Characteristic electronic structure and its doping evolution in lightly-doped to underdoped YBa2Cu3Oy
H. Yagi, T. Yoshida, A. Fujimori, K. Tanaka, N. Mannella, W. L. Yang, X. J. Zhou, D. H. Lu, Z.-X. Shen, Z. Hussain, M. Kubota, K. Ono, K. Segawa, Y. Ando, D. Iijima, M. Goto, K. M. Kojima, S. Uchida
aa r X i v : . [ c ond - m a t . s up r- c on ] F e b Characteristic electronic structure and its doping evolution in lightly-doped tounderdoped YBa Cu O y H. Yagi , T. Yoshida , A. Fujimori , K. Tanaka , N. Mannella , W. L. Yang , X. J. Zhou , D. H. Lu , Z.-X. Shen ,Z. Hussain , M. Kubota , K. Ono , K. Segawa , Y. Ando , D. Iijima , M. Goto , K. M. Kojima , and S. Uchida Department of Physics, Univerity of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan Department of Appplied Physics and Stanford Synchrotron Radiation Laboratory, Stanford University, Stanford, CA 94305 Advanced Light Source, Lawrence Berkeley National Lab, Berkeley, CA 94720 Institute of Materials Structure Science, Tsukuba, Ibaraki 305-0801, Japan Institute of Scientific and Industrial Research, Osaka University,Mihogaoka 8-1, Ibaraki, Osaka 567-0047, Japan (Dated: October 31, 2018)We have performed an angle resolved photoemission spectroscopy (ARPES) study of lightly-dopedto underdoped YBa Cu O y (YBCO) untwinned single crystals and a core-level x-ray photoemissionspectroscopy (XPS) study of YBCO single and polycrystals. In the zone diagonal (nodal) direction,dispersive quasi-particle (QP) features crossing the Fermi level were observed down to the holeconcentration of ∼ − x Sr x CuO , was observed. PACS numbers: 74.25.Jb, 74.72.Bk, 79.60.-i
INTRODUCTION
The doping evolution of the electronic properties oflightly-doped cuprates have attracted considerable inter-est because of their fundamental importance in the con-text of both physics near Mott transition and mecha-nism of superconductivity.. In the cuprates, in particu-lar, the phase competition and the nature of the com-peting phases in the underdoped region have providedmajor experimental and theoretical challenges. Angle-resolved photoemission spectroscopy (ARPES) studiesof lightly-doped La − x Sr x CuO (LSCO) [1] have shownthat a sharp dispersive quasi-particle (QP) peak crossesthe Fermi level ( E F ) in the nodal ~k = (0,0)-( π , π ) direc-tion, which explains their metallic behavior [2] and thatthe other part of the Fermi surface around ( π ,0) is gappedor pseudo-gapped, resulting in an “arc” of the Fermi sur-face around the nodal direction. A remnant of the lowerHubbard band (LHB) (or the polaronic side band [3])persists at ∼ − (0.4-0.6) eV as the QP peak appears near E F . As holes are further doped, spectral weight is trans-ferred from the “LHB” to the QP peak [4]. ARPES stud-ies on lightly-doped Ca − x Na x CuO Cl (Na-CCOC) [5]and Bi Sr − x La x CuO δ (Bi2201) [6], on the other hand,have shown quite different behaviors: With hole dop-ing, the “LHB” feature is shifted toward E F and mergesinto the QP band crossing E F , making the LHB-to-QPspectral weight transfer less obvious. These observationsare consistent with the pinning of the chemical potentialin LSCO and the rapid chemical potential shift in Na-CCOC, Bi2201 and Bi2212 as implied by core-level x-rayphotoemission spectroscopy (XPS) [4, 6–8].Recent in-plane transport studies of YBa Cu O y (YBCO) have revealed their metallic behavior ( dρ/dT >
