Two-dimensional superconducting fluctuations associated with charge density wave stripes in La_{1.87}Sr_{0.13}Cu_{0.99}Fe_{0.01}O_4
H. Huang, S.-J. Lee, Y. Ikeda, T. Taniguchi, M. Takahama, C.-C. Kao, M. Fujita, J.-S. Lee
HHuang et al.
Two-dimensional superconducting fluctuations associated with charge density wavestripes in La . Sr . Cu . Fe . O H. Huang, S.-J. Lee, Y. Ikeda, T. Taniguchi, M. Takahama, C.-C. Kao, M. Fujita, ∗ and J.-S. Lee † Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA Institute for Materials Research, Tohoku University, Katahira 2-1-1, Sendai, 980-8577, Japan SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA (Dated: January 5, 2021)The presence of a small concentration of in-plane Fe dopants in La . Sr . Cu . Fe . O isknown to enhance stripe-like spin and charge density wave (SDW and CDW) order, and suppress thesuperconducting T c . Here, we show that it also induces highly two-dimensional (2D) superconductingcorrelations that have been argued to be signatures of a new form of superconducting order, so-calledpair-density-wave (PDW) order. In addition, using the resonant soft x-ray scattering, we find thatthe 2D superconducting fluctuation is strongly associated with the CDW stripe. In particular, thePDW signature first appears when the correlation length of the CDW stripe grows over eight timesthe lattice unit ( ∼ a ). These results provide critical conditions for the formation of PDW order. It has been more than 30 years since high-temperaturesuperconductivity (HTSC) was discovered in 1986 [1].Although tremendous progress has been made in un-derstanding the fundamental mechanism of HTSC, es-pecially in the high- T c cuprates, the complexity of theirphase diagrams [2] has complicated the problem, hencethere still remain many open issues. Some of the remain-ing profound questions are: Why is the superconductingtransition temperature ( T c ) so high? How are differentelectronic and magnetic orders intertwined with HTSC?What is the pseudogap and how is it related to HTSC?Another interesting concerns is on the existence and char-acteristics of a possible new form of pairing, a so-calledpair density wave (PDW), that potentially intertwineswith several of the complex orders observed in the high- T c cuprates [3]. Indeed, it has even been suggested thata fluctuating version of a PDW may be responsible forthe famous pseudogap phenomenology [4–8].In 2007, Li et al . [9] reported the existence of two-dimensional (2D) superconductivity in a high- T c cuprate,La . Ba . CuO (LBCO). This, and closely relatedbut less clear-cut results by Tajima et al . [10], have beenidentified as signatures of PDW order [11, 12]. The mostdramatic evidence of this unusual superconducting orderis the existence of a range of temperatures, T c ≈ < T < T ≈
17 K, in which the system exhibits an ap-parently anisotropic superconducting state. Specifically,in this temperature range, despite the existence of suffi-ciently strong 2D superconducting correlations that theresistivity with the current flowing in the CuO planes isimmeasurably small, interlayer Josephson coupling is ap-parently absent, i.e., the c -axis resistivity remains large.Here T c is the transition temperature to the true super-conducting (Meissner) state. Furthermore, in a some-what higher range of temperatures T < T < T , a fluc-tuating version of the same state, with in-plane resistivityone or more order of magnitude smaller than the normalstate resistivity, onsets below a temperature, T whichis approximately equal to T sdw ≈
40 K [13, 14], the on- set temperature of spin density wave (SDW) stripe or-der in the CuO planes. Since the charge density wave(CDW) stripe develops at a still higher temperature ≈
