89Y NMR evidence for a fermi-liquid behavior in YBa2Cu3O6+x

Analogies of phonon anomalies and electronic gap features in the infrared response of Sr14-xCaxCu24O41and underdoped YBa2Cu3O6+x

We present an experimental and theoretical study which compares the phonon anomalies and the electronic gap features in the infrared response of the weakly coupled two-leg-ladders in Sr14-xCa_xCu₂₄O₄₁(SCCO) with those of the underdoped high-T_csuperconductor YBa₂Cu₃O6+x(YBCO) and thereby reveals some surprising analogies. Specifically, we present a phenomenological model that describes the anomalous doping- and temperature-dependence of some of the phonon features in thea-axis response (field along the rungs of the ladders) of SCCO. It assumes that the phonons are coupled to charge oscillations within the ladders. Their changes with decreasing temperature reveal the formation of a crystal (density wave) of hole pairs that are oriented along the rungs. We also discuss the analogy to a similar model that was previously used to explain the phonon anomalies and an electronic plasma mode in thec-axis response (field perpendicular to the CuO₂planes) of YBCO. We further confirm that an insulator-like pseudogap develops in thea-axis conductivity of SCCO which closely resembles that in thec-axis conductivity of YBCO. Most surprisingly, we find that thec-axis conductivity (field along the legs of the ladders) of SCCO is strikingly similar to the in-plane one (field parallel to the CuO₂planes) of YBCO. Notably, in both cases a dip feature develops in the normal state spectra that is connected with a spectral weight shift toward low frequencies and can thus be associated with precursor superconducting pairing correlations that are lacking macroscopic phase coherence. This SCCO-YBCO analogy indicates that collective degrees of freedom contribute to the low-energy response of underdoped highT_ccuprates and it even suggests that the charges in the CuO₂planes tend to segregate forming quasi-one-dimensional structures similar to the two-leg ladders, as predicted for the stripe-scenario or certain intertwinned states.

Pseudogap formation due to charge-transfer transition and Kondo effect

We investigate the doping evolution of the electronic state of the three-bandt-J-Umodel considering the normal state of the hole-doped high-Tcsuperconducting cuprate. In our model, when some number of holes are doped into the undoped state, thedelectron exhibits the charge-transfer (CT)-type Mott-Hubbard transition along with a chemical potential jump. A reduced CT gap is formed from thepband and the coherent component of thedband, and it shrinks due to charge fluctuations as more holes are doped as in the pseudogap (PG) phenomenon. This trend is reinforced as thed-pband hybridization is increased, and a Fermi liquid state is retrieved as in the Kondo effect. These suggest that the PG in the hole-doped cuprate emerges due to the CT transition and the Kondo effect.

The magnetic field driven superconductor-metal transition in disordered hole-overdoped cuprates

By solving the Bogoliubov-de Gennes equations for ad-wave superconductor, we explore how the interplay between disorder and the orbital depairing of an external magnetic field influences the superconductor-metal transition of the hole-overdoped cuprates. For highly disordered systems, we find granular Cooper paring to persist above the critical field where the superfluid stiffness goes to zero. We also show that because the vortices are attracted to regions where the superconducting pairing is already weak, the Caroli-de Gennes-Matricon zero-bias peak in the local density of states at the vortex cores disappears already at moderate disorder.

Pseudogap in underdoped cuprate seen in longitudinal magnetoresistance

We report the results of in-plane magnetotransport study of slightly underdoped cuprate La_1.85Sr_0.15CuO₄(LSCO15) with Ni impurity. Increasing Ni contentycauses a sharp drop in longitudinal magnetoresistance (LMR) in LSCO15 to broaden and move towards higher temperatures. TemperatureTmLMR(y)of this local maximum in LMR coincides with temperatureTdev(y), below which ideal resistivity from the parallel-resistor model deviates from itsT²-dependence. A direct comparison with the hole doping evolution of pseudogap (PG) in La2-xSr_xCuO₄(LSCO), possible through the mobile-carrier concentration extracted from the thermopower measurements, allows to equate both characteristic temperaturesTmLMR≅Tdevwith PG opening temperatureT∗. The rate of PG closing by magnetic field parallel to the CuO₂plane, in measurements up to 9 T, is consistent with spin-paramagnetic effect in this configuration and yields PG closing fieldB_pcclose to the second critical fieldBc2predicted for superconducting gap with the help of Werthamer-Helfand-Hohenberg theory. The field anisotropy ofB_pcsuggests that orbital degrees of freedom also play a role in PG formation.

