwithawidthabout
a
doped cuprates the normalstate resistivityincreaseslin- 2 K. The sample was mounted in an optical continuous
m
earlyoverawide rangeoftemperatureswhile for NCCO helium flow cryostat. Spectra were taken in a backscat-
-
d thein-planeresistivityisquadraticintemperaturewitha tering geometry using linearly polarized excitations of
n large residual value [3]. For the electron doped cuprates a Kr+ laser from near infrared to violet. An incident
o the superconducting (SC) transition temperature is rel- laserpowerless than2 mWwasfocusedto a 50µmspot
c
atively low and the superconductivity occurs in a nar- ontothesamplesurface. Thereferredtemperatureswere
[
row doping range [1]. From the early tunneling [4] and corrected for laser heating. The spectra were measured

1 microwavemeasurements an s-wave SC order parameter at temperatures between 5 and 35 K and were analyzed
v
(OP)wassuggested[5]thatisincontrastwiththed-wave by a custom triple grating spectrometer. The data were
8
symmetry established for hole doped compounds. The corrected for the spectral response of the spectrometer
3
5 earlyRamanmeasurementswereinterpretedas evidence andfor the opticalproperties ofthe materialatdifferent
1 fornearlyuniformlygappedFermisurface(FS)[6]consis- wavelengths as described in the Ref. [13].
0 tent with the s-wave OP. However, the interpretation of The polarization directions of the incident (e ) and
i
2 morerecentmicrowavemeasurements[7,8]alongwithan- scattered (e ) photons are indicated by (e ,e ) with
0 s i s
gleresolvedphotoemissionspectroscopy(ARPES)[9,10], x = [100], y = [010], x′ = [110], and y′ = [¯110]. The
/
at and phase sensitive scanning SQUID microscope experi- presenteddata were taken in (xy), (x′y′), and (xx) scat-
m ments [11] are consistent with d-wave OP. tering geometries. For tetragonal D4h symmetry these
- WereportpolarizedlowenergyelectronicRamanscat- geometriescorrespondtospectraofB2g+A2g,B1g+A2g,
d teringstudiesonNCCOsinglecrystalsandshowthatthe andA1g+B1g representations. In addition, by using ge-
n
o dataisconsistentwithaSCOPofthedx2−y2 symmetry. ometries with circularly polarized light we checked the
c However, as distinguished from the simplest commonly intensity of the A2g component and found it to be negli-
: assumed SC gap function, ∆(k) ∝ cos(kxa)−cos(kya), gibly weak.
v where k is a wavevectoron the FSand a is the ab-plane Raman scattering symmetries.– The electronic Raman
i
X lattice constant, the present results require a nonmono- response function for a given geometry (e ,e ) is pro-
i s
r tonic form of the OP. We find that in contrastwith hole portional to the sum over the density of states at the
a doped cuprates for NCCO the positions of the SC gap FS weighted by the momentum k dependent form factor
maxima are located closer to the nodes than to the Bril- [16–18]. By choosing the scattering geometries one can
louin zone (BZ) boundaries. The gap opens up rapidly selectively probe different regions of the FS and obtain
with departure from the diagonal nodal directions and information about the k dependence of the SC OP. For
quickly reaches its maximum value of 4.4kBTc at the theB1g channeltheRamanspectrumhasaformfactorof
intersections of the FS and the antiferromagnetic (AF) dx2−y2 symmetrythatvanishesatthe(0,0)→(π,π)and
BZ. However, the gap value drops to 3.3k T at the BZ the equivalentdiagonallines of the BZ (See Fig. 1). The
B c
boundaries. The implications of such nonmonotonic OP spectrum intensity in the B1g channel integrates mainly
1
(0,p) (p,p)
AA f 80 B anisotropic s-wave 8 units) 45
Q=(p,p) G N HS (ZpB,0) -1D2 (cm)246000 nonmonmootonnoitco ndi-cw da-vweave 2462 (meV)D nction (arb. D2/kTBC01230 0.5 1