0) at high temperatures even in the lightly-doped “in-sulating” region as in the case of LSCO [9]. The E F crossing of QP peak in the nodal direction has been ob-served in lightly-doped [10] as well as in underdoped tooverdoped YBCO [11]. It is therefore important to seewhether the electronic structure of lightly-doped YBCOis similar to that of LSCO or to that of Na-CCOC,Bi2201, and Bi2212. ARPES studies of YBCO havenot been advanced compared to those of other high- T c cuprates because intense surface-state signals near E F mask the bulk electronic states around the X [=( π ,0)]and Y [=(0, π )] points in the Brillouin zone. Lu etal. [12] have made high-resolution ARPES measurmentson YBa Cu O . and have succeeded in distinguishingbulk electronic states from the surface states around Xand Y by aging the sample surfaces and deduced thesuperconducting gap. They have reported that the su-perconducting peak is accompanied by a peak-dip humpstructure, similar to Bi2212. Yoshida et al. [10] andBorisenko et al. [11] have reported a bilayer splitting inlightly-doped and optimally-doped YBCO, respectively.In a recent ARPES study of optimally-doped YBCO byNakayama et al. [13], bulk and surface Fermi surfaceshave been separated. More recently, Hossain et al. re-ported the doping evolution of the electronic structureof the topmost CuO plane from overdoped to the un-derdoped region [14]. The recent Hall resistance mea-surment of underdoped YBCO revealed the existence ofan small electron pocket [15, 16], although in the ARPESstudies of other high- T c cuprates, only a Fermi arc aroundthe nodal direction has been observed. Therfore, it isimportant to clarify whether an small electron pocket isobserved in ARPES studies of underdoped YBCO or not. TABLE I: Oxygen content y , hole concentration δ in theCuO plane estimated from the electrical resistivity and ther-mopower [18], and T c of the YBCO samples studied in thepresent work. y δ T c (K)6.20 0.016.25 0.026.28 0.036.30 0.046.35 0.056.40 0.076.45 0.08 206.50 0.09 356.60 0.12 57 In this paper, ARPES and core-level XPS studies oflightly-doped to underdoped YBCO are presented toclarify the above issues and to gain further insight intothe electronic structure of YBCO.
EXPERIMENT
Untwinned single crystals of YBa Cu O y ( y =6.25,6.28, 6.30, 6.35, 6.40, 6.45, 6.60) were grown by the fluxmethod as described in Ref. [17]. In the XPS study,we measured polycrystals of YBa Cu O y ( y =6.20, 6.40,6.50, 6.60), too. In YBCO, how the in-plane hole concen-tration δ changes with oxygen content y has been con-troversial. We have adopted the estimates from electri-cal resistivity and thermopower [18]. y , δ and T c of themeasured samples are listed in Table I. The ARPESmeasurements were carried out at BL10.0.1 of AdvancedLight Source (ALS) using incident photons of 55 eV anda SCIENTA R4000 analyzer, at BL28 of Photon Fac-tory (PF) using incident photons of 65 eV, a SCIENTASES2002 analyzer, and at BL5-4 of Stanford SynchrotronRadiation Laboratory (SSRL) using photons of 28 eVand a SCIENTA SES-200 analyzer. An R-Dec Co. Ltd.i GONIO LT goniometer [19] was used at PF. The totalenergy and momentum resolution was about 20 meV and0.02 π in units of 1/ a ( a = 3 .
86 ˚A is the lattice constant),respectively. The samples were cleaved in situ in an ultrahigh vaccum of 10 − Torr and cooled to ∼
10 K duringthe measurement. The XPS measurements were carriedout using the Mg Kα line ( h ν = 1253 . Kα line ( h ν = 1253 . . ±
50 meV because most of the spectralline shapes were identical between different compositions.Details of the core-level XPS studies are described else- where [8, 20].
RESULTS AND DISCUSSION
Figure 1 shows energy distribution curves (EDC’s)along high symmetry lines in the second Brillouin zonefor the y =6.35 and 6.60 samples. Two dispersive featuresare observed and both of them become more pronouncedin going from y=6.35 to 6.60, reflecting the increasedhole doping. One (open circles) is around − . E F around 60 % of theΓX and ΓY lines. In optimally-doped YBCO, this featurewas assigned to surface states in Ref. [12] and assigned tosurface antibonding band in Ref. [13] The other feature(open triangles) was considered to be the surface bondingband according to Ref. [13]. The dispersion of the surfacebonding band is unclear around Γ because the broad andstrong antibonding band masks this feature. It shouldbe noted that the energy position of the surface bondingband showed clear anisotropy, − .
