Novel Electronic State and Superconductivity in the Electron-Doped High-Tc T'-Superconductors
T. Adachi T. Kawamata Y. Koike
cond-mat.supr-con cond-mat.str-el






Corresponding author: t-adachi@sophia.ac.jp
Department of Engineering and Applied Sciences, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8554, Japan



Department of Applied Physics, Tohoku University, 6-6-05 Aoba, Aramaki, Aoba-ku, Sendai 980-8579, Japan



In this review article, we show our recent results relating to the undoped (Ce-free) superconductivity in the electron-doped high-T_ c cuprates with the so-called T' structure.
For an introduction, we briefly mention the characteristics of the electron-doped T'-cuprates, including the reduction annealing, conventional phase diagram and undoped superconductivity.
Then, our transport and magnetic results and results relating to the superconducting pairing symmetry of the undoped and underdoped T'-cuprates are shown.
Collaborating spectroscopic and nuclear magnetic resonance results are also shown briefly.
It has been found that, through the reduction annealing, a strongly localized state of carriers accompanied by an antiferromagnetic pseudogap in the as-grown samples changes to a metallic and superconducting state with a short-range magnetic order in the reduced superconducting samples. 
The formation of the short-range magnetic order due to a very small amount of excess oxygen in the reduced superconducting samples suggests that the T'-cuprates exhibiting the undoped superconductivity in the parent compounds are regarded as strongly correlated electron systems, as well as the hole-doped high-T_ c cuprates. 
We show our proposed electronic structure model to understand the undoped superconductivity.
Finally, unsolved future issues of the T'-cuprates are discussed.






PACS numbers: 
Novel Electronic State and Superconductivity in the Electron-Doped High-T_ c T'-Superconductors
    Y. Koike
    May 29, 2018
===============================================================================================





§ INTRODUCTION

In the past three decades, cuprates exhibiting high-temperature superconductivity have been intensively studied.
The superconducting (SC) transition temperature T_ c ∼ 134 K <cit.> in the Hg-1223 cuprate is the highest among all SC materials at ambient pressure.
Although new high-T_ c superconductors of iron arsenides with the maximum T_ c of ∼ 55 K <cit.> and of sulfur hydrides with T_ c ∼ 203 K at 200 GPa <cit.> have been observed, the cuprates have been standing for potential materials of both exotic physics and future applications. 
All series of high-T_ c cuprates, La-214, Y-123, Bi-2212, etc., have the parent compounds, which are antiferromagnetic (AF) Mott insulators.
As shown in the phase diagram of Figure <ref>a, in the hole-doped cuprates, doping of hole carriers into the parent compound destroys an AF order quickly, and then, the superconductivity appears.
With increasing hole doping, T_ c is raised in the underdoped regime and exhibits the maximum in the optimally doped regime.
With further doping, T_ c turns into a decrease in the overdoped regime, and finally, the superconductivity disappears in the heavily-overdoped regime where the system becomes a metal.
Comprehensive neutron scattering <cit.> and muon spin relaxation (μSR) <cit.> experiments have uncovered AF fluctuations in the SC doping regime, suggesting that AF fluctuations are a glue to form SC electron pairs.
In the non-SC heavily-overdoped regime, recent theories <cit.> and experiments <cit.> have suggested the existence of ferromagnetic fluctuations of itinerant carriers.



Electron-doped high-T_ c cuprates were first discovered by Tokura et al. in 1989 <cit.>.
Pronounced features different from those in the hole-doped cuprates are not only the electron carrier, but also the reduction annealing, which is absolutely essential to obtain the superconductivity in the electron-doped cuprates.
The phase diagram depicted by the normally reduced samples is shown in Figure <ref>a, which roughly resembles that of the hole-doped cuprates. 
The doping of electrons into the parent compounds weakens the AF order, but the AF order is maintained around the optimally doped regime.
The superconductivity with the maximum T_ c appears around the optimally doped regime and is monotonically suppressed with over-doping. 
Since AF fluctuations were observed around the optimally doped regime <cit.>, the electron pairing mediated by AF fluctuations has been believed to be the case also in the electron-doped cuprates.
In 2005, a surprising result was obtained in thin films of the electron-doped cuprates with the Nd_2CuO_4-type structure (the so-called T' structure), in which the superconductivity appears without electron doping <cit.>. 
Following observations of the undoped (Ce-free) superconductivity in the parent compounds <cit.> and the suggestion of a new phase diagram shown in Figure <ref>b <cit.> opened a new era of research in the high-T_ c superconductivity. 
Yet to date, the mechanism of the undoped superconductivity is unclear.

