In high temperature cuprate superconductors, it was found that the superconducting transition temperature Tc depends on the number of CuO2 planes (n) in the structural unit and the maximum Tc is realized in the trilayer system (n=3). It was also found that the trilayer superconductors exhibit an unusual phase diagram that Tc keeps nearly constant in the overdoped region which is in strong contrast to the Tc decrease usually found in other cuprate superconductors. The electronic origin of the Tc maximization in the trilayer superconductors and its high Tc persistence in the overdoped region remains unclear. By taking high resolution laser-based angle resolved photoemission (ARPES) measurements, here we report our revelation of the microscopic origin of the unusual superconducting properties in the trilayer superconductors. For the first time we have observed the trilayer splitting in Bi2Sr2Ca2Cu3O10+d (Bi2223) superconductor. The observed Fermi surface, band structures, superconducting gap and the selective Bogoliubov band hybridizations can be well described by a three-layer interaction model. Quantitative information of the microscopic processes involving intra- and interlayer hoppings and pairings are extracted. The electronic origin of the maximum Tc in Bi2223 and the persistence of the high Tc in the overdoped region is revealed. These results provide key insights in understanding high Tc superconductivity and pave a way to further enhance Tc in the cuprate superconductors.
We use scanning tunneling microscopy to investigate Bi2Sr2Ca2Cu3O10+δ trilayer cuprates from the optimally doped to overdoped regime. We find that the two distinct superconducting gaps from the inner and outer CuO2 planes both decrease rapidly with doping, in sharp contrast to the nearly constant Tc. Spectroscopic imaging reveals the absence of quasiparticle interference in the antinodal region of overdoped samples, showing an opposite trend to that in single- and double-layer compounds. We propose that the existence of two types of inequivalent CuO2 planes and the intricate interaction betwee…
The proximity effect in a model manganite-cuprate system is investigated theoretically. We consider a situation in which spin-polarized electrons in manganite layers antiferromagnetically couple with electrons in cuprate layers as observed experimentally. The effect of the interfacial magnetic coupling is found to be much stronger than the injection of spin-polarized electrons into the cuprate region. As a result, the superconducting transition temperature depends on the thickness of the cuprate layer significantly. Since the magnetic coupling creates {\em negative} spin polarization, an appli…
Multilayered cuprates possess not only the highest superconducting temperature transition but also offer a unique platform to study disorder-free CuO$_2$ planes and the interplay between competing orders with superconductivity. Here, we study the underdoped trilayer cuprate HgBa$_2$Ca$_2$Cu$_3$O$_{8+ δ}$ and we report the first quantum oscillation and Hall effect measurements in magnetic field up to 88 T. A careful analysis of the complex spectra of quantum oscillations strongly supports the coexistence of an antiferromagnetic order in the inner plane and a charge order in the outer planes. Th…
The low-energy electronic structure of the trilayer cuprate superconductor Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+δ}$ near optimal doping is investigated by angle-resolved photoemission spectroscopy. The normal state quasiparticle dispersion and Fermi surface, and the superconducting d-wave gap and coherence peak are observed and compared with those of single and bilayer systems. We find that both the superconducting gap magnitude and the relative coherence-peak intensity scale linearly with $T_c$ for various optimally doped materials. This suggests that the higher $T_c$ of the trilayer system should …
Based on a hybrid interlayer coupling mechanism, we study the coexistence of superconductivity (SC) and antiferromagnetism (AFM) in trilayer cuprates. By introducing an interlayer magnetic scattering term, we solve the multilayer $t{-}J$ model with Josephson coupling under the framework of Gutzwiller projection. We show that both the SC and AFM orders in the multilayered system are enhanced and the range of AFM order is extended. The layer configuration of d-wave pairing gap and AFM order further plays an essential role in determining the interlayer magnetic and superconducting coupling phase …
Unique Charge-density-wave Order and Fluctuation-induced Phonon Softening in the Optimally-doped Trilayer Cuprate Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+δ}$
University of Hyogo（兵库大学）；National Institutes for Quantum Science and Technology (QST)（量子科学技术研究开发机构）；National Synchrotron Radiation Research Center（国家同步辐射研究中心）；Institute of Multidisciplinary Research for Advanced Materials (IMRAM), Tohoku University（东北大学先进物质多学科研究所）；University of Tokyo（东京大学）；National Institute of Advanced Industrial Science and Technology（产业技术综合研究所）