18 eV at X and − . E F ,which reflects the Fermi surface, for y =6.45. Not only alarge hole-like Fermi surface centered at the S point, butalso an apparently electron-like Fermi surface centered atΓ are observed, indicating the bilayer splitting [10, 11].Open circles in Fig. 2(a) are the k F positions of the Fermisurfaces determined by the peak positions of momentumdistribution curves (MDC’s) at E F . In Fig. 2(b), the k F positions thus determined are plotted for various compo-sitions in the same panel. The shape of the Fermi surfacedoes not vary appreciably in this doping range, suggest-ing that these Fermi surfaces are not derived from bulk.Because the cleaved surface of YBCO tend to be over-doped [11, 13], we compare the experiment with theFermi surfaces predicted by local-density-approximation(LDA) calculation for y =7 [21] in Fig. 2(b). In the LDAcalculation, the Fermi surface has four sheets derivedfrom the CuO planes and the CuO chain. However, be-cause we did not observe the CuO chain-derived bands,we have plotted only the CuO plane-derived sheets, thatis, those derived from the bonding and antibonding bandsof the CuO bilayer. The Fermi surfaces for two valuesof k z =0 and π/c are indicated because for the optimally-doped YBCO the CuO chain mediates orbital overlapalong the c -axis and therefore strong k z dispersions arepredicted. The experimental results are more similar tothe k z =0 cross-section than to the k z = π/c one. Theshape of the Fermi surface of the bonding band is moresimilar to that of Bi2212 than to that of LSCO. Accordingto the tight binding model including hopping parameters t , t ′ , and t ′′ , this suggests a large next-nearest-neighbourhopping | t ′ | in YBCO [22].In Fig. 3(a), we summarize the surface band disper-sions of YBCO for various y ’s obtained from EDC’s.Here, the surface bonding band for the y =6.28 samplewas taken in a different experimental geometry ( E ⊥ b )and photon energy ( h ν = 65 eV) than the rest of the data( E k XY), and was clearly resolved even around the Γpoint. Although the spectral line shape and intensitiesdramatically changed with hole doping (see Fig. 1), theband dispersions did not change appreciably in this dop-ing range. The lower bound for the bilayer splitting atX and Y is estimated to be 180 meV and 140 meV, re-spectively, because the surface antibonding band shouldbe above E F at these momenta. Figure 3(b) shows theLDA band dispersions of YBCO ( y =7) for k z =0 [21].Red curves are the bonding and antibonding bands of theCuO bilayer. The experimental surface band dispersionsare qualitatively reproduced by the LDA band structureexcept for the E F crossing points along the symmetrylines and the overall band narrowing (by a factor of ∼ bilayers at X and Y was 610 meVand 560 meV, respectively, which is much larger thanthe experimental value of &
180 meV and &
140 meV.The reason for this dicrepancy is that LDA calculationneglects electron correlation and generally overestimatesband dispersions. Indeed, overdoped Bi2212 has showna bilayer splitting of 88 meV [24], much smaller than300 meV predicted by LDA calculation [21, 25]. BilayerHubbard model calculations for two coupled CuO layers,which explicitly include the on-site Coulomb repulsion,predicted a maximum splitting of 40 meV [26]. y=6.60 Γ XS δ∼ δ∼ Energy relative to E F (eV) y=6.35 δ∼ Γ S δ∼ I n t en s i t y ( a r b . un i t s ) YBa Cu O y h ν =55 eV Γ XY S Γ XY S
FIG. 1: (Color online) EDC’s of lightly-doped to underdopedYBCO. Two features in the spectra are surface bonding state(open triangles) and surface antibonding state (open circles). h ν =55 eVy=6.45 SXY Γ δ∼ HIGHLOW y=6.35 δ∼ δ∼ δ∼ z =0) LDA(k z = π /c)(b)2.0 1.5 1.0 k y ( π / a ) k x ( π /a) FIG. 2: (Color online) (a) Spectral weight mapping at E F fora 40 meV integration window. Open circles are the k F posi-tions determined from MDC’s and the white arrow denotesthe polarization of the incident light. (b) Experimentally de-termined k F positions in each doping level and LDA Fermisurface for k z =0 and k z = π / c related to the CuO plane.FIG. 3: (Color online) Band dispersions in YBCO obtainedfrom EDC’s (a) compared with