In this review article, we show our recent results relating to the undoped superconductivity in the T'-cuprates <cit.>.
First, we present the characteristics of the electron-doped T'-cuprates including the reduction annealing, conventional phase diagram and undoped superconductivity.
The next three sections consist of our transport and magnetic results and results relating to the SC pairing symmetry.
Collaborating spectroscopic and nuclear magnetic resonance (NMR) results are also shown briefly.
Then, we discuss our proposed electronic structure model to understand the undoped superconductivity.
In the final section, unsolved future issues of the T'-cuprates are discussed.
Note that there are already excellent and complete reviews on the materials and physics focusing on the conventional electron-doped cuprates <cit.>.

 



§ ELECTRON-DOPED T'-CUPRATE


Electron-doped T'-cuprates were discovered in Nd_2-xCe_xCuO_4  <cit.>.
This class of materials are expressed as RE_2CuO_4 (RE = Pr, Nd, Sm, Eu) with the T' structure.
The electron doping is achieved by the substitution of the tetravalent Ce^4+ for the trivalent RE^3+.
The T' structure consists of the CuO_2 plane and fluorite-type blocking layer.
Because as-grown T'-samples are insulating and AF, the reduction annealing for the as-grown T'-cuprates is indispensable to obtain superconductivity.
One of the unsolved puzzles for the T'-cuprates is the exact mechanism of the reduction process.
To date, there are mainly two candidate mechanisms for this puzzle.
One is the removal of excess oxygen from the as-grown sample, which is mostly believed from the early stage of the research of the T'-cuprates.
This idea originated from early neutron-diffraction experiments in Nd_2-xCe_xCuO_4 <cit.>.
Because of the size mismatch between the CuO_2 plane and blocking layer, excess oxygen tends to be included right above Cu, resulting in the shrinkage of the blocking layer in the ab-plane.
Since the excess oxygen is understood to induce disorder of the electrostatic potential in the CuO_2 plane, electron pairs are destroyed, and the system shows no SC behaviors <cit.>. 
Therefore, the removal of excess oxygen from the as-grown sample is crucial for the appearance of superconductivity and the investigation of intrinsic properties of the T'-cuprates. 
The other is the Cu-vacancy scenario proposed by neutron and X-ray diffraction studies in Nd_2-xCe_xCuO_4 <cit.> and Pr_1-xLaCe_xCuO_4 <cit.>.
The diffraction experiments found that (i) the occupancy at the Cu site is imperfect (perfect) in the as-grown (reduced) samples and (ii) the so-called secondary phase of RE_2O_3 appears (disappears) through the reduction (oxidation) annealing, both of which are reversible processes through the reduction (oxidation) annealing.
Therefore, the role of the reduction annealing is to fill up Cu deficiencies in the as-grown samples where Cu deficiencies are regarded as causing the pair breaking.
The secondary phase was precisely investigated in Nd_2-xCe_xCuO_4 <cit.>.

The phase diagram of T'-cuprates was first obtained by μSR in Nd_2-xCe_xCuO_4 (Figure <ref>a) <cit.> and later in Pr_1-xLaCe_xCuO_4 <cit.>.
The AF phase expands up to the optimally doped regime, and the optimal superconductivity suddenly sets in at the same time of the suppression of the AF order.
In detail, both the superconductivity and AF order coexist around the boundary of two phases. 
With over-doping, T_ c monotonically decreases and disappears around the region of the solubility limit of Ce into the T'-structure.
Neutron-scattering experiments in Nd_2-xCe_xCuO_4 around the optimally doped regime of x=0.15 revealed commensurate AF fluctuations <cit.>.
This is in sharp contrast to incommensurate AF fluctuations <cit.> or stripe fluctuations <cit.> observed in the hole-doped cuprates.
Following neutron-scattering experiments in Pr_1-xLaCe_xCuO_4 <cit.> uncovered that commensurate AF fluctuations existed also in the overdoped regime and that both the spin stiffness and relaxation rate of AF fluctuations decreased toward the end point of superconductivity in the heavily overdoped regime.
These suggest the intimate relation between the superconductivity and AF fluctuations in the T'-cuprates, as well as in the hole-doped cuprates.

In 1995, Brinkmann et al. reported pioneering results, which later led to the discovery of undoped (Ce-free) superconductivity <cit.>.
They tried to expand the SC regime deeply into the AF underdoped regime in the phase diagram by improving the reduction process.
A thin single crystal of Pr_2-xCe_xCuO_4 was sandwiched by polycrystalline pellets of the same component to protect the surface of the crystal and annealed at a higher temperature of 1080 ^∘C for a longer time than in the conventional annealing.
They observed the superconductivity down to x=0.04 in the underdoped regime. 
Moreover, T_ c gradually increased with decreasing doping from the optimally doped regime.
They suggested that the superconductivity in underdoped Pr_2-xCe_xCuO_4 was a product of the appropriate reduction of excess oxygen.
Then, one would think of lower doping regime than x=0.04, namely whether Mott insulators like the hole-doped cuprates or superconductivity down to the parent compound. 