We report on an investigation of the redistribution of interlayer coherence in the trilayer cuprate Bi2Sr2Ca2Cu3O10. The experiment is performed under the same apical-oxygen phonon excitation discussed in the past for the bilayer cuprate YBa2Cu3O6.5. In Bi2Sr2Ca2Cu3O10, we observe a similar spectral weight loss at the transverse plasma mode resonance seen in YBa2Cu3O6.5. However, this feature is not accompanied by light-enhanced interlayer coherence that was seen in YBa2Cu3O6+x, for which the transverse plasma mode is observed at equilibrium even in the normal state. These new observations off…
Thermal Hall conductivity in the strongest cuprate superconductor: Estimate of the mean free path in the trilayer cuprate HgBa$_2$Ca$_2$Cu$_3$O$_{8 + δ}$
The recent discovery of superconductivity in hole-doped planar nickelates R1-xSrNiO2 (R=Pr,Nd) raises the foundational question of how the electronic structure and electronic correlations of these Ni1+ compounds compare to those of the Cu2+ cuprate superconductors. Here, we present an Angle-Resolved Photoemission Spectroscopy (ARPES) study of the trilayer nickelate Pr4Ni3O8, revealing an electronic structure and Fermi surface very similar to that of the hole-doped cuprates but with a few critical differences. Specifically, the main portions of the Fermi surface are extremely similar to that of…
We measure the magnetic susceptibility nearby Li spinless impurities in the superconducting phase of the high Tc cuprate YBaCuO. The induced moment which was found to exist above Tc persists below Tc. In the underdoped regime, it retains its Curie law below Tc. In contrast, near optimal doping, the large Kondo screening observed above Tc (T_K=135 K) is strongly reduced below Tc as expected theoretically when the superconducting gap develops. This moment still extends essentially on its 4 near neighbour Cu, showing the persistence of AF correlations in the superconducting state. A direct compar…
The discovery of superconductivity in Sr-doped NdNiO$_{2}$ is a crucial breakthrough in the long pursuit for nickel oxide materials with electronic and magnetic properties similar to those of the cuprates. NdNiO$_2$ is the infinite-layer member of a family of square-planar nickelates with general chemical formula R$_{n+1}$Ni$_n$O$_{2n+2}$ (R = La, Pr, Nd, $n= 2, 3, ... \infty$). In this letter, we investigate superconductivity in the trilayer member of this series (R$_4$Ni$_3$O$_8$) using a combination of first-principles and $t-J$ model calculations. R$_4$Ni$_3$O$_8$ compounds resemble cuprat…
Doping Evolution of Nodal Electron Dynamics in Trilayer Cuprate Superconductor Bi$_2$Sr$_2$Ca$_2$Cu$_3$O$_{10+δ}$ Revealed by Laser-Based Angle-Resolved Photoemission Spectroscopy
The nature of the spin excitations in superconducting cuprates is a key question toward a unified understanding of the cuprate physics from long-range antiferromagnetism to superconductivity. The intense spin excitations up to the over-doped regime revealed by resonant inelastic X-ray scattering bring new insights as well as questions like how to understand their persistence or their relation to the collective excitations in ordered magnets (magnons). Here, we study the evolution of the spin excitations upon hole-doping the superconducting cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ by disentangling…
We report on results of our analysis of published experimental data of the in-plane infrared response of two representative underdoped high-$T_{\mathrm{c}}$ cuprate superconductors, focusing on a characteristic gap feature in the spectra of the real part of the conductivity and the corresponding structures of the memory function, that develop below a temperature $T^{\mathrm{ons}}$ considerably higher than $T_{\mathrm{c}}$. Several arguments based on comparisons of the data with results of our calculations are provided indicating that the features are due to superconductivity and that $T^{\math…
The race to obtain a higher critical temperature (Tc) in the superconducting cuprates has been virtually suspended since it was optimized under high pressure in a hole-doped trilayer cuprate. We report the anomalous increase in Tc under high pressure for the electron-doped infinite-layer cuprate Sr0.9La0.1CuO2 in the vicinity of the antiferromagnetic critical point. By the application of a pressure of 15 GPa, Tc increases to 45 K, which is the highest temperature among the electron-doped cuprates and ensures unconventional superconductivity. We describe the electronic phase diagram of Sr1-xLax…