54 K [15–18] and thus coexists with the SDW at 40 K[14], it was suggested that this PDW signature originatesfrom an intertwining of the HTSC, SDW and CDW or-ders [3]. However, although the correlation between theSDW and CDW has been observed in multiple x-ray scat-tering measurements [14–18], no direct experimental ev-idence has unambiguously supported the association ofthis with PDW order.More recently, scanning tunneling microscopy (STM)experiments in the halo region surrounding the vortexcores of Bi Sr CaCu O δ (Bi2212) was performed byEdkins et al. [19], aimed to detect the field induced PDW.Through enhanced real- and Q -space resolutions in theSTM, they revealed a CDW with a period of approxi-mately eight times the lattice unit ( ∼ a ), twice thatof the normal CDW period ( ∼ a ). This observation isalso thought to be a signature of a PDW. More detailedcomparisons between microscopic theory and STM re-sults have provided additional support for the existenceof PDW order in Bi2212 [20–22]. However, the obser-vation of PDW order through STM in Bi2212 is distinctfrom that in the LBCO system, if for no other reason thanthat there is presently no evidence of any role of SDWin the Bi2212 case. Although (rather short-range cor-related) CDW order coexists with the superconductingphase of Bi2212 [23, 24], it doesn’t have a phase over-lapping with the magnetic order in the phase diagram[25, 26].In this Letter, we explore new evidence of the puta-tive PDW signature and its relation with other orders,such as CDW and SDW, in a La-based high- T c cuprateLa . Sr . Cu . Fe . O (LSCFO) [27]. It is importantto stress that the crystal structure [28] of this material(i.e., the low temperature orthorhombic - LTO - struc-ture) is different from that of LBCO (i.e., the low tem-perature tetragonal - LTT). The LTT structure is known a r X i v : . [ c ond - m a t . s up r- c on ] J a n to suppress T c and enhance SDW and CDW order [15–18, 28]. In the present case, the CDW and SDW cor-relations are instead “pinned” and T c is reduced by Fedoping rather than by the LTT structure. The pinnedbehavior is demonstrated by both the integrated inten-sity and peak position of CDW with the developmentof SDW. For this study, we carried out both transportmeasurements and resonant soft x-ray scattering (RSXS)around the Cu L -edge. Through the resistivity mea-surements along both the crystalline ab -axis (i.e., CuO plane) and the c -axis and the comparison between them,we have identified a state of 2D superconducting fluctua-tions that develops below T ≈
32 K. The RSXS measure-ment revealed that CDW short-range order (CDW-SRO)transforms into the CDW stripes with the developmentof SDW stripes below T sdw ≈
50 K. In contrast with thecase in LBCO, T sdw is significantly larger than T , al-though the onset of SDW order is visibly rounded, andbecomes notably sharper around T . We further observedthat the correlation length of the CDW stripe reachesaround 8 a , as the normal state undergoes a crossover tothe 2D fluctuating state. While we do not observe anyapparent vanishing of the in-plane resistivity at a tem-perature T > T c ∼ T in LBCO. In short, the similarities with theobserved relations between the different ordering phe-nomena in the present system strongly corroborate theintertwined character of the different orders, and corre-spondingly the association of it with PDW formation.A sizable LSCFO single crystal was grown by the stan-dard floating-solvent traveling-zone method. The growncrystal was annealed in 1 bar of O gas to minimize oxy-gen deficiencies. The doped Fe ions are in Fe state(3 d , S = 5/2), which have higher valence state than theCu atoms by one, resulting in a reduction of one hole perdoped ion. Thus, the concentration of hole (i.e., doping, p ) in our LSCFO is 0.12. We confirm that this crystaldoes not undergo the LTT by temperature dependenceof the (0 1 0) Bragg peak [30].We first measured the resistivity ( ρ ) of our sample aim-ing to explore a PDW signature in LSCFO [27, 31]. Thismeasurement was motivated by the fact that PDW orderwas observed in LBCO [9] and that La-based cupratesshare the same mutual relationship between the CDWand SDW orders [14, 18, 30, 32, 33]. As illustrated inFig. 