Ten years later, a surprising result was obtained by Tsukada et al. in T' thin films of Ce-free La_2-yRE_yCuO_4 (RE = Y, Lu, Sm, Eu, Gd, Tb) in which the superconductivity appears without Ce substitution (electron doping) <cit.>.
Subsequent systematic investigation by the same group using Nd_2-xCe_xCuO_4 thin films uncovered that T_ c of ∼ 28 K in the parent compound of x=0 decreased monotonically with increasing x and disappeared at x ∼ 0.20 (Figure <ref>b) <cit.>.
These findings were suggested to be due to the removal of excess oxygen from the as-grown thin films more effectively than that ever reported. 
Their unique procedure of the reduction annealing called two-step annealing was mentioned in the literature <cit.>.
At the first step, the as-grown thin films were annealed at a high temperature in an intermediate oxygen pressure of ∼ 10^2 Pa.
In this process, they insisted based on the increasing ab-plane electrical resistivity ρ_ ab and unchanged c-axis length that oxygen in the CuO_2 plane was mainly removed, and excess oxygen was not. 
At the second step, the thin films were further annealed at a low temperature in a low oxygen pressure of ∼ 10^-5 Pa.
In this process, they insisted based on the decreasing ρ_ ab and c-axis length that excess oxygen moved to the oxygen-defect site in the CuO_2 plane, and the superconductivity was realized. 
In fact, optical studies of the SC thin film of Pr_2CuO_x with x ≃ 4 have revealed a Drude-like peak centered at zero frequency, suggesting a metallic state of the SC parent compound <cit.>.
These results give us the following messages: (i) the newly-proposed phase diagram without the AF phase is seemingly different from the conventional one; and (ii) the AF Mott insulating state is not a starting point of the superconductivity in the T'-cuprates.
The superconductivity in the parent compounds of the T'-cuprates was also confirmed using polycrystalline samples of Ce-free La_2-ySm_yCuO_4 <cit.> and Ce-free La_1.8Eu_0.2CuO_4  <cit.>, while it has not yet been confirmed in single crystals of the parent compound.

From the theoretical viewpoint, the undoped (Ce-free) superconductivity in the parent compounds might be explained by the early local density energy band calculation in Nd_2-xCe_xCuO_4 <cit.> where the system was a simple band metal without electron correlation. 
On the assumption of the moderate electron correlation, the half-filled-band Hubbard model consisting of doublons and holons predicted the superconductivity in the parent compound <cit.>.
Under the strong electron correlation generating the Mott–Hubbard gap between the upper Hubbard band (UHB) and the lower Hubbard band (LHB) of the Cu 3d_x^2-y^2 orbital, calculations based on the local density approximation (LDA) combined with the dynamical mean-field theory (DMFT) revealed the possibility of the closing of the so-called charge-transfer (CT) gap between UHB of the Cu 3d_x^2-y^2 orbital and the O 2p band observed in the hole-doped cuprates <cit.>.
That is, both metallic and SC states were suggested to appear by eliminating the AF order in the parent compounds of the T'-cuprates. 
The recent calculation of a two-particle self-consistent analysis using the three-band model <cit.> revealed a monotonic decrease in T_ c with electron doping, which is consistent with the experimental observation shown in Figure <ref>b <cit.>.

The undoped (Ce-free) superconductivity challenges the long-thought understanding that the parent compounds of the high-T_ c cuprates are AF Mott insulators. 
To understand the mechanism of the undoped superconductivity, it is extremely important to clarify the evolution of the electronic state through the reduction process, for which the detailed investigation using single crystals is necessary.
One of critical questions is whether or not the undoped superconductivity in the T'-cuprates appears based on the strong electron correlation.
To answer this issue, it is significant to investigate the Cu-spin correlation, because localized Cu spins in LHB of the Cu 3d_x^2-y^2 orbital are generated and expected to correlate with one another in the case of the strong electron correlation.
To attain these aims, we used T' single crystals of Ce-underdoped Pr_1.3-xLa_0.7Ce_xCuO_4 + δ with x=0.10 and undoped (Ce-free) SC samples of La_1.8Eu_0.2CuO_4 + δ.
In the next section, we start from the preparation of single crystals and the improved reduction annealing in Pr_1.3-xLa_0.7Ce_xCuO_4 + δ.