u A T/T
0 N HS ZB 0 e F 1g C
0 10 20f 30 40 ns
FIG. 1. (A) A schematic representation of the electron po
s
doped FS of NCCO [9]. The occupied electron states are e
R
shaded. The AF BZ at half filling is shown as the square ro- n B
tated by 45◦. AF fluctuations enhance interactions between a 2g
m
fermions around the “hot spots” (filled circles), the regions a B
of the FS connected by the Q = (π,π) vector [14]. The lo- R 1g
cation of the “hot spots” sensitively depend on the doping 0 50 100 150
level. The FS shrinks with further electron doping until the Raman shift (cm-1)
intersectionwiththeAFBZvanishes(dottedlinesandempty
circle in the lower left quadrant). The hole doped cuprates FIG. 2. Low-frequency Raman scattering spectra with
exhibitalargeFSwiththe“hotspots”shiftedtothevicinity 1.9 eV excitation for different symmetry channels. The solid
of (π,0) and theequivalent points (dashed lines and hatched lines denote spectra at 11 K in the SC state and the dashed
circles in the lower left quadrant) [15]. The dotted diago- linesspectratakenaboveTcat35K.Thebaselinesareshifted
nal (dashed horizontal and vertical) lines denote the nodes asindicatedbytheticks. TheB1gspectracorrespondstox′y′,
of the B1g (B2g) Raman form factor. (B) The magnitude of theB2g toxy andtheA1g toxx−x′y′ scatteringgeometries.
the dx2−y2 OP as a function of the angle φ along the FS. The inset shows the temperature evolution of the 2∆-peak
Solidline: non-monotonicOPforNCCO.Thegapvaluerises energy in the B2g channel. The line indicates the mean field
rapidlyfromthenodaldiagonaldirection(N)toitsmaximum BCS temperature dependence.
value 2∆ =67 cm−1 at the “hot spot” (HS) observed in the
B2g channel. The 2∆-peak at 50 cm−1 in the B1g channel
corresponds to the value at the BZ boundary (ZB). Dashed
line: monotonicsin(2φ)form. Dottedline: anisotropics-wave areanorderofmagnitudestrongerthanintheB1g chan-
OP proposed in theRef. [6]. nel. ForB2g symmetrythepeakisatthehighestenergy,
at about67 cm−1, followedby the peaks in B1g and A1g
channels at 50 and 40 cm−1 correspondingly.
These results are in sharp contrast to the hole doped
from the regions of the FS distant from these diagonals,
cuprateswherethemostprominentscatteringisobserved
near intersections of the FS and the BZ boundary (ZB).
In contrast, the form factor for B2g spectrum has dxy finreqBu1egncchya[n2n0e–l26fo].r wFohrichthethheo2le∆d-poepaekdicsuaptrattheeshthigeheinst-
symmetry and therefore vanishes along (0,0) → (0,π)
andtheequivalentlines. TheintensityintheB2g channel OtePrproeftathtieonsimofpRleasmt amnondoattoaniiscc∝onssiisnt(e2nφt)wfoitrhmdxsh2−owy2nSiCn
is mainly determined by excitations near (π/2,π/2) and
the Fig. 1B. The role of orthorhombic distortions and
the equivalent points. All regions of momentum space
impurities has been discussed in the Refs. [18,27–29].
may contribute to the fully symmetric A1g channel [19]. The earlier low-temperature Raman data from NCCO
The pair breaking excitations.– In the Fig. 2 we com-
was measureddown to about 25 cm−1 with ω =2.6 eV
pare the low energy Raman spectra above and below L
[6]. Thedataexhibitedastrongresidualscatteringinten-
the SC transition takenwith the excitationenergyω =
1.9eVforthreesymmetryrepresentations: B1g,B2g Land saittya. tThhreeshobolsdervfreodm2∆th-epelaokwienntehrgeyBs1igdec.haTnnheelasutathrtoerds
A1g. Above Tc spectra exhibit a flat electronic Raman discusspossibleexperimentalartifactsfortheresidualin-
continuum. In the SC state the low-frequencytail of the
tensityandsuggestthattheobservedthresholdsupports
Raman continuum changes to reflect the opening of the
an anisotropic s-wave gap interpretation (see Fig. 1B).
