Coexistence of the Pseudogap and the Superconducting Gap Revealed by the \textit{c}-axis Optical Study of YBa$_{2}$(Cu$_{1-x}$Zn$_{x}$)$_{3}$O$_{7-δ}$

0.17 MB·English

by  Ece Uykur

Typesetbyjpsj3.cls DRAFT
Coexistence of the Pseudogap and the Superconducting Gap Revealed by the
c-axis Optical Study of YBa (Cu Zn ) O
2 1−x x 3 7−δ
EceUykur∗, KiyohisaTanaka, Takahiko Masui,ShigekiMiyasaka, SetsukoTajima
3
DepartmentofPhysics, GraduateSchoolof Science, OsakaUniversity,Osaka,560-0043,Japan
1
0
2 To address the issue of the pseudogap in the superconducting state of the high temperature supercon-

n
ductingcuprates,westudiedthetemperaturedependentredistributionofthespectralweightinthec-axis
a
J
polarized optical spectra for underdoped YBa (Cu Zn ) O single crystals with x = 0,0.007, 0.012,
8 2 1−x x 3 7−δ
2
and 0.04. It was found that for Zn substituted samples, the spectral weight transfer to the high energy

]
n region, which characterizes the pseudogap state, continues even below the superconducting transition
o
c temperature (Tc), indicating the coexistence of the pseudogap and the superconducting gap. Moreover,
-
r the observation of the pseudogap in the Zn-doped non-superconducting sample gives evidence that the
p
u
pseudogapis notaprecursorofsuperconductivity.
s
.
t
a KEYWORDS: YBa Cu O ,c-axisopticalspectra,Zn-substitutioneffects,pseudogap
2 3 7−δ
m
-
d
n
o Sincethediscoveryofhigh-T cupratesuperconductors,theaberrant normalstatepropertiesofthese
c
c
[ materialshavebeenunderintensivedebate.Especially,thepseudogapphenomenon,whichstronglydom-

1
inates the underdoped side of the electronic phase diagram, has long been a topic of discussion. There
v
6
areseveralmodelsthattrytoexplainthepseudogapanditsrelationtothesuperconductinggap.Someof
3
4
them explain the pseudogap as a precursor of superconductivity that reflects the pair fluctuations above
6
.
1 T [1,2), while in some other theories, the pseudogap is a competing order such as antiferromagnetic
c
0
3 orderorspin/chargedensitywave,etc[3–5).
1
: Thepseudogapstatehasbeenobservedbymanyspectroscopic probesasdiscussedinRef.6.Optical
v
Xi spectroscopy is an especially powerful probe because it can clearly distinguish a superconducting gap
r from theinsulatinggaps.In particular, the c-axis polarized opticalspectrum is very sensitiveto theelec-
a
tronicdensityofstatesin theantinodalregion[7,8)ofthe Fermi surfacenear(0,π)and (π,0), wherethe
pseudogaphas a strongeffect, whilea majorpseudogap effect on thein-plane spectrais thereduction of
the carrier scattering rate [9). Therefore, it is possible to observe the pseudogap state more easily in the
c-axisconductivity(σ (ω))thaninthea-axisone(σ (ω)).Althoughboththesuperconductingandthe
1,c 1,a
insulating gaps create seemingly similar features, namely the suppression of the low-ω σ (ω), we can
1,c
∗Email:[email protected]
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separate these two, based on the behavior of the spectral weight (SW) transfer. For a superconducting
gap, the lost SW is redistributed as a δ-function at ω = 0, while for an insulatinggap, it is transferred to
higherenergy region.
YBa Cu O is the best system to investigate the c-axis optical conductivity because it has a rel-
2 3 7−δ
atively high conductivity among all the cuprates. On the other hand, some complicated structures has
been observed in this system due to the multilayer structure. In the present work, we study the pseudo-
gap electronic state in a wide energy range, based on a detailed analysis of the SW redistribution with
temperature,fortheunderdopedYBa (Cu Zn ) O .TheaimoftheZn-substitutionistosuppressthe
2 1−x x 3 7−δ
so-called transverse Josephson plasma mode [10) that introduces an additional SW transfer and makes
theSWdiscussioncomplicated[11).
YBa (Cu Zn ) O single crystals (for x = 0, 0.007, 0.012, and 0.04) were grown by using a
2 1−x x 3 7−δ
pulling technique explained elsewhere [12). The sample surfaces, which were cut along the c-axis (ac-
plane∼ 2.5×2.5 mm2), weremechanicallypolishedbyusingAl O powdergraduallyas fineas0.3µm.
2 3
In this paper, we focus on the results for the doping levels p = 0.11 and p = 0.13 (estimated from the
p-T curve [13)), where the T values were determined by the dc magneticsusceptibilitymeasurements.
c c
The doping level was controlled by annealing under O flow at 675 ◦C and 625 ◦C for p = 0.11 and p
2
= 0.13, respectively; followed by a rapid quench into liquid nitrogen. In order to keep the same doping
levelforalltheZn-contentsamples,weannealedthesamplessimultaneously.TheT andthepseudogap
c
temperatures T∗ are summarized in Table.I. T∗ values have been obtained by the SW analysis of our
opticaldata, as explainedin detaillater, and inagreement withthepreviouslypublishedvalues[14).
Table I. Zn-content(x),dopinglevel(p),T ,transitionwidth∆T andT∗
c c
Zn-content(x) DopingLevel(p) T (K) ∆T (K) T∗(K)
c c
0 0.11 61 3 270±20
0.007 0.11 43 7 270±20
0.012 0.11 29 7 270±20
0 0.13 71 3 200±20
0.012 0.13 37 7 200±20
0.04 0.13 non-superconducting 200±20
The temperature dependent reflectivity spectra were measured with a Bruker 80v Fourier Transform
Infrared (FTIR) spectrometer from ∼ 20 to ∼ 20000 cm−1 with Ekc-axis at various temperatures from
10 to 300 K. The sample and the reference mirror were placed into a He-flow cryostat and their spectra
were compared successively at each measured temperature by checking their positions with a He-Ne
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1.0
YBa2(Cu1-xZnx)3O7- p = 0.11 (a)
0.8
300 K
0.6