§ EVOLUTION OF THE ELECTRONIC STATE THROUGH THE REDUCTION ANNEALING


Single crystals of Ce-underdoped Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10 were grown by the traveling-solvent floating-zone method <cit.>.
In order to reduce excess oxygen in the as-grown crystals, we grew single crystals in air atmosphere, which is at a lower partial pressure of oxygen than formerly reported <cit.>.
The composition of as-grown crystals was determined by the inductively-coupled plasma (ICP) analysis to be Pr_1.17(1)La_0.73(1)Ce_0.10(1)Cu_1.00(1)O_4, which is close to the nominal composition. 
For the as-grown crystals, we performed the reduction annealing in vacuum of ∼ 10^-4 Pa for 24 h at various temperatures.
In order to protect the surface of crystals during the annealing, the as-grown crystals were covered with polycrystalline powders having the same composition (protect annealing). 
This is an improved technique of the Brinkmann's <cit.>.
From the iodometric titration, the oxygen content was confirmed to be reduced by 0.03(1) through the reduction annealing for Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10.
Moreover, through the reduction annealing, the c-axis lengths estimated from the X-ray diffraction measurements were reduced by 0.028(1) Å for Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10, suggesting the removal of excess oxygen from the as-grown samples.
The scanning electron microscope also revealed that, in the reduced SC crystal, neither Cu metals nor rare-earth oxides were observed. 
Therefore, both the absence of Cu deficiency within the error of ICP and the oxygen reduction through the annealing suggest that the Cu deficiency model is not applicable to the present samples.
Polycrystalline samples of undoped (Ce-free) La_1.8Eu_0.2CuO_4+δ were prepared by a low-temperature technique using CaH_2 as a reductant and the subsequent annealing.
The SC samples were obtained through the reduction annealing at 700 ^∘C for 24 h in vacuum.
Details have been described in the literature <cit.>.


 

Figure <ref> shows the temperature dependence of the magnetic susceptibility of Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10 and La_1.8Eu_0.2CuO_4+δ.
For Pr_1.3-xLa_0.7Ce_xCuO_4+δ, the Meissner diamagnetism appears in the 750 ^∘C-reduced crystal, and the relatively sharp SC transition with the onset of 27 K is observed in the 800 ^∘C-reduced crystal.
Formerly, Sun et al. reported from transport properties of reduced single crystals of Pr_1.3-xLa_0.7Ce_xCuO_4+δ through the annealing in Ar that the crystals with x ≤ 0.10 are non-SC <cit.>.
The present successful observation of bulk superconductivity in Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10 suggests that the excess oxygen is effectively removed from the as-grown crystal through the protect annealing in vacuum at lower temperatures than in the conventional annealing.
The La_1.8Eu_0.2CuO_4+δ sample also shows the bulk Meissner diamagnetism below ∼ 15 K, which is almost the same as that formerly reported <cit.>.


 

The temperature dependence of ρ_ ab in Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10 exhibits characteristic behaviors depending on the reduction condition, as shown in Figure <ref>a.
The as-grown crystal shows semiconducting temperature dependence and no trace of superconductivity.
For the 650 ^∘C-reduced crystal, ρ_ ab is semiconducting at high temperatures, while a drop of ρ_ ab is observed below ∼ 7 K due to the SC transition. 
The drastic decrease in ρ_ ab is observed in the 750 ^∘C- and 800 ^∘C-reduced crystals in which the bulk superconductivity appears.
Both crystals show a metallic behavior at high temperatures and an upturn at low temperatures, followed by the SC transition.
In the normal state below ∼ 50 K, ρ_ ab exhibits log T dependence.
This behavior, as well as the saturation of ρ_ ab in the magnetic field and negative magnetoresistance <cit.> is most likely due to the Kondo effect <cit.>.
The present evolution of ρ_ ab through the reduction annealing suggests that the strongly localized state of carriers in the as-grown crystal changes to a metallic state with the Kondo effect in Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10.


Figure <ref>b shows the temperature dependence of the c-axis resistivity ρ_ c for Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10.
For the as-grown and 650 ^∘C-reduced crystals, a hump is observed at ∼ 200 K, which is similar to that observed in Nd_2-xCe_xCuO_4 with x<0.14 <cit.> and Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x ≤ 0.03 <cit.> and due to the opening of an AF pseudogap.
For the 750 ^∘C-reduced crystal, on the contrary, a simple metallic behavior without hump is observed, which resembles the behavior of ρ_ c in SC Nd_2-xCe_xCuO_4 with x=0.15 <cit.>. 
Therefore, it is inferred that the AF pseudogap disappears in the 750 ^∘C-reduced SC crystal.