SC gap: the strength of the low-frequency continuum
Our data extends to much lower frequencies (Figs. 2-3).
is reduced and the spectrum acquires the so-called 2∆-
The spectra for all scattering channels show a smoothly
peakasaresultofexcitationsacrosstheanisotropicgap,
dropping intensity below the 2∆-peak down to the low-
2∆(k). These peaks correspondto the excitations outof
estenergiesmeasured. Basedonourdataweexcludethe
the SC condensate. For different scattering geometries
anisotropic s-wave interpretation since any fully gapped
spectra differ in their intensity as well as in the position
FS would lead to a Raman intensity threshold as it has
ofthe 2∆-peaks. The peaksinthe A1g andB2g channels
2
been observed for classical superconductors [16]. The
smoothdecreaseofthescatteringintensityis asignature s) w L=2.6 eV w L=2.2 eV w L=1.9 eV w L=1.7 eV
of the nodes in the OP [23]. nit 30
icnhaTtnhhneeelgBas2puggacgnheiasstnostnreaolpnyao.t–nemTnohenregooitebosnsehicrivgaOhtePirontwhoiatfhnthmiena2tx∆hime-paBea1inkg e (rel. u xy 12 11055 1200 1200
s
∆(k) closer to the (0,0) → (π,π) diagonal than to the on
p
BZ boundary. The recent ARPES studies of NCCO ex- s 3 3
e 2 4
hibit a node in ∆(k) along this diagonaldirection [9,10]. n rx’y’ 2 2
Our Raman data can be reconciled with the ARPES re- ma 1 1 1 2
sults by including higher harmonics, like sin(6φ), to the a
R 0 40 80 0 40 80 0 40 80 0 40 80 120
monotonic sin(2φ) form of the dx2−y2 OP. The resulting
nonmonotonic form is shown in Fig. 1B. In Fig. 1A we Raman Shift (cm-1)
sketch the FS as seen by ARPES [9]. The latter data
exhibits regions of suppressed spectral weight at the in- FIG.3. LowenergyRamanspectraat8KintheB2g (xy)
and B1g (x′y′) channelsfor excitations from blue tonear IR.
tersections with the AF BZ boundary, a behavior sim-
Notethatforshorterwavelengthexcitationstheintensitiesof
ilar to the destruction of the FS at the “hot spots” in
the 2∆-peaks in two channels are comparable while for the
thepseudogapphaseseeninhole-dopedcuprates[15,30]. red excitations the intensities in the B2g channel is an order
StrongAFfluctuations arebelievedto be responsiblefor of magnitude stronger than in theB1g channel.
such “hot spot” behavior [14,31–33].
We assume that the AF interactions are responsible
forthe SC couplingmechanismandthatlikeinthe hole-
excitationsfrombluetonearIRareshowninFig.3. For
doped cuprates the SC gap reaches its maximum value
the blue excitation (ω = 2.6 eV) our data is consistent
in the vicinity of the “hot spots”. For the hole-doped L
with the earlier results of Ref. [6] showing comparable
cuprates with a large FS the “hot spots” are close to
the BZ boundary. For electron-doped cuprates the po- intensities in both B1g and B2g channels. The relative
intensities change drasticallywhen the excitationenergy
sition of the “hot spots” sensitively depends on the size
of the FS and, hence, on the amount of doping. As it is decreased below 2.5 eV. While the peak in the B1g
channelonlyslightlyincreasesinintensitythepeakinthe
is seen in the ARPES data [9] for the optimally doped
NCCOthe“hotspots”areclosetotheBZdiagonalsand B2g channel rapidly increases by an order of magnitude
andexhibits amaximumaroundexcitationω =1.9eV.