the LDA band dispersions forYBCO (y=7) at k z =0 [21] (b). In (b), red curves are theantibonding and bonding bands of the CuO planes. Figure 4(a)-(c) shows spectral weight mapping at E F with a 40 meV integration window in the first Brillouinzone for the y =6.35, 6.45 and 6.60 samples. A Fermi”arc” around the nodal direction is observed as in theLSCO case, which is completely different from Fig. 2(a).Figure 2(a) does not show a Fermi arc but a hole-likeand an electron-like Fermi surface arising from the sur-face state. Figure 4(e) shows the intensity plot in the E - k plane in the nodal direction for the y =6.35 sam-ple together with the energy band dispersion determinedfrom MDC peaks. The dispersion of this band showsa kink structure around ∼
50 meV like in many otherhigh- T c cuprates, while the surface bonding band is re-ported to show a straight dispersion [13]. In addition,the k F positions in the nodal direction in the first Bril-louin zone are different from those in the second Brillouinzone. These findings suggest that the Fermi arc observedin the first Brillouin zone is distinct from the Fermi sur-faces observed in the second BZ and we attribute it toa bulk-derived feature. To investigate the doping evolu-tion of the Fermi arc, the k F positions determiend by thepeak positions of the MDC’s are plotted by filled circlesin Fig. 4(a)-(c). The k F positions for y =6.35, 6.45, and6.60 are overlaid in Fig. 4(d). As holes are doped, thehole-like Fermi surface centered at S slightly expands inthe nodal region, which is also consistent with the as-sumption that these Fermi surfaces are bulk derived. -0.20-0.100.00 E ne r g y r e l a t i v e t o E F ( e V ) k x ( π /a) (e)y=6.351.00.50.0 1.00.50.0 h ν =55 eVy=6.60 δ∼ ν =55 eV δ∼ XY S Γ k x ( π /a) k y ( π / a ) LOWHIGH ν =55 eVy=6.35 δ∼ FIG. 4: (Color online) (a)-(c) Spectral weight mapping at E F for a 40 meV integration window in the first Brillouin zone.Filled circles are the k F positions determined from MDC’sand the white arrow denotes the polarization of the incidentlight. (d) k F positions for y =6.35, 6.45, and 6.60 determinedfrom MDC’s. (e) Intensity plot in the E - k plane in the nodaldirection for the y =6.35 sample. Filled circles denote theenergy band dispersion determined by fitting the MDC’s toLorentzians. Next, we present the result of the measurements ofXPS core levels in YBCO, and deduce the chemical po-tential shift as a function of doping. As shown in theinset of Fig. 5, the O 1 s and Y 3 d core levels show thesame shifts. As for the Ba 4 d core level, the peak be-comes broader with hole doping, perhaps due to some surface effects, but apart from this the Ba 4 d peak po-sition follow the shifts of the O 1 s and Y 3 d core levels,too. The line shape of the Cu 2 p peak was not identicalbetween the different compositions but its peak positionmoved in the opposite direction to those of the O 1 s ,Y 3 d and Ba 4 d core levels. The different behavior ofthe Cu 2 p core level can be attributed to the creationand the growth of “Cu ” signals with hole doping onthe higher binding energy side of the Cu main compo-nent [4]. The inset of Fig. 5 shows the binding energyshifts referenced to y =6.2 of each core level thus esti-mated. As in the previous studies [20], we consider thatthe parallel shifts of the O 1 s , Y 3 d and Ba 4 d core levelsreflect the chemical potential shift ∆ µ . Recently, Maiti et al. reported the shifts of the core levels in YBCO us-ing hard x-ray photoemission spectroscopy [27]. Our Y3 d and O 1 s shifts are consistent with their results ex-cept for their lowest doped sample ( y = 6.15). In themain panel of Fig. 5, therefore, ∆ µ has been obtained bytaking the average of the O 1 s and Y 3 d core-level shiftsas shown in the figure. In the same panel, the chemicalpotential shift in other high T c cuprates are plotted forcomparison [4, 7, 8, 28]. Theoretically, if the long-rangeantiferromagnetic order of the parent Mott insulator dis-appears for a very small hole concentration, the chargesuceptibility ∂n / ∂µ diverges in the limit δ → δ . In YBCO and NCCO, onthe other hand, the antiferromagnetic order perisits upto δ ∼ .