 

The electronic state of Pr_1.3-xLa_0.7Ce_xCuO_4+δ was further investigated by the angle-resolved photoemission spectroscopy (ARPES) by Horio et al. using our as-grown and reduced single crystals, as shown in Figure <ref> <cit.>.
For the as-grown and 650 ^∘C-reduced crystals, the AF pseudogap is clearly observed around the hot spots, namely, crossing points of the Fermi surface with the AF Brillouin zone boundary.
For the 800 ^∘C-reduced crystal, on the contrary, the sharp quasi-particle peaks are observed on the entire Fermi surface without the signature of the AF pseudogap unlike the previous works <cit.>.
These results are consistent with the ρ_ c results in Figure <ref>b and indicate the dramatic reduction of the AF correlation length and/or of magnetic moments in the 800 ^∘C-reduced crystal.
The quasi-particle peaks around the anti-nodal region are broader than those around the nodal region, suggesting the strong scattering of quasiparticles by the AF fluctuations and/or charge fluctuations in relation to the recent observation of the charge order in Nd_2-xCe_xCuO_4 <cit.>.


The Hall effect of the electron-doped T'-cuprates is highly informative.
Thin-film studies in Pr_2-xCe_xCuO_4 reduced in the conventional annealing revealed that the Hall coefficient R_ H was negative in the underdoped regime and increased with increasing x, followed by the sign change of R_ H at x ∼ 0.17 <cit.>.
Moreover, the Hall resistivity ρ_xy exhibited a nonlinear behavior in the magnetic field in Pr_2-xCe_xCuO_4 thin films <cit.>.
Our results of ρ_xy in Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10 also revealed a nonlinear behavior in the magnetic field.
These suggest that multiple carriers (most likely electrons and holes) reside in the T'-cuprates.
The existence of multiple carriers of electrons and holes has also been suggested from NMR in single crystals of Nd_2-xCe_xCuO_4 and Pr_2-xCe_xCuO_4 <cit.>.
Note that the undoped SC thin films exhibit positive R_ H in the ground state, suggesting the existence of predominant hole-like carriers <cit.>.






§ RELATIONSHIP BETWEEN CU-SPIN CORRELATION AND SUPERCONDUCTIVITY


For the detailed investigation of the Cu-spin correlation, we used the μSR technique which is highly sensitive to the local magnetism in a sample and has an advantage to distinguish between a long-range and short-range magnetic order.
Zero-field (ZF) and longitudinal-field (LF) μSR measurements of Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10 and La_1.8Eu_0.2CuO_4+δ were performed using a pulsed positive muon beam at the Material and Life Science Experimental Facility at J-PARC in Japan and using a continuous positive muon beam at the Paul-Scherrer Institute (PSI) in Switzerland, respectively.





Figure <ref>a,b show the ZF-μSR time spectra of as-grown non-SC and 700 ^∘C-reduced SC samples of La_1.8Eu_0.2CuO_4+δ, respectively <cit.>.
For both samples, Gaussian-like slow depolarizations due to nuclear dipole fields are observed at high temperatures, indicating a paramagnetic state of Cu spins.
With decreasing temperature, fast depolarizations of muon spins are observed, suggesting the development of the Cu-spin correlation.
For the as-grown sample, clear muon-spin precessions appear at low temperatures, indicating the formation of a long-range magnetic order.
For the reduced SC sample, the spectrum consists of a fast depolarization without precession and a following time-independent behavior above 1 μs, which is typical of a short-range magnetically ordered state.
In the LF-μSR spectra at 1.6 K shown in Figure <ref>c <cit.>, a parallel shift up with LF indicates the formation of a static magnetically ordered state in ZF.
In Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10, the as-grown non-SC crystal exhibits muon-spin precessions at low temperatures as shown in Figure <ref>d <cit.>. 
The spectra of the 800 ^∘C-reduced SC crystal in Figure <ref>e <cit.> show both fast and slow depolarizations without muon-spin precession at 3 K.
The LF-μSR spectra at 10 K shown in Figure <ref>f <cit.> reveal a parallel shift as well as a slow depolarization with LF, suggesting the existence of both a short-range magnetic order and fluctuating Cu spins.
These results indicate the coexisting state of the superconductivity and the short-range magnetic order in both La_1.8Eu_0.2CuO_4+δ and Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10.
Note that μSR results of the undoped (Ce-free) thin film of La_2-xY_xCuO_4+δ have shown the development of the Cu-spin correlation at low temperatures <cit.>. 



The analysis of volume fractions of SC and short-range magnetically ordered regions leads to the detailed information on the electronic state in the T'-cuprates.
The magnetic volume fractions were estimated from the μSR results <cit.>.
For the reduced SC La_1.8Eu_0.2CuO_4+δ, the volume fraction of the short-range magnetically ordered region is almost 100% in the ground state.
As the SC volume fraction is estimated from the Meissner fraction to be above 15%, both the SC and short-range magnetically ordered regions coexist in the sample.
For the reduced SC Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10, the estimated magnetic volume fraction is 80% in the ground state.
The SC volume fraction was estimated from the recovery of the electronic specific heat coefficient in the ground state by the application of magnetic field.
It was at least 60%, suggesting the coexistence of the SC and short-range magnetically ordered regions in the sample.
Numerically, a part of the short-range magnetically ordered regions appear to be spatially overlapped with the SC regions. 
However, it is plausible that the short-range magnetically ordered and SC regions are phase-separated, because the volume fraction of the short-range magnetically ordered region might be overestimated due to electronic dipole fields extending to the paramagnetic SC region. 





