Evidence for Multiple Underlying Fermi Surface and Isotropic Energy Gap in the Cuprate Parent Compound Ca 2 CuO 2 Cl 2
Cheng Hu, Jian-Fa Zhao, Ying Ding, Jing Liu, Qiang Gao, Lin Zhao, Guo-Dong Liu, Li Yu, Chang-Qing Jin, Chuang-Tian Chen, Zu-Yan Xu, Xing-Jiang Zhou
EEvidence for Multiple Underlying Fermi Surface and IsotropicEnergy Gap in the Cuprate Parent Compound Ca CuO Cl Cheng Hu , , Jian-Fa Zhao , , Ying Ding , , Jing Liu , , QiangGao , , Lin Zhao , Guo-Dong Liu , Li Yu , Chang-Qing Jin , , ,Chuang-Tian Chen , Zu-Yan Xu and Xing-Jiang Zhou , , , ∗ Beijing National Laboratory for Condensed Matter Physics,Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China University of Chinese Academy of Sciences, Beijing 100049, China Technical Institute of Physics and Chemistry,Chinese Academy of Sciences, Beijing 100190, China Collaborative Innovation Center of Quantum Matter, Beijing 100871, China (Dated: May 28, 2018) a r X i v : . [ c ond - m a t . s up r- c on ] M a y he parent compounds of the high-temperature cuprate superconductors areMott insulators. It has been generally agreed that understanding the physics ofthe doped Mott insulators is essential to understanding the mechanism of hightemperature superconductivity. A natural starting point is to elucidate the basicelectronic structure of the parent compound. Here we report comprehensivehigh resolution angle-resolved photoemission measurements on Ca CuO Cl , aMott insulator and a prototypical parent compound of the cuprates. Multipleunderlying Fermi surface sheets are revealed for the first time. The high energywaterfall-like band dispersions exhibit different behavior near the nodal andantinodal regions. Two distinct energy scales are identified: a d -wave-like lowenergy peak dispersion and a nearly isotropic lower Hubbard band gap. Theseobservations provide new information on the electronic structure of the cuprateparent compound, which is important for understanding the anomalous physicalproperties and superconductivity mechanism of the high temperature cupratesuperconductors. The parent compounds of the high temperature cuprate superconductors are known asMott insulators[1]. These materials have one unpaired electron per Cu site, which are pre-dicted to be half-filled metal by band theory. The large onsite Coulomb repulsion, however,prohibits electron hopping between neighboring sites and leads to an insulating ground statewith antiferromagnetic ordering. When charge carriers are introduced into the CuO planes,the insulating phase is destroyed and the system turns into a metal. Upon further doping,superconductivity emerges. It has been suggested that the physics of high temperature su-perconductivity is doping a Mott insulator[2]. A natural starting point is to elucidate thebasic electronic structure of the parent Mott insulator, i.e., to study the doped single holebehavior in the presence of strong electron correlations.The oxychloride cuprate Ca CuO Cl (CCOC) is a half-filled Mott insulator which hasthe crystal structure of La CuO [3]. It can be doped into a high-temperature superconduc-tor by replacing Ca with Na[4]. Optical spectroscopy[5] and scanning tunnelling microscopy(STM)[6] measurements reveal a charge transfer gap to be ∼ ∼ t-J model[8]. In2ddition, the low-energy peak exhibits a d -wave-like dispersion and forms a single remnantFermi surface in the Mott gap region[9]. Later in this parent compound, ARPES measure-ments reveal a high energy kink feature near 0.8 eV along the nodal direction and a rapidlydispersing high energy band, widely known as “waterfall”[10]. The waterfall-like behavioris found to be rather common in cuprates, and great efforts have been made to understandthe nature of this feature[11–31]. Yet a systematic momentum-dependent study of this highenergy anomaly in the parent compound CCOC is still lacking, and it is still under debatewhether it represents intrinsic band structure or not.In this letter, we present detailed high resolution angle-resolved photoemission measure-ments on CCOC. Using different experimental geometries and examining carefully the un-derlying Fermi momentum k F , we reveal, for the first time, the existence of multiple under-lying Fermi surface sheets (labeled as α and β ) in CCOC. The shape of the α underlyingFermi surface seems to be quite similar to the hole-like Fermi surfaces in hole-doped cupratesuperconductors, while the β underlying Fermi surface is anomalous and seems to form anelectron-like pocket around Γ point. We also investigate the detailed momentum dependenceof the waterfall-like high energy bands along the α underlying Fermi surface. Near the nodalregion, the high energy band dispersions resemble an LDA calculated bare band, while in theantinodal region, the high energy bands