Evidence of two distinct charge carriers in underdoped high Tc cuprates
aa r X i v : . [ c ond - m a t . s t r- e l ] O c t Evidence of two distinct charge carriers in underdoped high T c cuprates. S. Sanna, ∗ F. Coneri, A. Rigoldi,
1, 2
G. Concas, and R. De Renzi Unit`a CNISM di Parma e Dipartimento di Fisica, I 43100 Parma, Italy Unit`a CNISM di Cagliari e Dipartimento di Fisica, I 09042 Monserrato (Ca), Italy (Dated: November 29, 2018)We present results on heavily underdoped Y − x Ca x Ba Cu O y which provide the evidence thatthe doping mechanism (cation substitution or oxygen loading) directly determines whether thecorresponding injected mobile holes contribute to superconductivity or only to the normal metallicproperties. We argue that this hole tagging calls for a subtler description of the correlated bandsthan the usual one. We also map in great detail the underdoped superconducting phase diagram T c vs hole doping which shows that the number of mobile holes is not the critical parameter for thesuperconductivity. The behaviour of a hole in the cuprate doped Mott-Hubbard insulator is often described in a universal pic-ture, where, above some critical concentration, it formsthe Zhang-Rice singlet [1], in a single correlated-bandscheme. However structural and compositional detailsof each specific compound do influence the fine grainbehaviour. This is particularly true in the region ofthe metal-insulator (MI)transition , where there is grow-ing evidence that the competition between antiferromag-netic (AF) order and superconductivity is strongly influ-enced by disorder [2], leading to different phase diagrams[3, 4, 5] in different real materials.Growing evidence that more than one band is neededcomes from Ca x La . Ba . − x Cu O y , where two dis-tinct charge fluids have been reported [6] by NQR. Atoptimum doping tunneling spectroscopy directly detects[7] two CuO gaps in Y − x Ca x Ba Cu O y , and µ SRprovides additional supporting evidence [8] in the case ofLa − x Sr x CuO . In the underdoped regime early NMR[9, 10] and recent magnetotransport [11] results demon-strate additional thermally activated doped holes. Theactivation energy, proportional to x − , has been shownto scale with relevant ARPES Fermi-arc features and ithas been linked directly to the pseudogap [12]. Furtherdetails, such as the presence of Fermi pockets, from highfield quantum oscillations [13], call for a subtler bandstructure implementation [14]. Activated holes are alsoindirectly detected through the magnetic order parame-ter reduction measured with NQR and µ SR [15, 16]. Itseems that at least two bands[17] are needed to correctlydescribe real cuprates.In order to focus this issue we zoomed into the MItransition region of Y − x Ca x Ba Cu O y , where twodistinct doping mechanisms can be independently con-trolled. Charge doping is provided both by heterovalentCa +2 → Y +3 substitution, x , and by interstitial oxygencontent, y , in the Cu(1)O chain layer, yielding a totalhole concentration h = h Ca + h O transferred to the activeCu(2)O layers. We thus directly show that the two con-tributions behave very differently with respect to roomtemperature normal properties and superconductivity.Polycrystalline samples were prepared by a topotactic technique, which consists in the oxygen equilibration ofstoichiometric quantities of the two end members, tightlypacked in sealed vessels [18]. Low temperature annealingyields high quality homogeneous samples with an abso-lute error of δx = ± .
02 in oxygen content per formulaunit (reduced to ± .
01 after recalibrating end member ofdifferent batches). Besides this determination, absoluteoxygen content is cross checked by iodometric titration,thermogravimetry on each sample and selected neutronRietveld refinements. Ca content is checked by X-rayand neutron Rietveld refinements. Reported error barsare the global error from this procedure. Transition tem-peratures correspond to the linear extrapolation of the90 % to 10% diamagnetic drop of the susceptibility, mea-sured in a field µ H = 0 . µ SR, when available). The width of the interval wherethe resistance drops from 90% to 10% of the onset valueis typically 6 K for y ≤ .
4, like for Ca free pellets andlarge single crystals (see Ref. [4] and Refs. therein).The inset in Fig. 1 shows the progressive reduction of T c vs. x in the y ≃ . T c = 92 K at x = 0 (optimal doping), as Ca substitu-tion injects additional holes: both h Ca and h O contributeto superconductivity, driving the samples into the over-doped region. The smooth linear dependence of T c ( x )of the inset in Fig. 1 also guarantees an effective Ca-Ysubstitution in the whole explored range.However, when tuning of the oxygen content drivesthese same samples to low doping, close to the MI bound-ary, we find a markedly different behaviour. Figure 1displays the critical temperature, T c , versus oxygen con-tent, y , for series of samples at fixed calcium content,0 ≤ x ≤ .
14. Surprisingly T c falls on the same curve forall series with x ≤ .
09, giving rise to superconductiv-ity at the same critical oxygen concentration, y c = 0 . T c , in our underdoped, x ≤ . FIG. 1: Superconducting transition temperatures T c ofY − x Ca x Ba Cu O y samples vs. oxygen concentration forthe whole set of samples: The y ≤ .
09 data fall on the sameline (curves are guides to the eye). Inset: transitions T c de-tected by zero field cooling SQUID magnetization vs. calciumconcentration, for the fully oxygenated, y ≈ . T c with increasing y is the signature of overdop-ing due to Ca substitution. samples.Why are holes transferred by Ca and O not additive forsuperconductivity in the low doping regime? The differ-ent cationic radii ( R Ca +2 /R Y +3 ≈ .