The Cu-spin dynamics was further investigated by NMR using our reduced SC T'-samples by Yamamoto et al. <cit.> and Fukazawa <cit.>.
As shown in Figure <ref>, the temperature dependence of T_1 T, where 1/T_1 is the ^63Cu nuclear spin-lattice relaxation rate exhibited the Curie-Weiss behavior in a wide temperature range for Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10 and 0.15, suggesting the existence of strong AF fluctuations in the underdoped and overdoped T'-cuprates.
For the undoped (Ce-free) La_1.8Eu_0.2CuO_4+δ, the bulk superconductivity was evidenced by the significant decrease in the Knight shift below T_ c and AF fluctuations were observed in the normal state from the temperature dependence of 1/T_1.
These results suggest that AF fluctuations are related to the formation of electron pairs in the T'-cuprates as well as in the hole-doped cuprates.






§ SUPERCONDUCTING PAIRING SYMMETRY





While the SC pairing symmetry in the hole-doped cuprates is widely recognized to be d-wave, it is controversial in the electron-doped T'-cuprates.
Early studies of impurity effects in Nd_2-xCe_xCu_1-y(Zn,Ni)_yO_4 with x=0.15 revealed that T_ c was depressed by the magnetic impurity Ni much more rapidly than by the nonmagnetic impurity Zn <cit.>.
This is typical of conventional s-wave superconductors.
On the contrary, ARPES <cit.> and penetration depth <cit.> experiments etc. insisted the occurrence of d-wave superconductivity in Nd_2-xCe_xCuO_4+δ with x=0.15 and Pr_2-xCe_xCuO_4+δ with x=0.15.
To clarify the SC pairing symmetry of the undoped (Ce-free) superconductivity in the T'-cuprates, impurity effects on T_ c were precisely investigated in La_1.8Eu_0.2Cu_1-y(Zn,Ni)_yO_4+δ <cit.>.
Figure <ref> displays the impurity-concentration dependence of T_ c normalized by T_ c of y=0 T_ c^y=0 in La_1.8Eu_0.2Cu_1-y(Zn,Ni)_yO_4+δ together with the preceding results of T'-cuprates <cit.> and hole-doped La_2-xSr_xCu_1-y(Zn,Ni)_yO_4 <cit.>.
Obviously, the depression of T_ c is almost the same between the Zn and Ni substitution in contrast to the preceding results of Nd_2-xCe_xCu_1-y(Zn,Ni)_yO_4+δ with x=0.15 <cit.>.
Moreover, the change of T_ c/T_ c^y=0 in La_1.8Eu_0.2Cu_1-y(Zn,Ni)_yO_4+δ follows the results of La_2-xSr_xCu_1-y(Zn,Ni)_yO_4 in the optimally doped x=0.15 and overdoped x=0.20. 
Therefore, in La_1.8Eu_0.2CuO_4+δ, the depression of T_ c by the Zn and Ni substitution is probably due to the pair-breaking effect and the SC pairing symmetry is d-wave mediated by spin fluctuations as in the case of the hole-doped cuprates.
In fact, our μSR <cit.> and NMR <cit.> results also revealed strong spin fluctuations in La_1.8Eu_0.2CuO_4+δ.
The characteristic temperature dependence of 1/T_1 observed in La_1.8Eu_0.2CuO_4+δ implies the existence of nodal lines in the SC gap, supporting the above statement of the d-wave superconductivity <cit.>.
Moreover, optical studies in the SC thin film of Pr_2CuO_x with x ≃ 4 have suggested that the temperature dependence of the magnetic penetration depth λ exhibits the d-wave-like behavior <cit.>.
In future, we will further investigate the SC pairing symmetry by the transverse-field μSR technique.
Accumulating results of λ, inversely proportional to the SC carrier density, in electron-doped T'-cuprates <cit.> and infinite-layer cuprates <cit.> revealed that the T_ c vs. λ relation seemed not to intersect the origin, which is contrary to the results of hole-doped cuprates suggesting the Bose–Einstein-condensation-like pairing mechanism <cit.>.