0.4
y x = 0
vit 0.2 x = 0.007
cti x = 0.012
e
efl 0.0
R
(b)
0.8
10 K
0.6

0.4
0.2
JP
0.0
0 200 400 600 800
-1
Frequency (cm )
Fig. 1. (Coloronline)ComparisonofthereflectivityspectraofYBa (Cu Zn ) O at300K(a)andat10K(b)forp=
2 1−x x 3 7−δ
0.11.
laser. The optical conductivityspectra were obtained from the reflectivity spectra by using the Kramers-
Kronig transformation. At the high energy region from 2.5 eV up to 40 eV, we used room-temperature
reflectivity spectra, which were measured with the use of synchrotron radiation at UV-SOR, Institute
for Molecular Science (Okazaki). Above 40 eV, R ∼ ω−4 extrapolation has been adopted. For the low
energyextrapolationswefittedourreflectivitydatawithDrude(fortheweakelectronicbackground)and
Lorentz oscillators (for the phonon contributions that are dominated the c-axis spectra) in the normal
state. In the superconducting state, we used two-fluid approximation to fit the electronic response.These
extrapolationsworkwell,whichcanbeseeninthecoincidenceofdcandfar-infraredconductivityvalues.
(Forexample,seeFig 2.).
Figures 1(a) and (b) showthe reflectivityspectra at p = 0.11 forall the Zn-contentsat 300 and 10 K,
respectively.Similarspectralbehaviorscanbeseenalsoforp=0.13.At300K,allthespectraarenearly
thesame.Sincethepeakintensitiesofthetwophononmodesaround550and625cm−1 areverysensitive
totheoxygencontent[15),thealmostidenticalspectraforthethreesamplesprovethatthedopinglevels
ofthesesamplesare thesame.
While there is almost no Zn effect at 300 K, a clear Zn-effect is observed at lower temperatures.
WhenwecooldownthesamplesbelowT ,asharpJosephsonplasma(JP)edgeappearsbelow100cm−1
c
(pointedbythearrowsinFig.1(b)). WithincreasingZn-content,theJPedgeshiftstothelowerenergies,
indicatingthedecreaseofthesuperfluiddensity[10,16).ThisisnaturallyexpectedsincetheZnisawell
known impurity that causes pair breaking [17–19). Another significant change is the growth of a broad
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200
(a)
x = 0 300 K
150 T Tc = 60 K
-1 m) 10 K
c
-1 100
(1,c
50
p = 0.11