1) may trivially alteroxygen order in the Cu(1)O chains, reducing their chargetransfer efficiency. This is the case, e.g., for substantialY substitutions [21], where the formation of chains takesplace at much larger oxygen content. An independentassessment of the hole content is required to rule out thiseffect. The Seebeck coefficient is an independent measureof the mobile carrier content, since an exponential depen-dence of S vs h is observed in YBa Cu O y in a largerange of doping. [19, 20] We systematically measured thevalue of S at T =290 K (RT) in our samples, calibratingthe dependence on the fully reduced compounds, y ≈ h O = 0, by assuming an averagehole content per Cu plane h = h Ca = x/
2. We iden-tify two regions, as in previous work [19], and our bestfit to S ( h ) = αexp ( − βh ) shown in the inset of Fig. 2,yields values α = 480 µ V/K and β = 25 for h > . α = 650 µ V/K and β = 44 for h < . h values obtained for all ourY − x Ca x Ba Cu O y samples (0 ≤ x ≤ .
14) by com-paring their RT Seebeck coefficient S with the calibrationcurve of the inset in Fig. 2, under the assumption[19, 20]of nearly equal mobilities for the two types of holes, h O and h Ca . [31]The figure shows the well known fact that oxygen doesnot contribute to hole transfer up to y t ≈ . − .
15 (redarrow), since below this threshold O concentration only
FIG. 2: Total hole content of Y − x Ca x Ba Cu O y samples, h , obtained from thermopower, vs oxygen content, y , for dif-ferent Ca families. Inset: calibration of holes h per Cu(2)O layer from thermopower, S , at T = 290 K for the fully reducedsamples. locally charge-neutral Cu(1)OCu(1) dimers are formed[22], while above y t hole doping increases almost linearlywith y , as oxygen ions start forming negatively chargedtrimers. This is true whatever the calcium content, whichproves that the oxygen doping mechanism remains nearlythe same, with a minor dependence of y t on x (dashedline in Fig. 2). The samples ( x = 0, 0.05 and 0.08), whichcollapse on the same curve in Fig. 1, still show a largedifference in their total RT mobile hole content h ( y ) atthe critical oxygen concentration y c = 0 . T c /T c,max versus h , ( T c,max is the maximum transitiontemperature of each calcium series, at optimum doping[23]), showing beyond doubt that the onset of supercon-ductivity does not fall on the same curve as a functionof the total hole content h . Each series of samples atconstant x follows its own curve, contradicting the sug-gested universal parabolic relation [24] between T c and h , which is not the critical parameter in cuprate super-conductivity, as it is often assumed. A similar situationis evidenced by NMR[6] in Ca x La . Ba . − x Cu O y ,where the NQR interaction shows that not all doped car-riers contribute to the superconducting order parameter.The supercarrier pair density, n s , was directly deter-mined by transverse field (TF) µ SR experiments. Wemeasured two series with x = 0, x = 0 .
05, and variable y , plus two further samples ( x = 0 . y = 0 .
43 and x = 0 . y = 0 . µ SR experiment were per-formed on the MUSR spectrometer of the ISIS pulsedmuon facility in the transverse field (TF) geometry[25],where an external magnetic field H is applied perpen- FIG. 3: Scaling of transition temperatures with total holes: T c /T c,max does not scale with total hole content, h . Here T c,max = 93 , , ,
89 and 87 K, respectively for x =0 , . , . , .
08 and 0.14 (from Ref.23). dicular to the initial muon spin S µ polarization. Fieldcooling the samples in µ H = 0 .
022 T a flux lattice isformed, whose field inhomogeneity determines a depo-larization rate of the muon spin precession, σ ( T ), pro-portional to the inverse square of the London penetra-tion depth, λ L , hence to the supercarrier density n s [26]: σ ( T ) ∝ n s ( T ) /m ∗ (where m ∗ is the electron effectivemass). All samples with y < . T f , andsuperconductivity, below T c . The supercarrier density atzero temperature σ = σ ( T = 0) must be obtained byextrapolating the data between these two transitions, asin Ref. [4, 27].The dependence of T c on σ ∝ n s /m ∗ , shown inFig. 4, approaches the characteristic linear Uemura-plot behaviour [28]. The upper axis of the plot represents thesupercarrier density n s per CuO plane, calculated in theclean limit approximation as n s [hole/CuO ] ≈ · σ ,obtained by combining the relation σ = 7 . · − λ − L inSI units[29]) with λ − L = µ e n s /m ∗ . We assume a dop-ing independent value of the effective mass, m ∗ = 3 m e [30]. The plot of supercarrier density vs. oxygen content, n s ( y ), displayed in the inset of Fig. 4, shows that all sam-ples with calcium content 0 < x < .
08 collapse on thesame line, i.e. the dependence of n s on y is linear. Sincealso holes injected by oxygen scale with y , h O ∝ y − y t (Fig. 2), the two linear relations imply that only the frac-tion of holes injected by oxygen, h O , contributes to thesupercarrier density for low calcium content.Summarizing, our results show that in heavily un-derdoped compounds additional holes transferred fromCa participate to the RT normal metal behaviour (ther-mopower) with h Ca ∝ x . Their contribution however dis- FIG. 4: Scaling of transition temperatures with pair density: T c does scale with the µ SR linewidth, σ , proportional to thesupercarrier density, n s . Inset: supercarrier density vs oxygencontent. The samples for 0 < x < .