therefore in Raman the maximum gap value appears in L
the B2g channel. The peak position at about 67 cm−1 The resonance profiles of the 2∆-peak for both B1g and
is consistent with the maximum gap value of 3.7 meV B2g channels are presented in the Fig. 4A and are com-
pared with optical conductivity data [34] that exhibits
observed in tunneling spectroscopy [4]. The 2∆-peak in
a band between 1.7 eV and 2.5 eV. This band has been
the B1g channel reflects the gap magnitude at the BZ
ascribedto the charge-transferprocess between the fully
boundary (See Fig. 1B). Indeed, the peak position at
about 2∆ =50 cm−1 correspondsto 3 meV for a sin- occupied oxygen 2p band and the upper Hubbard band
gle ∆(k B)1gthat is consistent with the leading edge gap (UHB) [35] that has been suggested to be a doubly oc-
ZB
cupied hybridized oxygen 2p and copper 3d state.
estimatesbetween1.5and3meVattheBZboundaryby
In the Fig. 4B we show a schematic diagram for the
ARPES [9,10]. For slightly stronger electron doping the
resonant Raman scattering process in strongly corre-
intersection of the AF BZ and the FS disappears. This
lated electron doped cuprates. The lower Hubbard band
naturallyexplainsthenarrowdopingrangeforsupercon-
(LHB) and the oxygen band above are fully occupied.
ductivity in the electron-doped cuprates.
DopedelectronsshifttheFermienergytotheUHB.Res-
The superconducting gap temperature dependence.– In
onant enhancement of the Raman scattering process oc-
the insetofFig.2weshowthetemperaturedevelopment
curs when the energy of the incoming or scattered pho-
of the 2∆-peakposition in the B2g channel. The SC gap
tons, or both, are in resonance with the interband tran-
opensupveryrapidlywithcoolingbelowT andsoonap-
c
sitions. Ourresultsimply thatthe intermediatestatefor
proachesits maximumvalue4.4k T whichiswithinthe
B c
the Raman process is the same state which is seen near
marginofthestrongcouplinglimitandisclosetothegap
2.1 eV in the optical conductivity. Moreover, because
value observed for heavily hole overdoped cuprates. Op-
timally and especially hole underdoped cuprates exhibit the observed resonance enhancement for the B2g chan-
much larger gap values [25,26]. nel is much stronger than for the B1g channel we antici-
patethattheinterbandtransitionoccursnear(π/2,π/2)
TheresonantRamanexcitationprofile.–Weperformed
point. Angle-resolved valence-band photoemission spec-
a systematic study of the Raman scattering efficiency as
tra indeed exhibits a band that is peaked at this point
a function of the excitation photon energy. The low fre-
at about 2.6 eV below the Fermi energy [10]. The ex-
quency response at 8 K in the B1g and B2g channels for
3
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drops to 3.3k T . The enhancement of the gap value in comes from proximity of the (π,0) → (0,π) and the
B c
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Acknowledgements.– We acknowledgediscussions with
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N.P. Armitage, A. Chubukov, E.J. Singley and T. Taka- Chem. Solids 59, 1932 (1998).
hashi. AK is supported in part by the Studienstiftung [26] H.L. Liu et al.,Phys. Rev.Lett. 82, 3524 (1999).
desDeutschenVolkes. NRLsupportisprovidedbyONR. [27] M.T. Beal-Monod, J.B. Bieri, and M. Maki, Europhys.
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P.F. acknowledges the support from CIAR, NSERC and [28] R. Nemetschek et al.,Eur. Phys. J. B 5, 495 (1998).
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[email protected] [33] L.B. Ioffe, A.J. Millis, Phys. Rev.B 58, 11631 (1998).
¶ Permanent address: Centre de recherche sur les [34] E.J. Singley et al., Phys.Rev.B 64, 224503 (2001).
propri´et´es ´electroniques de mat´eriaux avanc´es and [35] S. Uchidaet al., Phys.Rev.B 43, 7942 (1991).
D´epartement de Physique, Universit´e de Sherbrooke,
Sherbrooke,Qu´ebec, CANADA,J1K 2R1.
4