§ ELECTRONIC STRUCTURE MODEL BASED ON THE STRONG ELECTRON CORRELATION



Our transport and μSR results of Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10 and La_1.8Eu_0.2CuO_4+δ revealed the following evolution of the electronic state through the reduction annealing.
The ρ_ ab showed that a strongly localized state of carriers in the as-grown sample changes to a metallic state with the Kondo effect in the reduced SC sample. 
The Hall resistivity of the reduced SC sample revealed the existence of multiple carriers. 
The μSR spectra revealed that, in the ground state, a long-range magnetic order of Cu spins in the as-grown sample changed to a short-range one coexisting with the superconductivity in the reduced SC samples. 
It would be a reasonable speculation that an ideal T'-cuprate in which the excess oxygen is completely removed exhibits no AF order.
The formation of the short-range magnetic order due to a very small amount of excess oxygen in the reduced SC sample suggests that the Cu spins are correlated with one another in the absence of excess oxygen in the ideal T'-cuprates. 
Therefore, the T'-cuprates exhibiting the undoped (Ce-free) superconductivity are regarded as strongly correlated electron systems as well as the hole-doped SC cuprates. 
Not the simple band-metal state without the electron correlation <cit.> but both the doublon-holon model <cit.>, calculations using LDA with DMFT <cit.> and the two-particle self-consistent analysis <cit.> under the electron correlation would be able to explain the superconductivity in the undoped (Ce-free) and Ce-underdoped T'-cuprates.


 


The present transport and μSR results are able to be understood in terms of the electronic structure model based on the strong electron correlation.
The electronic structure models and schematic drawings of Cu spins and carriers in the CuO_2 plane are displayed in Figure <ref>a–c,e–g, .
In the hole-doped high-T_ c cuprates, the parent compounds are CT insulators as shown in Figure <ref>a characterized by the CT gap between UHB of the Cu 3d_x^2-y^2 orbital and O 2p band.
In the ideal undoped (Ce-free) T'-cuprates without excess oxygen shown in Figure <ref>c, on the other hand, the square-planar coordination of Cu and oxygen in the CuO_2 plane gives rise to a decrease in the Madelung energy of the Cu 3d orbitals compared with the octahedral coordination in the hole-doped cuprates. 
This brings about the lowering energy of UHB of the Cu 3d_x^2-y^2 orbital, leading to the mixing of UHB with the Zhang-Rice singlet band.
That is, the CT gap is collapsed, so that both mobile electrons and holes simultaneously emerge at the Fermi level in the parent compounds of the T'-cuprates, leading to the appearance of superconductivity without nominal doping of electrons by the Ce substitution.
This is plausible, because the calculation of the Madelung energy results in a decrease in the energy of the Cu 3d orbitals by ∼ 4 eV compared with the hole-doped cuprates with the CT gap ∼ 2 eV <cit.>. 
In the case of excess oxygen residing adjacent to the CuO_2 plane, assuming that two holes are produced in the CuO_2 plane by one excess oxygen, the doped holes in the CuO_2 plane tend to be localized near the excess oxygen due to the disorder of the electrostatic potential.
The holes are doped into the Cu 3d and O 2p orbitals taking into account the strong electron correlation. 
This is because the energy of the Cu 3d orbitals is raised by the excess oxygen due to increasing coordination number, as shown in Figure <ref>d.
The doped hole in the Cu 3d orbital resides not in LHB of the Cu 3d_x^2-y^2 orbital but in UHB of the Cu 3d_3z^2-r^2 orbital in order to gain the energy of the Zhang–Rice singlet of Cu 3d_x^2-y^2 (LHB) and O 2p spins.
This is reasonable, because the splitting of Cu 3d_x^2-y^2 and Cu 3d_3z^2-r^2 in energy is smaller than the Mott–Hubbard gap of ∼ 8 eV.
Accordingly, Cu 3d_3z^2-r^2 (LHB) free spins are probably induced at the Cu site adjacent to the excess oxygen.
Both hole and electron carriers tend to be localized because of the disorder of the electrostatic potential near the excess oxygen, resulting in the recovery of the AF order of Cu 3d_x^2-y^2 (LHB) spins.
This is able to explain the increase in ρ_ ab due to the strong localization and the hump of the temperature dependence of ρ_ c due to the opening of the AF pseudogap.



In the CuO_2 plane in the as-grown non-SC samples of La_1.8Eu_0.2CuO_4+δ and Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10, because of the moderate number of excess oxygen, carriers are strongly localized, as confirmed by ρ_ ab <cit.>, and the AF order is long-ranged, as illustrated in Figure <ref>e. 
In reduced SC La_1.8Eu_0.2CuO_4+δ, as shown in Figure <ref>f, the CuO_2 plane should be mostly covered by short-range magnetically ordered regions, and superconductivity should appear around the boundary between the short-range magnetically ordered regions.
In reduced SC Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10, because the amount of excess oxygen is smaller than that of reduced SC La_1.8Eu_0.2CuO_4+δ, the short-range magnetically ordered regions decrease in correspondence to the increase in the SC volume fraction, as shown in Figure <ref>g.
It is noted that the introduction of excess oxygen gives rise to free Cu spins of LHB of the Cu 3d_3z^2-r^2 orbital in the CuO_2 plane just around itself, leading to the occurrence of the Kondo effect as confirmed by ρ_ ab of reduced Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10 <cit.>.
Accordingly, it is suggested that the short-range magnetically ordered regions are formed around excess oxygen and superconductivity appears far from the excess oxygen. 