1(a), it is well-known that the ordering q -vectors ofthe CDW and SDW ( q cdw and q sdw ) are related by q cdw ∼ × q sdw [32, 33]. It was demonstrated that the LSCFOsystem also follows this relation [30]. Figure 1(b) showsthe resistivity along the c -axis ( ρ c ) as well as that paral-lel to the CuO plane ( ρ ab ), which reveals an anisotropicbehavior occurring around 32 K ( T ). Below the T , thevalue of ρ ab gets as low as ∼ − mΩ cm, while ρ c ∼ mΩ cm slightly increases. The anisotropy is even moreobvious in the ρ c / ρ ab ratio plot (see the inset), showing -4 -3 -2 -1 cab T C T T c / ab Temperature (K)SC Periodicity ~ 4 aq CDW ~ 2 × q SDW
Periodicity ~ 8 a CDWSDW
PDW c ) m c Ω m ( ab ( m Ω c m ) (a)(b) FIG. 1. (color online) (a) A schematic diagram of CDW andSDW stripes, and their intertwining that results in PDW or-der, implying the importance of their respective modulationphases. (b) Temperature dependence of the zero-field resis-tivity. ρ c is along the c -axis and ρ ab is parallel to the CuO planes. The green shade and dashed line denote the first andsecond transitions in ρ ab , respectively, above the Meissnerstate of both ρ ab and ρ c ( T c ∼ ρ c to ρ ab as a function of temperature. an increase of one order of magnitude. This result showsstrong resemblance to the resistivity behavior in LBCO[9] and Zn-doped LBCO [34], lending an interpretationthat our LSCFO sample exhibits 2D fluctuating super-conductivity (i.e., PDW fluctuation) around T . Notethat we also observed magnetic field dependent ρ ab [27].A second drop of ρ ab occurs around 11 K ( T ), deducingthat the PDW fluctuation may change to a pure 2D su-perconducting state. Note that T is still higher than thebulk T c ∼ θ ) by a CCDdetector. During the θ -scan, the detector image cov-ers scattering intensities from the well-aligned scatteringplane ( h , 0, l ) near the detector center as well as fromoff-scattering planes ( h , ± k , l ) at the top/bottom area of V e r . p i x e l I n c i den t X -r a y LSCFO (b) (c)
Fluo. θ ang l e (a)
100 K h (r.l.u.)-0.4 -0.3 -0.2 -0.123.6 K-0.0300.03-0.0300.03 h (r.l.u.) h (r.l.u.) h (r.l.u.) h (r.l.u.) h (r.l.u.) k (r . l . u . ) k (r . l . u . ) CDWarea
Min.Max. -5 -0.26 -0.2-0.26 -0.2-0.26 -0.2 -0.26 -0.2-0.26 -0.2 x FIG. 2. (color online) (a) A schematic sketch showing the RSXS experiment on LSCFO using an area detector (CCD). At thefixed CCD angle (150 ◦ ), θ -scans were performed. The CDW signal is aligned on the center of the CCD detector. The bottomedge area of the image is regarded as the fluorescence (Fluo.) background-dominated region. (b) RSXS patterns in h / k spaceof LSCFO for various sample temperatures after subtracting the fluorescence background. The CDW patterns are centered at q cdw ∼ (-0.233, 0, l ). Below ∼
50 K, the pattern tends to elongate along the k -direction. (c) Projected scattering profiles alongthe h -direction as a function of temperature. The solid lines are Lorentzian fits. the CCD. As depicted in the figure, we used the bottompart of the CCD images to subtract out the fluorescencebackground signal. After the background subtraction, we (a)(b) x - -0.240-0.235-0.230 I n t eg r a t ed i n t en s i t y ( a r b . un i t ) I n t en s i t y ( a r b . un i t ) q CD W (r . l . u . ) Temperature (K)SDW T SDW
FIG. 3. (color online) (a) Integrated intensity (up-triangles)of the CDW order (left y-axis) and its wavevector q cdw (down-triangles, right y-axis) as a function of temperature. Below ∼
50 K (denoted by the vertical, dotted line), both the intensityand the q cdw incommensurability show a different trend. Theerror bars represent 1 standard deviation (s.d.) of the fitparameters. (b) Temperature dependence of the SDW peakintensity measured by elastic neutron scattering. This datawas taken from Ref.[30]. The vertical, dotted line at ∼
