Table Of ContentInsensitivity of the superconducting gap to variation in T in Zn-substituted Bi2212
c
Y. Lubashevsky,1 A. Garg,1 Y. Sassa,2 M. Shi,3 and A. Kanigel1
1Department of Physics, Technion, Haifa 32000, Israel
2Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
3Swiss Light Source, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
(Dated: February 1, 2011)
Thephasediagramofthesuperconductinghigh-Tccupratesisgovernedbytwoenergyscales: T∗,
thetemperaturebelowwhichagapisopenedintheexcitationspectrum,andT ,thesuperconduct-
c
ing transition temperature. The way these two energy scales are reflected in the low-temperature
energy gap is being intensively debated. Using Zn substitution and carefully controlled annealing
1
we prepared a set of samples having the same T* but different T ’s, and measured their gap using
1 c
Angle Resolved Photoemission Spectroscopy (ARPES). We show that T is not related to the gap
0 c
shape or size, but it controls the size of the coherence peak at the gap edge.
2
n PACSnumbers: 74.25.Jb,74.72.Hs,79.60.Bm
a
J
1 The relation between the pseudo-gap (PG) and super-
3 conductivity(SC)inthehigh-temperaturesuperconduct-
ing cuprates (HTSC) remains a matter of controversy.
]
n In fact, many believe that therein lies the key to under-
o standing the cuprates’ physics. During the last years a
c
large body of experimental data was gathered but the
-
r results are inconclusive. While there is support for the
p
concept of the PG being a state in which Cooper pairs
u
s are pre-formed [1], there are also numerous experiments
. providing evidence for a competing order [2].
t
a
A simple, but potentially very powerful, approach
m
would be to look for correlations between measurable
-
d quantities and the two obvious energy scales that govern
n thecupratephasediagram: T andT∗. Thisapproachis
c
o complicated by the fact that the parameter which sam-
c
plegrowerscontrol,thedopinglevelofthesample,affects
[
both T and T∗ simultaneously. Here we overcome this
c
2 problem using Zinc (Zn) substitution. Zn substitution
v allows us to manipulate T and T∗ separately. We mea- FIG.1: (a)PhasediagramofZn-Bi2212. TheZnsubstitution
4 c
7 sure and compare the superconducting gaps of different ceraecahtedsompaerdaellpelenddosmoenstohfeTZcnvasmdooupnitn,gi.ncTohnetrmasatxTim∗arelmTacinosf
5 samples, in that way we can observe directly the corre-
unchanged. (b)Resistivityasfunctionoftemperatureforfour
6 lation between T , T∗ and the most basic property of a
c optimallydopedsampleswithdifferentZnsubstitutionlevels,
. superconductor, its energy gap.
1 normalizedbytheresistivityatT =250K. T decreaseswith
c
1 ZnreplacesCuintheCuO planes[3],withoutchang- the addition of Zn. The dashed line is the resistivity of a
2
0 ing the carrier concentration. s-wave SCs are immune to pristine underdoped sample. Inset: Tc as function of the Zn
1 scatteringcausedbynon-magneticimpurities[4],butbe- substitution level for Bi2212 and YBCO[6]. (c) Deviation
: fromlinearityoftheresistivity. Theparameterαistheslope
v cause of the d-wave symmetry of the order parameter in
Xi thecuprates, ZncanreduceTc veryeffectively, although orefsitshteivihtiyg.h Atelml pZenr-aBtiu2r2e12linheaavreptahret,saanmdeρT0∗i,sbthuet trheseidUuaDl
r it is non-magnetic[5]. The rate at which Zn reduces Tc, sample has a higher T∗.
a dT /d(Zn %), is different for different systems, rang-
c atom
ing from about −4.5K for YBa Cu O [6] to −9K for
2 3 δ
L2−xSrxCuO4 [7](see the inset in Figure 1b). that Zn, being a strong scatterer, induces pair-breaking
µSR experiments have shown that Zn substitution re- [9].
duces the superfluid density (n ) [8, 9]; interestingly, the For the purpose of this experiment we grew thin
s
reduced n and the lower T ensures that the Uemura films of Zn substituted Bi Sr CaCu O (Zn-Bi2212)
s c 2 2 2 8+δ
relation [10] remains intact. The question of how Zn re- on LaAlO substrates using DC sputtering. The sol-
3
ducesthen remainsopen;ithasbeensuggestedthatSC ubility limit of the Zn in the films is 3%. Higher Zn
s
isexcludedfromavolumearoundeachZnatom,leavinga concentration produced spurious phases in the samples.