07 and δ ∼ .
14, respectivly, and thefore it isreasonable that little or no suppression of the shift wasobserved for small δ .According to t - t ′ - t ′′ - J model calculations [30], thelarger the | t ′ | becomes, the stronger the chemical po-tential shift becomes. The observed differences betweenBi2212 and LSCO, such as the different dispersion widthof the LHB from k ∼ ( π/ , π/
2) to ∼ ( π, | t ′ | value in Bi2212 than that in LSCO [30, 31].∆ µ in YBCO is the largest among those compounds,which means that the | t ′ | of YBCO may be the largest,consistent with the conclusion from the ARPES resultsdescribed above. The suppression of the shift in the un-derdoped LSCO is too strong compared to the t - t ′ - t ′′ - J model calculation and has been attributed to a fluctua-tion of charge stripes [4]. The dynamical stripes seen inLSCO change their periodicity linearly with doping [32].As a result, the local charge density is nearly unchangedso that the hole rich region expands and the hole poorregion shrinks as the average hole concentration is in-creased. Under such a circumstance, the chemical poten-tial would not move with doping. If the periodicity ofthe stripes remains unchanged with doping, on the otherhand, the chemical potential is expected to move in arigid-band-like manner. In this regard, the observationsof in-plane anisotropic magnetoresistance [33] and elec-trical resistivity [9] in untwinned single crystals of YBCOare most consistent with the idea that charge stripes alsoexist in lightly-doped YBCO. The presence of the stripesand the strong chemical potential shift can be reconciledif the stripes in the lightly-doped YBCO are of the typeof fixed periodicity. doping level / Cu C he m i c a l P o t en t i a l S h i ft ∆ µ ( e V ) YBCO Bi2212 LSCO Na-CCOC NCCO
AF AF R e l a t i v e E ne r g y ( e V ) δ O 1s Y 3d Cu 2p Ba 4d
FIG. 5: (Color online) Chemical potential shift in YBCO com-pared with those in other high T c superconductors [4, 7, 8, 28].The antiferromagnetic region is displayed by shaded region forYBCO and NCCO. Inset shows the shift of each core level forYBCO as a function of hole concentration δ . To investigate the doping dependence of the shape ofthe Fermi surface and the QP band quantitatively, wehave fitted the k F positions shown in Fig. 4(d) to thetwo-dimensional t - t ′ - t ′′ tight binding model ǫ k − µ = − t [cos( k x a ) + cos( k y a )] − t ′ cos( k x a )cos( k y a ) − t ′′ [cos(2 k x a ) + cos(2 k y a )] + ǫ Here, ǫ is the position of the band center relative to thechemical potential. We have assumed that t ′′ /t ′ = − / − t ′ /t and − ǫ /t as fitting parameters. Figure 6(a) shows the shape ofthe Fermi surface from the tight-binding fit. One cansee the squarelike Fermi surface which suggests large − t ′ /t [22]. Figure 6(b) shows fitted tight-binding param-eters as function of hole concentration. As in the caseof LSCO and Bi2201, − t ′ /t shows weak doping depen-dence [6, 34]. However, the − t ′ /t value is much larger inYBCO ( ∼ ∼ ∼ µ/t = ǫ /t ,as is not the case in YBCO and LSCO. The doping depen-dence of ǫ /t in YBCO is similar to that in LSCO while − ∆ µ/t increases faster than that in LSCO. This differ-ence may be attributed to the different type of chargestripes as described above. -t ' / t , ε / t , - µ / t hole concentration δ -t'/t, ε /t - µ /t (b)1.00.50.0 k y ( π / a ) k x ( π /a) y=6.35 y=6.45 y=6.60(a) FIG. 6: (Color online) Doping dependence of the electronicstructure in YBCO. (a) Doping dependence of the Fermi sur-face shape. (b) Doping dependence of the fitted