2000
x = 0.012 (b)
300 K
-1 m) 150 T10 K Tc = 29 K
c
-1 100
(1,c
50
p = 0.11
0
0 200 400 600 800 1000 2000 3000 4000 5000
-1
Frequency (cm )
Fig. 2. (Color online) Temperature dependent high energy optical conductivity spectra at T∗, T and 10 K for
c
YBa (Cu Zn ) O with (a) x = 0, (b) x = 0.012, respectively in p = 0.11 doping region. Low energy part clearly
2 1−x x 3 7−δ
demonstratethedisappearanceoftheTJPmodefor x=0.012.
peak around ∼ 450 cm−1. This additional mode has been intensively studied and attributed to the trans-
verse Josephson plasma (TJP) resonance [11,20), which appears as a response of the superconducting
carriers in the multilayer structure. It is clearly seen that the TJP mode is weakened by Zn-substitution
(arrow inFig. 1(b)), as was reported previously[10).
Figures 2(a) and (b) present the optical conductivities up to ∼ 5000 cm−1 for x = 0 and 0.012,
respectively,whichwerecalculatedfromthereflectivityspectrainFig1.ThedatafortheZn-freesample
isingoodagreementwiththepublishedspectra[15,21,22).Lowenergyconductivitiesareclosetothedc
conductivityvalues(solidsquares),andconsistentwiththepreviouslyreporteddata[16).Thisguarantees
the reliability of our measurements and analyses. Since the TJP mode is completely suppressed by Zn-
substitution (Fig. 2(b)), we can more clearly observe the low-ω conductivity suppression due to the
pseudogap for x = 0.012 than for x = 0. In the latter ( x = 0), the grown TJP mode peak seems to
compensate for the lost SW at low energies. The high energy spectra, on the other hand, show a similar
behaviorforboth samples. One can see that the suppressed SW below ∼ 1200 cm−1 is transferred to the
higherenergy regionabove ∼ 1200cm−1,andthattheenhancementofSWextendstoaveryhighenergy
(∼ 5000cm−1).
TheSWredistributionismoreclearlydemonstratedinthedifferencespectra(σ (T ≈ T )−σ (T ≈
1,c c 1,c
T∗)) in Fig. 3(a). One can see that the SW redistribution occurs within the energy range below ∼ 5000
cm−1 forallthesamples.Thetransferred SWdoesnotchangesignificantlybyZn-substitution.BelowT
c
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-1 m) 10
-1 c YBa2(Cu1-xZnx)3O7- p = 0.11 (a)
*) (
T
(1,c
c (T) - 1,c 0 xx == 00.007
x = 0.012

-10
-1 m)
c 3 x = 0
-1 x = 0.007
c)(T 2 x = 0.012
(1,c 1
K) - 0
0
1
(1,c -1 p = 0.11 (b)

-2
0 1000 2000 3000 4000 5000
-1
Frequency (cm )
40
-1 m) (c)
c
-1 20
c)(T x = 0
(1,c 0
K) -
10 -20 p = 0.13
(1,c p = 0.11