”swiss cheese”-like medium for SC [8]. Others suggested The doping level was controlled by annealing the films
2
at low oxygen pressure. We used Wavelength-Dispersive 1.0 Pristine 1 (a) Pristine OP (c)
x-raySpectroscopy(WDS)tomeasurethesamples’com- Zn-3% OP
M Y
position. The results indicate that the films are uni- f
0.8 2 f =0o
form and have the correct stoichiometry. For each Zn a]
concentration a number of different samples were grown, p/K [Y0.6 G M 3 1
with different doping levels from slightly underdoped to 4 f =12o
slightlyoverdoped,asshowninthephasediagraminFig
0.4 2
1(a). The Zn substitution produces parallel T vs. dop- 5
ingdomes,wherethedopingissetbytheoxygecnamount. 1.0 High 1 (b) f =22o
The T s are from resistivity measurements and the dop- Low 3
c 0.8 2
ing level was calculated using the Presland formula [11], a] f =33o
with the appropriate Tmc ax for each Zn concentration. p/K [Y0.6 3 4
In contrast to the noticeable change in T the Zn seems
c 4
to have no effect on T∗. This is in agreement with the f =45o
results of various other experiments [12–14]. 0.4 Zn-3% 5 5
Four optimally-doped samples were chosen for the -0.8 -0.4 0.0 0.4 -0.6 -0.4 -0.2 0.0
ARPES experiment, with different Zn/Cu ratios: Zn- KX [p/ a] Energy [eV]
0% pristine Bi2212, Zn-1% with 1.06(15)%, Zn-2% with
1.762(61)% and Zn-3% with 3.025(75)%. In Fig 1(b) the
resistanceasfunctionoftemperatureforthesesamplesis FIG. 2: (a) and (b) ARPES intensity map at EF for the
shown. T variesfrom90Kforthepristinesampleto74K pristineand3%sample,respectively. Thedataisintegrated
c
over40meVtorevealtheunderlyingFermi-surface. Thesolid
forthe3%sample. Wealsopresentinthesamefigurean
lines represent the tight-binding Fermi-surface for optimally
underdoped pristine Bi2212 sample, with T =77K.
c doped Bi2212. Both samples have the same Fermi-surface
The pseudogap temperature was extracted from the
areaindicatingthattheyhavethesamecarrierconcentration.
resistance data by measuring the temperature at which Theinsetshowsthemomentumrangecoveredinpanelsaand
the resistance starts to deviate from the linear behavior b. (c)EDCsatseveralk points(Representedinpanelsaand
F
found at high temperature [15]. For each sample, we bbytheblackandreddots)forthepristine(black)and3%
measuredthehightemperatureslope,α,andtheresidual Zn ( red) sample.
resistivity, ρ . InFig1(c), weplot(ρ(T)−ρ )/αT; T∗ is
0 0
thepointatwhichthevalueof(ρ(T)−ρ )/αT decreases
0
below one. We find all the optimally doped samples to and b of figure 2. The black solid lines represent the
have the same T(cid:63) of 200K, while the UD sample has a tight-binding Fermi-surface of optimally-doped Bi2212
higherT∗of270K.BymanipulatingtheZnconcentration [17]. In agreement with previous results, we do not find
andtheoxygenlevelitwaspossibletoprepareaseriesof anychangeintheFermisurfacevolumewhenZnisadded
samples having the same T∗ but different T ’s and two [18, 19], an indication that the Zn does not change the
c
samples having similar T but completely different T∗. doping level. The Energy Distribution Curves (EDC) at
c
Over the years ARPES has proven to be one of the the momentum points that are marked in panels a and
most useful techniques for studying the electronic struc- b are shown in panel c. Well defined peaks can be ob-
ture of the cuprate HTSC [16]. Here we used ARPES served in all the EDCs. Two conclusions can be drawn
to measure the momentum dependence of the gap in the from figure 2c: the height of the peaks is smaller in the
excitations spectrum at low temperature. The ARPES Znsubstitutedsample,butthepeakpositionremainsthe
measurementsweredoneattheSISbeamlineattheSLS, same indicating that there is no change in the gap.