50 Kdenotes the onset of SDW order. achieved clear CDW maps along the h -/ k -direction cen-tered at q cdw ∼ (-0.23, 0, l ) reciprocal lattice units (r.l.u.)(see Fig. 2(b) for the background-subtracted scatteringmaps at selected temperatures). As shown in the figure,the CDW peaks are elongated along the k -direction as thetemperature is decreased below T sdw ∼
50 K. This obser-vation is consistent with previous reports on LSCO whereCDW signals showed peak-splitting through intertwiningbetween striped CDW and SDW [33, 36, 37], suggestingthat CDW stripes are also formed in LSCFO. Figure 2(c)shows projected CDW signals along the h -direction as afunction of temperature. We fitted the projected CDWpeaks with the Lorentzian function (blue lines in this fig-ure) and the results are summarized in Fig. 3.Similarly to the LSCO case [33], CDW order in LSCFOcontinuously develops as the sample is cooled down fromabove 120 K. As shown in Fig. 3(a), the integrated inten-sity (left y -axis) of the CDW peak keeps growing with de-creasing temperature. Notably, the growing trend showsa change around 50 K, indicating a transition of theCDW. Note that the transition behavior is not sharp be-cause the characteristics of density wave orders is typi-cally glassy in the cuprates. The high temperature CDW-SRO phase is transformed into the CDW stripe aroundthis temperature, as was the case for LSCO [33]. Fur-thermore, this slope change in the integrated intensitycoincides with a slope change in the wavevector of CDWorder ( q cdw , right y-axis). The q cdw decreases with de-creasing temperature, but is locked in below 50 K. Con-sidering the LBCO case [18], this locking in LSCFO canbe explained by the development of the SDW stripe. Asshown in Fig. 3(b), 50 K is the temperature where theSDW stripe develops [30]. These results indicate thatthe CDW stripe phase is developed by intertwining withthe SDW. However, the discrepancy between this inter-twining temperature and the onset temperature of PDW x - a disorder~8 a T W ~ a n ( o f P D W w a v e l eng t h s ) ) . u . l . r( M H W F SC Temperature (K) (a)(b)
FIG. 4. (color online) (a) FWHM (squares) of the CDWorder (left y -axis) and the number of wavelengths (circles) forthe PDW order (right y -axis). The number of wavelengths( n ) is estimated by ξ CDW /8 a , where ξ CDW is calculated as2/FWHM. Note that the FWHM and n show the same trendbecause they are inversely proportional with each other; theyare plotted with the different axis scale. The vertical greyshade denotes a characteristic temperature ( T w ), at which theFWHM of CDW starts to change while cooling down. Thevertical green shade denotes another slope change in FWHM,close to the first anisotropic transition ( T ) in ρ ab . Below T ∼
32 K, n is larger than 1. (b) A schematic diagram of a CuO plane in LSCFO illustrating the formation of the PDW order.The PDW (fluctuation) starts to form when the domain sizeof CDW is over ∼ a . The dashed green curves represent asituation where PDW cannot be formed because of insufficient ξ CDW . The black shades denote intrinsic disorders. fluctuation obtained by the transport measurement (Fig.1(b)) calls for explanation.To understand the discrepancy, we further scrutinizethe CDW correlation lengths ( ξ CDW ) in LSCFO. Figure4(a) shows the full width at half maximum (FWHM)of the CDW peak as a function of temperature (left y -axis). For T >
70 K, the FWHM does not change withinthe error, representing a T -independent region. This T -independent FWHM corresponds to ξ CDW ∼ ξ CDW ∼ a ∼
15 ˚A. For
T <
70 K, on the other hand, the FWHMstarts to decrease ( ξ CDW increases) with decreasing tem-perature. Following the discussion in Ref.[33], we assign70 K to the characteristic temperature ( T w ).The FWHM behavior shows another noteworthy fea- ture. The increasing trend of ξ CDW below the T w ap-pears to undergo another slope change around 34 ± T ) ofPDW fluctuating states. A very interesting observationis that the measured ξ CDW at this temperature is around35(2) ˚A, which is close to the PDW wavelength, λ PDW ∼ a ∼