strikingly exhibit a nearly vertical dispersion. Thehigh energy kink is found to be ∼ α and β under-lying Fermi surface sheets, we identify two energy scales in the energy distribution curves(EDCs) at underlying k F : the peak maximum, which shows a d -wave-like form, and thespectral weight onset position, which is found to be ∼ d -wave-like gap is consistent with previousARPES results[9]. The isotropic ∼ CuO Cl at different binding energiesmeasured under two distinct experimental geometries. To avoid an obvious sample charging,3he samples were measured at 86 K. Under both experimental geometries, no spectral weightis observed at the Fermi level (not shown in Fig. 1), consistent with the insulating natureof CCOC. At a binding energy of 0.25 and 0.3 eV, spectral weight begins to emerge around( π/ π/ π , π ) point at a binding energy of 1.0 eV and above in Fig. 1a.For a better view of the first Brillouin zone, the original data in Fig. 1a is symmetrized,as shown in Fig. 1c. A close inspection reveals some weak spectral weight along (0,0)-(0, π )direction at a binding energy of 0.8 eV and above, which is more obvious under geometryII (Fig. 1b), indicating the existence of a second sheet of underlying Fermi surface, whichis illustrated in Fig. 2c.Figure 2 shows the detailed momentum evolution of the band structures in CCOC. Theband images in Fig. 2 d and e are measured under the experimental geometry I along thevertical and horizontal cuts labeled in Fig. 2a, respectively. The band images in Fig. 2 fand g are measured under the geometry II along the vertical and horizontal cuts labeledin Fig. 2b, respectively. For each momentum cut, there are two features to be noticed:one is the low energy charge transfer band feature located approximately at 0.5-0.9 eV, theother is the rapidly dispersing high energy feature above ∼ F is extracted by energydistribution curve (EDC) and momentum distribution curve (MDC) analysis methods. Forthe EDC analysis, the corresponding momentum where the EDC peak position is closestto the Fermi level, is defined as the EDC underlying k F . For the MDC analysis, the bandtop can be inferred from the MDC-fitted band dispersion which starts to become vertical;the corresponding momentum is defined as the MDC underlying k F . In our case, the two4ethods give quantitatively similar underlying k F . By tracing the underlying k F from twoindependent measurements under two different experimental geometries (Fig. 2a and Fig.2b), the underlying Fermi surface contours are extracted and shown in Fig. 2c. For thefirst time, with different experimental geometry to check matrix element, improved energyand angle resolution and detailed mapping in the momentum space, two underlying Fermisurface sheets are clearly revealed, labeled as α and β in Fig. 2c. From the band structureevolution, we can identify that the α sheet is “hole-like” and centered around ( π , π ), the β sheet is “electron-like” and centered around Γ, which indicate a balance of the hole numberand electron number in this system, as expected in the half-filled parent compound.Figure 3 shows the MDC-fitted high energy band dispersions along the α underlyingFermi surface sheet. Fig. 3 a-j shows the band structures along the momentum cuts markedin Fig. 3k. The original data in a and j are symmetrized for a better view of the highenergy dispersion. Fig. 3l shows the MDC-derived dispersions of the bands in Fig. 3 a-j.From the momentum dependent behavior of the MDC dispersions, two distinct momentumregions can be identified. Near the nodal region, the high energy kink position is found tobe ∼ F of the α sheet underlying Fermi surface areobtained and shown in Fig. 3k. It matches well with the intensity plot of the constantenergy contour at 0.3 eV. We note that the bands of the β underlying Fermi surface sheet istoo weak to be discerned from the bands in a-j along the selected cuts under the geometry I.It becomes relatively stronger when measured in the geometry II (Fig. 2b). Fig. 3m showsthe extracted MDC width of the bands in a-j. In the intermediate region between nodal andantinodal regions, the high energy spectral peaks are too broad to be fitted well, leading toa relatively large width, like in the case of cut 4 and 5. The drop at high energy ∼ F . In the nodal EDCs (Fig. 4a), a broadpeak feature can be observed which disperses fast towards the low energy band top ∼ F . In the antinodal EDCs(Fig. 4b), only a broad hump near ∼ α and β underlying Fermi surface sheets (Fig. 4c) areshown. The EDCs are vertically offset for clarity. Fig. 4 e and 4g shows the logarithm plotof the original EDCs in Fig. 4d and 4f, respectively. From Fig. 4d-g, two energy scalescan be identified: the low energy peak position and the spectral weight onset position. Themomentum