-40
0 500 1000 1500 2000
-1
Frequency (cm )
Fig. 3. (coloronline)TheopticalconductivitydifferencebetweenT andT∗ (a)andbetween10KandT (b)for p=0.11.
c c
Thebottomfigure(c)showsthecomparisonofthedifferencespectrabetween10KandT (σ (10K)−σ (T ))at x = 0for
c 1 1 c
p=0.11and p=0.13.ArrowindicatethepositionofthetransverseJosephsonplasmafrequencyathighenergyregion.
(Fig.3(b)),ontheotherhand,thespectrumshowsacleardifferencefortheZn-freeandtheZn-substituted
samples.Forx = 0,theSWtransferstopsatT ,whileitcontinuesevenbelowT forx = 0.007and0.012.
c c
ThecontinuousSWtransferbelow T indicatesthatthepseudogapsurvivesinthesuperconductingstate.
c
At the doping level p = 0.11, the TJP is located near 450 cm−1 giving no effect on the spectra above
800 cm−1. Therefore, we can conclude that the observed SW transfer from low to high energy region
can be solely attributed to the pseudogap. On the other hand, this is not the case for p = 0.13. In Fig.
3(c), when pisincreased, theTJPmodecreates anadditionalenhancementofσ (ω)around1000cm−1
1,c
( [23), which complicates the discussion of the pseudogap effect. Therefore, it is important to suppress
thismodeby Zn-substitution.
To see a more precise temperature dependence, we calculated the T-dependent SW normalized at
300 K for the specific energy regions for p = 0.11 (Fig. 4(a) and (b)) and p = 0.13 (Fig. 4(c) and (d)).
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b
Here, SWb = R σ (ω)dω, where ‘a’ is the initial value and ‘b’ is the final value of wave number for
a a 1,c
the integral. Hereafter, we discuss the SWs in the two energy regions. The first is the low energy region
(50 − 800 cm−1), where the SW is suppressed with decreasing T. The second is the high energy region
(800−5000 cm−1), where the SW is enhanced with decreasing T. The higherlimit 5000 cm−1 has been
chosen,because alltheSWtransferoccurs belowthisenergy as can beseen in Fig.3(a).
Figure 4(a) shows the SW below 800 cm−1, where we can see a gap-like suppression due to both
the pseudogap and the superconducting condensation. In this energy region, the suppression starts well
above T at the temperature T∗ that corresponds to the pseudogap opening. T∗ does not change signifi-
c
cantly with Zn-substitutionas was reported by many groups [24–26). Below T , a furthersuppression is
c
observed for the Zn-substituted samples, while the decrease of the SW is small for the Zn-free sample,
probably because the developed TJP mode compensates the decrease of the SW due to superconducting
condensation. Here we note that the optically determined value of T∗ is in good agreement with the dc
resistivityresultsreported previouslyforthisdopinglevel[14).
Fig. 4(b) plots the SW between the 800 and 5000 cm−1- high energy range. The temperature depen-
dent behavior is just opposite to that is seen in Fig. 4(a), which indicates the decreased SW below 800
cm−1 moves to the SW above 800 cm−1. As pointed out previously [27), the fact that SW5000 never de-
800
creasesbelowT givesevidenceagainsttheprecursorscenariothatexplainsthepseudogapasaprecursor
c