tight-bindingparameters. -0.8 -0.4 0.0Energy relative to E F (eV) ( π , π )(0,0) HIGHLOWy= 6.30 δ∼ ( π , π )(0,0) h ν =55.5 eV (a) 0.500.400.300.20 k F x = k F y ( π / a ) LSCO CCOC YBCO Bi2201 Bi2212 (c) -0.8 -0.6 -0.4 -0.2 0Energy relative to E F (eV) y=6.256.306.356.40 h ν =28 eV(b) S Γ E FIG. 7: (Color online) ARPES spectra taken at 10 K forlightly-doped YBa Cu O y along the nodal direction in thefirst Brillouin zone. δ indicates hole concentration per CuO plane. (a) Top panel shows EDC’s and bottom panel showsintensity plot in the E - k plane. (b) EDC’s at k F for y =6.25,6.30, 6.35, and 6.40 samples. (c) k F positions for variousdoping levels in YBCO, LSCO [1], Na-CCOC [5], Bi2201 [6],and Bi2212 [36]. Figure 7(a) shows EDC’s (top) and corresponding in-tensity plots in E - k space (middle) in the nodal (0,0)-( π , π ) direction of the y =6.30 sample. As in the case ofLSCO, a dispersive QP feature crossing E F is seen forthe lightly-doped y ≥ δ =0.04) sample and its inten-sity increased with doping as shown in Fig. 7(b), givingrise to the metallic transport at high temperatures [9].Figure 7(c) shows the k F positions along the nodal di-rection for various doping levels in YBCO, LSCO, Na-CCOC, Bi2201, and Bi2212. In the antiferromagnetic(AF) insulating state of the undoped compound, thevalence-band maximum along the nodal direction shouldbe located at the AF zone boundary, that is, exactly at( π/ , π/
2) due to the band folding in the AF state. InNa-CCOC and the Bi-based compounds, indeed, with de-creasing hole concentration the k F position moves toward( π/ , π/ k F extrapolatesto ∼ (0 . π, . π ) and not to ( π/ , π/
2) [34]. In LSCO,in addition to the QP feature crossing E F , the broad“LHB” or the polaronic feature at ∼ -(0.4-0.6) eV is rec-ognized for low hole concentrations x ≤ .
05. Such anelectronic structure has been regarded as the presence ofthe coherent and incoherent parts of the spectral func-tion influenced by electron-electron and electron-phononinteracitons [3] and/or due to a nano-scale electronic in-homogeneity such as charge stripes [35]. Since such aninhomogeneity is also expected to exist in lightly-dopedYBCO [9, 33], the fact that k F in YBCO did not extrapo-late to ( π/ , π/
2) suggests that QP band is also separatedfrom the “LHB” in YBCO. Unfortunately, such a rem-nant of the “LHB” is not seen in YBCO at least downto ∼ − p band and partly becausespectral weight transfer from the LHB to the QP bandoccurs very quickly with hole doping. CONCLUSION
We have observed the band dispersions and Fermi sur-faces of lightly-doped to underdoped YBCO by ARPESusing untwinned single crystals. The shape of the Fermisurface and the large chemical potential shift indicatedlarge | t ′ | like Bi2212, Bi2202, and Na-CCOC. On theother hand, we observed a rather clear dispersive QPfeature crossing E F along the nodal direction, revealinga similarity to LSCO. Although the coexistence of theremnant LHB could not be confirmed unlike the othercuprates, we conclude that very rapid spectral weighttransfer ocurrs from the LHB to the QP band upon holedoping in the lightly-doped to underdoped YBCO. Wehave also studied the chemical potential shift with holedoping by the XPS measurements of single and poly-crystals. The shift was as rapid as those in Na-CCOC,Bi2201, and Bi2212 in spite of the fact that charge stripesare observed in lightly-doped YBCO like LSCO. We at-tribute the different chemical potential shifts betweenYBCO and LSCO to different types of charge stripes. ACKNOWLEDGEMENT
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