Magic Gap Ratio for Optimally Robust Fermionic Condensation and Its Implications for High-T_{c} Superconductivity

Bardeen-Schrieffer-Cooper (BCS) and Bose-Einstein condensation (BEC) occur at opposite limits of a continuum of pairing interaction strength between fermions. A crossover between these limits is readily observed in a cold atomic Fermi gas. Whether it occurs in other systems such as the high temperature superconducting cuprates has remained an open question. We uncover here unambiguous evidence for a BCS-BEC crossover in the cuprates by identifying a universal magic gap ratio 2Δ/k_{B}T_{c}≈6.5 (where Δ is the pairing gap and T_{c} is the transition temperature) at which paired fermion condensates become optimally robust. At this gap ratio, corresponding to the unitary point in a cold atomic Fermi gas, the measured condensate fraction N_{0} and the height of the jump δγ(T_{c}) in the coefficient γ of the fermionic specific heat at T_{c} are strongly peaked. In the cuprates, δγ(T_{c}) is peaked at this gap ratio when Δ corresponds to the antinodal spectroscopic gap, thus reinforcing its interpretation as the pairing gap. We find the peak in δγ(T_{c}) also to coincide with a normal state maximum in γ, which is indicative of a pairing fluctuation pseudogap above T_{c}.

High-T c Cuprates: a Story of Two Electronic Subsystems

A review of the phenomenology and microscopy of cuprate superconductors is presented, with particular attention to universal conductance features, which reveal the existence of two electronic subsystems. The overall electronic system consists of 1 + p charges, where p is the doping. At low dopings, exactly one hole is localized per planar copper-oxygen unit, while upon increasing doping and temperature, the hole is gradually delocalized and becomes itinerant. Remarkably, the itinerant holes exhibit identical Fermi liquid character across the cuprate phase diagram. This universality enables a simple count of carrier density and yields comprehensive understanding of the key features in the normal and superconducting state. A possible superconducting mechanism is presented, compatible with the key experimental facts. The base of this mechanism is the interaction of fast Fermi liquid carriers with localized holes. A change in the microscopic nature of chemical bonding in the copper oxide planes, from ionic to covalent, is invoked to explain the phase diagram of these fascinating compounds.

Scattering interference signature of a pair density wave state in the cuprate pseudogap phase

An unidentified quantum fluid designated the pseudogap (PG) phase is produced by electron-density depletion in the CuO2 antiferromagnetic insulator. Current theories suggest that the PG phase may be a pair density wave (PDW) state characterized by a spatially modulating density of electron pairs. Such a state should exhibit a periodically modulating energy gap [Formula: see text] in real-space, and a characteristic quasiparticle scattering interference (QPI) signature [Formula: see text] in wavevector space. By studying strongly underdoped Bi2Sr2CaDyCu2O8 at hole-density ~0.08 in the superconductive phase, we detect the 8a0-periodic [Formula: see text] modulations signifying a PDW coexisting with superconductivity. Then, by visualizing the temperature dependence of this electronic structure from the superconducting into the pseudogap phase, we find the evolution of the scattering interference signature [Formula: see text] that is predicted specifically for the temperature dependence of an 8a0-periodic PDW. These observations are consistent with theory for the transition from a PDW state coexisting with d-wave superconductivity to a pure PDW state in the Bi2Sr2CaDyCu2O8 pseudogap phase.