We study electronic states of multilayer cuprates in the normal phases as functions of the number of CuO_2 planes and the doping rate. The resonating valence bond wave function and the Gutzwiller approximation are used for a two-dimensional multilayer t-t'-t''-J model. We calculate the electron-removal spectral functions at (π,0) in the CuO_2 plane next to the surface to understand the angle-resolved photoemission spectroscopy (ARPES) spectra. We find that the trilayer spectrum is narrower than the bilayer spectrum but is wider than the monolayer spectrum. In the tri- and tetralayer systems, t…
We present results of a systematic study of the c axis lattice dynamics in single layer Bi2Sr2CuO6 (Bi2201), bilayer Bi2Sr2CaCu2O8 (Bi2212) and trilayer Bi2Sr2Ca2Cu3O10 (Bi2223) cuprate superconductors. Our study is based on both experimental data obtained by spectral ellipsometry on single crystals and theoretical calculations. The calculations are carried out within the framework of a classical shell model, which includes long-range Coulomb interactions and short-range interactions of the Buckingham form in a system of polarizable ions. Using the same set of the shell model parameters for Bi…
We report resonant electronic Raman scattering in optimally doped single layer HgBa$_2$CuO$_{4+δ}$ (Hg-1201) and trilayer HgBa$_2$Ca$_2$Cu$_3$O$_{8+δ}$ (Hg-1223) single crystals. Analysis of the $B_{1g}$ and B$_{2g}$ channels in the superconducting state of Hg-1201 advocates for a gap having d-wave symmetry. In addition a resonant study $B_{1g}$ pair-breaking peak and the $A_{1g}$ peak suggests that the $A_{1g}$ peak is not directly related to the d-wave superconducting gap amplitude. Comparison with trilayer Hg-1223 demonstrates the universal behavior of this two energy scales in optimally do…
We present an extension of the model proposed recently to account for dramatic changes below Tc (anomalies) of some c-axis polarized infrared-active phonons in bilayer cuprate superconductors, that applies to trilayer high-Tc compounds. We discuss several types of phonon anomalies that can occur in these systems and demonstrate that our model is capable of explaining the spectral changes occurring upon entering the superconducting state in the trilayer compound Tl2Ba2Ca2Cu3O10. The low-temperature spectra of this compound obtained by Zetterer and coworkers display an additional broad absorptio…
We report a detailed inelastic neutron scattering study of the collective magnetic excitations of overdoped superconducting La1.78Sr0.22CuO4 for the energy range 0-160 meV. Our measurements show that overdoping suppresses the strong response present for optimally doped La2-xSrxCuO4 which is peaked near 50 meV. The remaining response is peaked at incommensurate wavevectors for all energies investigated. We observe a strong high-frequency magnetic response for E >= 80 meV suggesting that significant antiferromagnetic exchange couplings persist well into the overdoped part of the cuprate phase di…
Electronic structure and magnetic tendencies of trilayer La$_4$Ni$_3$O$_{10}$ under pressure: structural transition, molecular orbitals, and layer differentiation
We explore the layered palladium oxides La$_2$PdO$_4$, LaPdO$_2$ and La$_4$Pd$_3$O$_8$ via ab initio calculations. La$_2$PdO$_4$, being low spin $d^8$, is quite different from its high spin nickel analog. Hypothetical LaPdO$_2$, despite its $d^9$ configuration, has a paramagnetic electronic structure very different from cuprates. On the other hand, the hypothetical trilayer compound La$_4$Pd$_3$O$_8$ ($d^{8.67}$) is more promising in that its paramagnetic electronic structure is very similar to that of overdoped cuprates. But even in the $d^9$ limit (achieved by partial substitution of La with…
To elucidate the superconductor to metal transition at the end of superconducting dome, the overdoped regime has stepped onto the center stage of cuprate research recently. Here, we use scanning tunneling microscopy to investigate the atomic-scale electronic structure of overdoped trilayer Bi-2223 and bilayer Bi-2212 cuprates. At low energies the spectroscopic maps are well described by dispersive quasiparticle interference patterns. However, as the bias increases to the superconducting coherence peak energy, a virtually non-dispersive pattern with sqrt(2)*sqrt(2) periodicity emerges. Remarkab…
Citing the disappearance of a sharp peak in the electron self-energy, extracted from optics and angle-resolved photoemission spectroscopy (ARPES) experiments in deeply over-doped copper-oxide superconductors with Tc of 55-60K, Hwang, Timusk et al. argue that sharp modes, be they phononic or magnetic in origin, are not important for superconductivity in the cuprates. If true, this would have been an important progress. We show, however, their conclusions are unfounded because of the insensitivity of the optics experiment in studying strongly anisotropic material like the cuprates, and a misrepr…