dependence of the two energy scales is shown in Fig. 4h. It can be seen that,the gap size obtained from the peak positions is anisotropic from nodal to antinodal regionsand follows an offset d -wave-like gap form ∆ = ∆ n + ∆ cos(2Φ) with ∆ n representing thenodal gap (black line in Fig. 4h)[9, 35]. The gap size obtained from the spectral weightonset position is ∼ n ( k ), i.e. |∇ n ( k ) | , is used to determine the underlying k F .From the experimental point of view, there are a number of issues associated with thismethod, making it difficult to extract precisely the underlying k F point[9]. One is thestrong momentum-dependence of the matrix elements, as can be seen in our case in the twodifferent experimental geometries. The second is the need to integrate over a large energywindow, leading to a distribution n ( k ) mixed with contribution both from the low energyand high energy bands. Due to the large background intensity at high energy or near antin-odal region, the n ( k ) lineshape may not reflect the low energy dispersing feature anymore.Here, with improved energy and momentum resolution, the implementation of the EDC andMDC analysis methods provides more reliable results. We also note that, the β underlyingFermi surface sheet is not the corresponding shadow Fermi surface of the α sheet becausethe two sheets are clearly not symmetrical with respect to the antiferromagnetic Brillouinzone boundary beyond the experimental uncertainty.6he peculiar momentum dependence of the high energy waterfall-like bands can not beunderstood by a simple LDA bare band picture nor t-J model. From an experimentalpoint of view, considering the nearly vertical dispersing low energy bands in the antinodalregion, the high energy band may be intrinsic to the cuprate parent compound and may playan important role to connect the low energy charge transfer band with the valence band athigher energy which is assumed to be of strong oxygen orbital character[31]. The multipleunderlying Fermi surface nature and the anomalous momentum dependence of the highenergy bands reflect the strong electron correlation nature in Mott insulator and need furthertheoretical study. Although ARPES probes only the occupied states which cannot explorethe upper Hubbard band, our identification of the nearly isotropic full gap upon the lowerHubbard band may indicate a similar behavior of the upper Hubbard band. In this case,these may finally lead to an isotropic Mott gap in momentum space. Further experimentalinvestigations are needed to obtain the complete momentum dependent information of theMott-Hubbard gap.In conclusion, by taking high resolution ARPES measurements, for the first time, we haveclearly revealed multiple underlying Fermi surface sheets and the anomalous momentumdependence of the high energy waterfall-like bands in the parent Mott insulator CCOC. Wealso identify two distinct energy scales in the spectra: the low energy peak dispersion whichshows a d -wave-like form and a nearly isotropic lower Hubbard band gap. Our observationsprovide new information on the electronic structure of the Mott insulator and indicate thatthe strong electron correlation effect is important to understand the anomalous physicalproperties of the cuprate parent compound. Methods
High quality Ca CuO Cl (CCOC) single crystals are grown by the flux method[32].Polycrystalline samples are synthesized by mixing the powders of CaO and CuCl with amolar ratio of 2:1 in an alumina crucible and heating at 1,073 K for 24 h with intermediategrindings. The CCOC precursor is then heated to 1,203 K at a ramp rate of 60 K/h andkept there for 10 h. Finally, CCOC single crystals are obtained by cooling down to roomtemperature at a ramp rate of 60 K/h.The ARPES measurements are performed on our lab photoemission system equippedwith a Scienta DA30L electron energy analyzer and a Helium discharge lamp with a photon7nergy 21.218 eV[33]. The incident light is partially polarized, with a major s polarization.The overall energy resolution was set at 10 meV and the angular resolution is ∼ ◦ . TheFermi level is referenced by measuring the Fermi edge of a clean polycrystalline gold thatis electrically connected to the sample. The samples were cleaved in situ and measured invacuum with a base pressure better than 5 × − Torr. ∗ Corresponding author: [email protected]. [1] Anderson PW, Schrieffer R 1991 Phys. Today
22] Markiewicz RS et al 2007 Phys. Rev. B Acknowledgement
XJZ thanks financial support from the National Key Research and Development Programof China (2016YFA0300300), the National Natural Science Foundation of China (11334010and 11534007), the National Basic Research Program of China (2015CB921000) and theStrategic Priority Research Program (B) of Chinese Academy of Sciences (XDB07020300).