PSI,Switzerland,andattheNIM1beamlineattheSRC, In Fig. 3(a) the momentum dependence of the energy
Madison USA. All data were obtained using a Scienta gap at T=25K of the four optimally doped samples is
R4000 analyzer using 22eV photons. To measure the SC shown. The gaps are plotted as a function of the Fermi-
gap, we took 12-15 momentum scans parallel to the Γ-M surface angle, which is defined in the inset. The energy-
direction. For each cut we follow the peak-position in gap of all the samples is identical although their Tc’s
the Energy Distribution Curve (EDC). k is defined as differ by up to 20%. We emphasize that the gaps are
F
the point at which the separation between the peak and identical over the entire Fermi surface, both in the nodal
the chemical potential is minimal. The peak-position of and anti-nodal regions. This is a remarkable result: it
the EDC at k , after division by a resolution-broaden contradicts everything we know about Bardeen-Cooper-
F
Fermi-function, defines the gap size at that point. E is Schrieffer (BCS) SCs and about the way impurities re-
F
found by measuring the density of states of a gold layer duce Tc in these SCs.
evaporated on the sample holder. On the other hand our results reinforce the viewpoint
The ARPES intensity maps at the Fermi energy of that in the cuprates the gap is proportional to T∗ [20];
the pristine and Zn-3% samples are shown in panels a we kept T∗ constant and so the gap remains unchanged.
3
pens around that point when T is lowered. Moreover,
35 c
Pristine OP if there were a change of 20% (The change in T ) in the
30 Zn-1% OP c
Zn-2% OP gapvaluearoundthatpoint, weshouldbeabletodetect
25 Zn-3% OP
V]20 PFriti sOtiPne UD it easily. Our data prove that there is no gap around
me Fit UD the nodes which is proportional to T . We cannot rule
D[15 c
out, however, a scenario in which the gap-shape changes
10
withdoping. Thequestionofdeviationsfromasimpled-
5
(a) wave gap in Bi2212 for very low doping samples remains
0 T=25K
Anti-Node controversial [21, 26].
40 M f X
In Fig 4, the anti-nodal EDCs at 25K of all the sam-
30 plesareshown. TheEDCswerenormalizedtotheirhigh
V] Node
me binding-energy values and the background was removed
D[20 G M bysubtractinganEDCmeasureddeepintheunoccupied
10 region. Thisfigurecontainsourmostimportantfindings.
(b) Inpanela,wecomparealltheEDCsoffsetverticallyand
0
10 20 30 40 50 orderedaccordingtotheirTcs. Thepeakposition,which
f[deg] isameasureofthegap,ofallthesampleshavingaT∗ of
200K (optimally doped samples) is the same regardless
of their T . Only the underdoped sample has a higher
FIG. 3: (a) The momentum dependence of the supercon- c
ductinggapofallZn-Bi2212samplesat25K.Nodependence T∗ (270K) and, as a result, a larger gap. In panel b
ontheZnamountisobserved,andthesamed-wavefunction the same EDCs are shown, this time with an horizontal
fitsalldata. (b)Themomentumdependenceofthesupercon- offset, again ordered according to their T . The peak
c
ductinggapoftwosampleswithsimilarTcs: ThepristineUD height clearly increases with Tc, and it does not depend
sample and the Zn-2%. The lines are fits to the data using on T∗. We emphasize that all the Zn-substitued samples
the simple d-wave function. A clear difference in gap can be
(solid-lines) have the same doping, so the peak-height is
seen. (Inset) The Brillouin zone of Bi2212 and the definition
notsimplyrelatedtotheamountofchargecarriersinthe
of the Fermi-surfce angle φ.