This thesis presents a systematic study of magnetotransport and magnetic ordering in manganite-high T$_c$ cuprate spin valve structures. YBa$_{2}$Cu$_{3}$O$_{7}$ - La$_{2 / 3}$Sr$_{1 / 3}$MnO$_{3}$ heterostructures of (110) orientation are grown to allow direct injection of spin polarized holes from the La$_{2 / 3}$Sr$_{1 / 3}$MnO$_{3}$ (LSMO) into the CuO$_2$ superconducting planes of the YBa$_{2}$Cu$_{3}$O$_{7}$ (YBCO). Galvanomagnetic studies on the LSMO-YBCO-LSMO trilayers reveal unusually high AMR ($\sim$72000%) on rotating the field in the plane of the heterostructure whose magnetic grou…
We report measurements of the anisotropy of the spin echo decay for the inner layer Cu site of the triple layer cuprate, Hg_0.8Re_0.2Ba_2Ca_2Cu_3O_8 (T_c=126 K) in the pseudogap T regime below T_pg ~ 170 K and the corresponding analysis for their interpretation. As the field alignment is varied, the shape of the decay curve changes from Gaussian (H_0 \parallel c) to single exponential (H_0 \perp c). The latter characterizes the decay caused by the fluctuations of adjacent Cu nuclear spins caused by their interactions with electron spins. The angular dependence of the second moment (T_{2M}^{-2}…
The highest superconducting transition temperatures in the cuprates are achieved in bilayer and trilayer systems, highlighting the importance of intralayer interactions for high Tc. It has been argued that interlayer hybridization vanishes along the nodal directions by way of a specific pattern of orbital overlap. Recent quantum oscillation measurements in bilayer cuprates have provided evidence for a residual bilayer-splitting at the nodes that is sufficiently small to enable magnetic breakdown tunneling at the nodes. Here we show that several key features of the experimental data can be unde…
Although iron-based superconductors are multi-orbital systems with complicated band structures, we demonstrate that the low energy physics which is responsible for high-$T_c$ superconductivity is essentially governed by one effective Hamiltonianwith two almost decoupled orbitals near half filling. This underlining electronic structure is protected by the $S_4$ symmetry. With repulsive or strong next nearest neighbor antiferromagnetic exchange interactions, each single-orbital effective Hamiltonian results in a robust $A_{1g}$ s-wave pairing which can be exactly mapped to the d-wave pairing obs…
Particle-hole symmetry in the pseudogap phase of moderately underdoped cuprate high temperature superconductors evidenced from joint density of states analysis
The superconductivity precursor phenomena in high temperature cuprate superconductors was studied by direct measurements of superconducting condensate with the use of the $c$-axis optical conductivity of YBa$_{2}$(Cu$_{1-x}$Zn$_{x}$)$_{3}$O$_{y}$ for several doping levels ($p$) as well as for several Zn-concentrations. Both of the real and imaginary part of the optical conductivity clearly showed that the superconducting carriers persist up to the high temperatures $T$$_{p}$ that is higher than the critical temperature $T$$_{c}$ but lower than the pseudogap temperature $T$$^{\ast}$. $T$$_{p}$ …
Empirical evidence in heavy fermion, pnictide, and other systems suggests that unconventional superconductivity appears associated to some form of real-space electronic order. For the cuprates, despite several proposals, the emergence of order in the phase diagram between the commensurate antiferromagnetic state and the superconducting state is not well understood. Here we show that in this regime doped holes assemble in "electronic polymers." Within a Monte Carlo study we find, that in clean systems by lowering the temperature the polymer melt condenses first in a smectic state and then in a …
Alkali-fulleride superconductors with a maximum critical temperature Tc of 40 K exhibit similar electronic phase diagram with unconventional high-Tc superconductors where the superconductivity resides proximate to a magnetic Mott-insulating state. However, distinct from cuprate compounds, which superconduct through two-dimensional (2D) CuO2 planes, alkali fullerides are attributed to the three-dimensional (3D) members of high-Tc family. Here, we employ scanning tunneling microscopy to show that trilayer K3C60 displays fully gapped strong coupling s-wave superconductivity that coexists spatiall…
The electron-doped cuprates Pr_{2-x}Ce_xCuO_4 and Nd_{2-x}Ce_xCuO_4 have been studied by electronic Raman spectroscopy across the entire region of the superconducting (SC) phase diagram. The SC pairing strength is found to be consistent with a weak-coupling regime except in the under-doped region where we observe an in-gap collective mode at 4.5 k_{B}T_c while the maximum amplitude of the SC gap is ~8 k_{B}T_{c}. In the normal state, doped carriers divide into coherent quasi-particles (QPs) and carriers that remain incoherent. The coherent QPs mainly reside in the vicinity of (π/2, π/2) region…
The observation of a strong nonlinear diamagnetic signal well above T_c in several cuprate superconductors constitutes clear evidence of the persistence of local superconducting correlations.