As mentioned above, the ARPES experiment of Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10 by  revealed that the AF pseudogap was closed on the whole Fermi surface, which is contrary to the former ARPES results in the T'-cuprates <cit.>.
Considering both results of ARPES without the AF pseudogap and μSR with the short-range magnetic order, it is likely that Cu spins forming the short-range magnetic order have tiny magnetic moments. 
That is, the reduction annealing gives rise to not only the change of the long-range AF order to the short-range one but also the reduction of the magnetic moments of Cu spins, which is compatible with the decrease in the internal magnetic field at the muon site estimated from μSR results <cit.>.






§ FUTURE ISSUES



The present transport and μSR results of the undoped (Ce-free) and Ce-underdoped T'-cuprates uncovered that the superconductivity appeared under the strong electron correlation as in the case of the hole-doped cuprates.
Here we discuss remaining unsolved issues of the T'-cuprates.

One is that the oxygen dynamics through the reduction annealing must be directly clarified.
To date, several candidates of effects of the reduction annealing have been proposed; the removal of excess oxygen at the apical site <cit.>, filling up Cu deficiencies <cit.>, etc.
Our crystal of Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10 seems to be the case of the reduction of excess oxygen.
Intriguing in our results is that the introduction of Cu vacancies into SC La_1.8Eu_0.2Cu_1-yO_4+δ does not change T_ c so much up to y=0.015 <cit.>, which seems to be incompatible with the Cu-deficiency model.
In any case, this issue would be clarified by the recent high resolution neutron and X-ray diffraction experiments. 
Another issue is about carriers in the undoped (Ce-free) SC T'-cuprates.
Our proposed electronic structure model indicates the presence of both electron and hole carriers, which is compatible with the present and former <cit.> Hall resistivity and NMR <cit.> results suggesting the existence of multiple carriers.
On the other hand, the ARPES results shown in Figure <ref> in Pr_1.3-xLa_0.7Ce_xCuO_4+δ with x=0.10 showed a hole-like Fermi surface without the AF pseudogap <cit.>.
This is probably explained by considering that the overlapping UHB of the Cu 3d_x^2-y^2 orbital and Zhang–Rice band form a mixing band in which both hole-like and electron-like carriers reside. 
The actual carrier concentration is also under debate.
It has been suggested from the Hall effect results <cit.>, etc. that the removal of excess oxygen does not simply correspond to the electron doping.
Intriguing is the estimation of the electron concentration from the Fermi-surface volume observed in ARPES that T_ c is unchanged in a wide electron concentration range in Pr_1.3-xLa_0.7Ce_xCuO_4+δ <cit.>.
On the contrary, very recent ARPES results in Pr_1-xLaCe_xCuO_4+δ revealed that T_ c exhibited a parabolic change against the electron concentration estimated from the Fermi-surface volume <cit.>. 

The hole doping into the parent compounds of the T'-cuprates is an interesting way to clarify the electronic structure.
Based on the proposed electronic structure model, the parent compounds of the T'-cuprates are no longer reference materials and T_ c might continue to increase with hole doping into the parent compounds.
Takamatsu et al. reported that the hole doping by the Sr/Ca substitution for La in La_1.8-xEu_0.2(Ca,Sr)_xCuO_4+δ results in the decrease in T_ c <cit.>.
As Zn/Ni impurity effects on T_ c in La_1.8Eu_0.2Cu_1-y(Zn,Ni)_yO_4+δ suggest that the electronic state of the parent compounds is similar to the overdoped regime of the hole-doped cuprates <cit.>, it may be natural that further hole doping results in the decrease in T_ c. 






Our works were done in collaboration with Yosuke Mori, Akira Takahashi, Takuya Konno, Taro Ohgi, Tomohisa Takamatsu, Kensuke M. Suzuki, Koki Ohashi, Malik Angelh Baqiya, Koshi Kurashima, Masatsune Kato, Isao Watanabe, Masanori Miyazaki, Akihiro Koda and Ryosuke Kadono. 
Our works were supported by JSPS KAKENHI Grant Number 23540399 and 23108004 and by Sophia University Special Grant for Academic Research.




mdpi

999


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