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IG. 1:
Constant energy contours of Ca CuO Cl measured at 86 K. (a-b) Constantenergy contours of Ca CuO Cl measured in geometry I and geometry II, respectively, obtained byintegrating the photoemission spectral weight over a 30 meV energy window at different bindingenergies (E B ) of 0.25 eV, 0.3 eV, 0.4 eV, 0.6 eV, 0.8 eV, 1.0 eV, 1.2 eV and 1.5 eV (from leftcolumn to right column). In geometry I, the cut orientation is parallel to the (0,0)-( π , π ) direction.In geometry II, the cut orientation is parallel to the (0,0)-( π ,0) direction, which is Cu-O-Cu bonddirection. The electric field direction of the incident light in each geometry is shown in the leftmostpanels. The first Brillouin zone is indicated by a gray square. (c) Constant energy contours ofCa CuO Cl in geometry I obtained by a four-fold symmetrization of the original data from (a)within the region between (0,0)-( π , π ) line and (0,0)-(- π , π ) line. Only the first Brillouin zone isshown here. IG. 2:
Momentum dependence of the band structure in Ca CuO Cl . (a) Constantenergy contour of Ca CuO Cl measured in geometry I (same as Fig. 1a) at a binding energy of0.7 eV, with vertical momentum cuts labeled from VA1 to VA11, and horizontal momentum cutslabeled from HA1 to HA11. (b) Constant energy contour of Ca CuO Cl measured in geometry II(same as Fig. 1b) at a binding energy of 0.7 eV, with vertical momentum cuts labeled from VB1 toVB11, and horizontal momentum cuts labeled from HB1 to HB11. (c) Multiple underlying Fermisurface sheets obtained by tracing the underlying “Fermi momentum k F ” which is determinedby MDC (momentum distribution curve) analysis and EDC (energy distribution curve) analysisof the bands in (d-g). The MDC fitting and EDC analyses quantitatively give similar results.We note that, near the antinodal region where the EDC analysis does not work well, only MDCfitting results are used. The red curve represents underlying Fermi surface α while the black curverepresents underlying Fermi surface β . (d) Band structure along various momentum cuts from VA1to VA11. (e) Band structure along various momentum cuts from HA1 to HA11. (f) Band structurealong various momentum cuts from VB1 to VB11. (g) Band structure along various momentumcuts from HB1 to HB11. IG. 3:
Momentum dependence of the band structure along the α sheet of the under-lying Fermi surface and the corresponding MDC-fitted dispersions. (a-j) Band structurealong momentum cuts from 1 to 10 shown in (k). The momentum cuts are nearly perpendicularto the underlying Fermi surface sheet α . The data in (a) is obtained by symmetrization around Γpoint. The data from (b) to (i) are original data. The data in (j) is obtained by symmetrizationaround (0, π ). (k) Constant energy contour of Ca CuO Cl at a binding energy of 0.3 eV, withmomentum cuts labeled from 1 to 10. The red circles represent the underlying k F determined foreach cut. It matches well with the intensity plot of the low energy contours. (l) MDC-derived banddispersions for the momentum cuts 1 to 10. The blue dashed line is a guideline to the high energykink position. The black dashed line represents LDA calculated bare band. (m) Extracted MDCwidth (Full width at half maximum, FWHM). IG. 4:
Determination of the two energy scales in Ca CuO Cl . (a) Typical EDCs along(- π ,- π )-(0,0)-( π , π ) direction. The data are symmetrized around Γ point (corresponding to Fig.3a). The red curves represent the EDCs at the underlying k F . (b) Typical EDCs along (- π , π )-(0, π )-( π , π ) direction. The data are symmetrized around (0, π ) (corresponding to Fig. 3j). The redcurves represent the EDCs at the underlying k F . (c) The location of the underlying k F along theunderlying Fermi surface sheets α and β . (d) Corresponding EDCs at underlying Fermi momentafrom 1 to 10 along the α underlying Fermi surface in (c). (e) The logarithm plot of the EDCs in (d),showing how the spectral weight onset position is determined. The red dashed lines are guidelinesto show the existence of a full gap. (f) Corresponding EDCs at underlying Fermi momenta from 1to 11 along the β underlying Fermi surface in (c). (g) The logarithm plot of the EDCs in (f). (h)Extracted two kinds of energy scales as a function of momentum angle (Φ) that is defined in (c).Note that for the α underlying Fermi surface, the Φ is defined from ( π , π ) point, while for the β underlying Fermi surface, Φ is defined from Γ point. The red circle and triangle represent the peakposition and spectral weight onset position along the α underlying Fermi surface, respectively. Theblue square and inverted triangle represent the peak position and spectral weight onset positionalong the β underlying Fermi surface, respectively. The black line depicts the offset d -wave form∆ = ∆ n + ∆ cos(2Φ) with ∆ n = 0 .
54 eV and ∆ = 0 .
28 eV, in which ∆ n represents the nodalpeak position.represents the nodalpeak position.