sample. In panel c, the difference between the pristine
optimally doped sample and the Zn substituted samples
In Fig 3(b) we compare the gap-shape of the optimally are shown. The normalized EDC of the pristine sam-
doped samples (all having the same T∗) with that of the ple was subtracted from the normalized EDC of each of
underdopedsamplewhereT∗ ishigherby70Kandwhere the Zn substituted samples. The results indicate that
T is similar to the T of the Zn-2% sample. The under- the Zn reduces the coherence-peak weight, but creates
c c
doped sample with the higher T∗ has a larger gap, as states in other energy regions. In-gap states are created
expected. in agreement with STM data [27] and previous ARPES
Recently,anumberofgroupsreportedgap-shapesthat experiments [28]. At higher binding energies there is ac-
deviate substantially from the simple d-wave shape ( cumulation of states that washes-out the characteristic
∆ = ∆(0)cos(2φ)) in various cuprate systems [21–24]. peak-dip-hump line shape[29]. Figure 4 suggests that
According to these observations, there are two gaps cov- the Zn reduces the coherence peaks at the gap-edge in a
ering different regions of the Fermi surface. The real SC way which follows the decrease in Tc and in ns in a very
gap opens in the nodal region, with a gap size propor- similarwaytowhatisfoundinpristineBi2212wherethe
tional to T , while around the anti-nodal region there is coherence peak weight was found to be proportional to
c
a second gap, the Pseudogap, this gap-size follows T∗ as Tc [30].
in the older data. We, on the contrary, could fit all the As the beam-spot size is much larger than the average
data using a single simple d-wave gap function. The fit Zn spacing, we are measuring an average over regions
is represented by the dashed lines in Fig 3. If one needs near the impurities and regions far from the impurities.
to choose a border-line in k-space that separates the two The data is consistent with the Zn imputies being very
gaps, then a natural choice would be the Fermi-arc tip. local disturbers. If the Zn destroys SC, but its effect is
The Fermi-arcs are segments of the Fermi-surface, cen- veryshortrangedwewouldexpectaverysmalleffecton
tered around the nodes, that are gapless above T and the average gap, since the overall volume-fraction taken
c
are gapped-out below T (apart for the node itself), as bytheZnisverysmall. Ontheotherhand, likeinmany
c
expected for a superconductor. The rest of the Fermi- other systems even a small amount of defects can sub-
surface remains gaped above T up to T∗. The longest stantiallyreducethestiffnessoftheentiresystem. Inthe
c
Fermi-arc is found in optimally doped samples [25]. We cuprates the superfluid stiffness sets T [10]. The differ-
c
measuredtheFermi-arcinthepristinesamplejustabove ent response of the gap and of T to the Zn substitution
c
T ; the tip of the arc is located at a Fermi-angle of 15o. is a manifestation of the short coherence length and low
c
It is easy to see from Fig. 3a that nothing special hap- superfluid density in the cuprates.
4
A more complete review of the data reveals the role of
T . Takingintoaccountthatthecoherencepeaksappear
c
only below T , the dramatic change in the gap-shape on
c
crossingT [31]andthefactthatatlowtemperaturethe
c
height of the coherence peaks follows T suggests an un-
c
usual picture. In this picture, unlike in the conventional
SC, the low temperature SC gap is not simply related
to T , but T affects other parts of the low temperature
c c
electronic spectra.
We are grateful to M. Randeria, A. Balatsky and U.
Chatterjee for helpful discussions and to G. Koren for
help with the sample preparation. This work was sup-
ported by the Israeli Science Foundation. The Syn-
chrotron Radiation Center is supported by NSF DMR-
0084402. Part of this work was performed at the Swiss
Light Source, Paul Scherrer Institut, Switzerland.
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c