We performed an experimental study of the temperature and doping dependence of the energy-loss function of the bilayer and trilayer Bi-cuprate family. The primary aim is to obtain information on the energy stored in the Coulomb interaction between the conduction electrons, on the temperature dependence thereof, and on the change of Coulomb interaction when Cooper-pairs are formed. We performed temperature-dependent ellipsometry measurements on several Bi$_2$Sr$_2$CaCu$_2$O$_{8-x}$ single crystals: under-doped with $T_c=60, 70$ and 83K, optimally doped with $T_c=91$K, overdoped with $T_c=84, 81…
Bi-based cuprate superconductors are important materials for both fundamental research and applications. As in other cuprates, the superconducting phase in the Bi compounds lies close to an antiferromagnetic phase. Our density functional theory calculations based on the strongly-constrained-and-appropriately-normed (SCAN) exchange correlation functional in Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ reveal the persistence of magnetic moments on the copper ions for oxygen concentrations ranging from the pristine phase to the optimally hole-doped compound. We also find the existence of ferrimagnetic solutions…
One of the most intensely studied scenarios of high-temperature superconductivity (HTS) postulates pairing by exchange of magnetic excitations [1]. Indeed, such excitations have been observed up to around optimal doping in the cuprates [2-7]. In the heavily overdoped regime neutron scattering measurements indicate that magnetic excitations have effectively disappeared [8-10], and this was argued to cause the demise of HTS with overdoping [1, 8, 10]. Here we use resonant inelastic x-ray scattering (RIXS), which is sensitive to complementary parts of reciprocal space, to measure the evolution of…
Theoretical analysis on the possibility of superconductivity in a trilayer Ruddlesden-Popper nickelate La$_4$Ni$_3$O$_{10}$ under pressure and its experimental examination: comparison with La$_3$Ni$_2$O$_7$
One of the most striking universal properties of the high-transition-temperature (high-$T_c$) superconductors is that they are all derived from the hole-doping of their insulating antiferromagnetic (AF) parent compounds. From the outset, the intimate relationship between magnetism and superconductivity in these copper-oxides has intrigued researchers. Evidence for this link comes from neutron scattering experiments that show the unambiguous presence of short-range AF correlations (excitations) in cuprate superconductors. Even so, the role of such excitations in the pairing mechanism and superc…
We survey recent experimental results including quantum oscillations and complementary measurements probing the electronic structure of underdoped cuprates, and theoretical proposals to explain them. We discuss quantum oscillations measured at high magnetic fields in the underdoped cuprates that reveal a small Fermi surface section comprising quasiparticles that obey Fermi-Dirac statistics, unaccompanied by other states of comparable thermodynamic mass at the Fermi level. The location of the observed Fermi surface section at the nodes is indicated by a body of evidence including the collapse i…
To investigate the origin of the enhanced $T_c$ ($\approx$ 110 K) of the trilayer cuprate superconductor Bi$_{2}$Sr$_{2}$Ca$_{2}$Cu$_{3}$O$_{10+δ}$ (Bi-2223), we have performed systematic magnetoresistance (MR) measurements on this superconductor, as well as on the bilayer superconductor, Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ (Bi-2212). The in-plane coherence length, $ξ_{ab}$, and the specific-heat jump, $ΔC$, have been estimated using the theory of renormalized superconductive fluctuations, and the doping dependence of these parameters has been qualitatively explained using the Fermi arc approa…
Motivated by the premise that superconductivity in iron-based superconductors is unconventional and mediated by spin fluctuations, an intense research effort has been focused on characterizing the spin excitation spectrum in the magnetically ordered parent phases of the Fe-pnictides2,3 and - chalcogenides4. For these undoped materials it is well-established that the spin excitation spectrum consists of a sharp, highly dispersive magnon spanning an energy range of up to 200 meV (ref. 3). The fate of these high-energy magnetic modes upon sizable doping is hitherto unresolved. Using resonant inel…