1.0 (a) p = 0.11 (c) 1.0
800 W50 YBa2(Cu1-xZnx)3O7- p = 0.13 No
Normalized S 00..89 x = 0~ T* xxx ~=== T000..*00142 00..89 50rmalized SW 800
x = 0.007
x = 0.012
0.7 0.7
5000 Normalized SW8001111....00001234 SW(T)/SW(Tc)11p..00 00=05 0.11 xxx === 000..~0001 (T72b*) p = 0 .xx1 3== 00.012 5000 Normalized SW11800..00 68 0Tem2~0p Te4r*0atu6r(0ed )(8K0) 1111....00002468800 Normalized SW 5000
1.00
0.0 T0/.T5c 1.0 x = 0.04 1.00
0 50 100 150 200 250 3000 50 100 150 200 250 300
Temperature (K) Temperature (K)
Fig. 4. (Coloronline)TemperaturedependentSWsnormalizedat300Kforx=0,0.007,and0.012atp=0.11.(a)from50
to800cm−1(lowenergyregion)and(b)from800to5000cm−1(highenergyregion).Theinsetof(b)istheSW5000normalized
800
atT thatdemonstratestheSWtransferbelow T moreclearly.(c)and(d)showtemperaturedependentSWsnormalizedat
c c
300Kforx=0,0.012,and0.04at p=0.13.(c)from50to800cm−1and(d)from800to5000cm−1
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ofsuperconductivity.In thisscenario, theSWthat istransferred to thehigh energy regionwiththepseu-
dogap opening should come back to a δ-function at ω = 0 below T . However, such a decrease was not
c
observedforanysamples.
IncontrasttotheZn-insensitivebehaviorathightemperatures,thelower-T SWshowssomeZn-effect
such as the continuous increase of SW5000 with decreasing T, which can be clearly seen in the inset of
800
Fig. 4(b). While for the Zn-free sample, the increase due to the pseudogap saturates below T , for the
c
Zn-substituted samples an increase can be seen. This implies that the pseudogap state coexists with the
superconducting state below T . This coexistence possiblytakes place even in the Zn-free sample, if we
c
suppose that the SW saturation below T is due to the strong competition between the decrease due to
c
superconductivityand theincreaseduetothepseudogap.
The overallspectral behavioris the sameforthe otherdoping level p = 0.013, as can beseen in Fig.
4(c)and(d).Onecleardifferencefrom p = 0.11isthattheSW800 startstodecreaseatalowertemperature
50
( Fig. 4(c)), as one can expect from theestablished doping dependence of T∗. Anotherimportant finding
isthatthepseudogapbehavior(thedecreaseofSW800 andtheincreaseofSW5000)isobservedeveninthe
50 800
non-superconductingsamplewith x = 0.04atthesameT∗ (Fig.4(c)and(d)).Thisisthestrongevidence
againstthetheory thatthepseudogapis aprecursorofsuperconductivity.
In Fig. 4(d) all the samples show the continuous increase of the high energy SW (SW5000) down to
800
the lowest temperature. For x = 0.012, this increase can be solely attributed to the pseudogap, and thus
implies that the pseudogap remains intact even below T . On the other hand, for x = 0, the increase
c
of SW5000 below T is mainly due to the effect of TJP resonance mode (see Fig. 3(c)). The increasing
800 c
behavioraboveT∗ seeninFig.4(d)isnotrelatedtothepseudogap,butrepresentstheoverallSWgainin
thepresentedenergyregion,probablyduetotheweakmetallicbehavioraboveT∗,whichalsocreatesthe
weak increasein thelowenergy region(Fig. 4(c)) above T∗.
ThecoexistenceofthepseudogapandthesuperconductinggapbelowT hasbeensuggestedbyother
c
probes,too.Recentangleresolvedphotoemissionspectroscopy(ARPES)studiesonBi Sr CuO single
2 2 6+x
crystals showed that the portion of the pseudogap remain intact even below T [28). Moreover, time-
c
resolved pump-probe optical studies [29) and scanning tunneling microscopy/spectroscopy (STM/STS)
[30) on Bi Sr CaCu O have revealed the coexistence of the pseudogap and the superconducting gap
2 2 2 x
belowT .Thisisattributedtothestabilizationofthefluctuatingchargeorderobservedasacheckerboard
c
pattern inSTM/STS.
In summary, we studied the temperature dependence of the c-axis optical conductivity spectra for
YBa (Cu Zn ) O single crystals with various Zn-concentrations and doping levels. It has been
2 1−x x 3 7−δ
revealedthattheSWtransferredtothehigherenergyregion belowT∗ nevercomesbacktotheδ-function
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atω = 0atT .Thisindicatesthatthepseudogapisnotaprecursorofsuperconductivity.Thisconclusion
c
is also supported by the observation of the pseudogap in the heavily Zn-doped non-superconducting
sample. In the Zn-substituted samples, the high energy SW continues to increase even below T ,
c
which suggests the coexistence of the pseudogap state and the superconducting condensation in the
superconducting state. Moreover, the observed SW behavior difference between the Zn-free and the
Zn-substituted samples suggests that the pseudogap not only coexists but also competes with supercon-
ductivity.
Acknowledgements
This work was supported by the Grant-in-Aid for Scientific Research from the Ministry of Education,
Culture,Sports,Science andTechnologyofJapan(KIBAN(A)No.19204038).WethankT.Tohyamafor
hisuseful discussion.
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