30 ˚A. For easier comparison between the twowavelengths, we plotted the ratio n = ξ CDW / λ PDW onthe right y -axis in Fig. 4(a). At T , n is slightly overone. This observation implies that ξ CDW ≥ λ PDW isa critical condition, together with the presence of theCDW stripe, for the formation of PDW order, as high-lighted in Fig. 4(b). When the domain size of CDWstripe is smaller than 8 a , PDW fluctuation cannot beformed (green dashed line in Fig. 4(b)) even when boththe SDW and CDW are present. These conditions arefully compatible with the LBCO case, where PDW wasreadily formed when CDW stripes were formed aroundthe SDW temperature [9], because at this temperaturethe ξ CDW is fairly long and already meets the ξ CDW ≥ λ PDW condition due to the LTT [14, 17].We now discuss the implications of our findings. First,the new evidence of the 2D superconducting signaturein this LSCFO system means the PDW order observedin LBCO is not a consequence of some material sciencespecific to LBCO, but could be ubiquitous in La-basedcuprates. Second, our findings, especially the criticalprerequisite conditions for PDW, are compatible withthe two PDW (or its fluctuation) signatures observed inLBCO and Bi2212 [9, 19, 38], which are seemingly con-tradicting each other. Considering the enhancement of ξ CDW below T c under the magnetic field as a result of thewell-known competition between the CDW and SC orders[39–41], the vortex halo region in Bi2212 under the mag-netic field is expected to have a large CDW domain size,satisfying the correlation length condition to trigger thePDW. In La-based cuprates, this condition is met by adifferent mechanism; the SDW stripe order helps developa long-ranged CDW stripe through intertwining. The dif-ferent situations between Bi2212 and La-based cuprateslead to another critical implication that of the two orders,namely the CDW and SDW stripes, the CDW stripe (or ξ CDW ) is the more essential ingredient for prompting thePDW. This implication is also supported by the observa-tion that for LSCO with 10% hole-doping, the measured c -axis superconducting coherence is abruptly quenchedwith a magnetic field (smaller than H c2 ) while the samemagnetic field strongly enhances the stripe order [42, 43].Finally, one may extend the implications to a broadercontext of the pseudogap phenomenology in the high- T c cuprates [4–8]. There are some pieces of evidence onthe unusual gap features that suggest a PDW fluctuationmay be responsible for the pseudogap phenomenology [5–8]. Nevertheless, due to different energy and temperaturescales between these two phenomena, it is still early toconnect them directly. On the other hand, we may con-template that the CDW could play a bridging role be-tween them, because the CDW is associated with eachphenomenon. For example, in the LSCO case, the uppercritical doping boundary of the CDW phase is strikinglyclose to the pseudogap critical doping [33, 44, 45], sup-porting the close relationship between the CDW and thepseudogap.In summary, we carried out resistivity and Cu L -edge RSXS measurements on a single crystal of La-basedcuprate, La . Sr . Cu . Fe . O . We found new ev-idence of PDW in this system. We also found that itsemergence is attributed primarily to the CDW striperather than the SDW stripe, although the CDW stripeis developed through intertwining with SDW stripes inthis system. In particular, the PDW signature starts toappear when the correlation length of the CDW stripegrows over 8 a . These results indicate the critical role ofthe CDW stripe for the formation of PDW order in high- T c cuprates. 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