Intrinsic Spin Susceptibility and Pseudogaplike Behavior in Infinite-Layer LaNiO_{2}

The recent discovery of superconductivity in doped infinite-layer nickelates has stimulated intensive interest, especially for similarities and differences compared to that in cuprate superconductors. In contrast to cuprates, although earlier magnetization measurement reveals a Curie-Weiss-like behavior in undoped infinite-layer nickelates, there is no magnetic ordering observed by elastic neutron scattering down to liquid helium temperature. Until now, the nature of the magnetic ground state in undoped infinite-layer nickelates was still elusive. Here, we perform a nuclear magnetic resonance (NMR) experiment through ^{139}La nuclei to study the intrinsic spin susceptibility of infinite-layer LaNiO_{2}. First, the signature for magnetic ordering or freezing is absent in the ^{139}La NMR spectrum down to 0.24 K, which unambiguously confirms a paramagnetic ground state in LaNiO_{2}. Second, a pseudogaplike behavior instead of Curie-Weiss-like behavior is observed in both the temperature-dependent Knight shift and nuclear spin-lattice relaxation rate (1/T_{1}), which is widely observed in both underdoped cuprates and iron-based superconductors. Furthermore, the scaling behavior between the Knight shift and 1/T_{1}T has also been discussed. Finally, the present results imply a considerable exchange interaction in infinite-layer nickelates, which sets a strong constraint for the proposed theoretical models.

Field-dependent specific heat of the canonical underdoped cuprate superconductor [Formula: see text]

The cuprate superconductor [Formula: see text], in comparison with most other cuprates, has a stable stoichiometry, is largely free of defects and may be regarded as the canonical underdoped cuprate, displaying marked pseudogap behaviour and an associated distinct weakening of superconducting properties. This cuprate 'pseudogap' manifests as a partial gap in the electronic density of states at the Fermi level and is observed in most spectroscopic properties. After several decades of intensive study it is widely believed that the pseudogap closes, mean-field like, near a characteristic temperature, [Formula: see text], which rises with decreasing hole concentration, p. Here, we report extensive field-dependent electronic specific heat studies on [Formula: see text] up to an unprecedented 400 K and show unequivocally that the pseudogap never closes, remaining open to at least 400 K where [Formula: see text] is typically presumed to be about 150 K. We show from the NMR Knight shift and the electronic entropy that the Wilson ratio is numerically consistent with a weakly-interacting Fermion system for the near-nodal states. And, from the field-dependent specific heat, we characterise the impact of fluctuations and impurity scattering on the thermodynamic properties.

Temperature-Independent Cuprate Pseudogap from Planar Oxygen NMR

Planar oxygen nuclear magnetic resonance (NMR) relaxation and shift data from all cuprate superconductors available in the literature are analyzed. They reveal a temperature-independent pseudogap at the Fermi surface, which increases with decreasing doping in family-specific ways, i.e., for some materials, the pseudogap is substantial at optimal doping while for others it is nearly closed at optimal doping. The states above the pseudogap, or in its absence are similar for all cuprates and doping levels, and Fermi liquid-like. If the pseudogap is assumed exponential it can be as large as about 1500 K for the most underdoped systems, relating it to the exchange coupling. The pseudogap can vary substantially throughout a material, being the cause of cuprate inhomogeneity in terms of charge and spin, so consequences for the NMR analyses are discussed. This pseudogap appears to be in agreement with the specific heat data measured for the YBaCuO family of materials, long ago. Nuclear relaxation and shift show deviations from this scenario near Tc, possibly due to other in-gap states.

Preformed Cooper Pairs in Layered FeSe-Based Superconductors

Superconductivity arises from two distinct quantum phenomena: electron pairing and long-range phase coherence. In conventional superconductors, the two quantum phenomena generally take place simultaneously, while in the underdoped high- T_{c} cuprate superconductors, the electron pairing occurs at higher temperature than the long-range phase coherence. Recently, whether electron pairing is also prior to long-range phase coherence in single-layer FeSe film on SrTiO_{3} substrate is under debate. Here, by measuring Knight shift and nuclear spin-lattice relaxation rate, we unambiguously reveal a pseudogap behavior below T_{p}∼60  K in two kinds of layered FeSe-based superconductors with quasi2D nature. In the pseudogap regime, a weak diamagnetic signal and a remarkable Nernst effect are also observed, which indicates that the observed pseudogap behavior is related to superconducting fluctuations. These works confirm that strong phase fluctuation is an important character in the 2D iron-based superconductors as widely observed in high-T_{c} cuprate superconductors.

Peculiarities of pseudogap in Y0.95Pr0.05Ba2Cu3O7-δ single crystals under pressure up to 1.7 GPa

The effect of hydrostatic pressure up to P = 1.7 GPa on the fluctuation conductivity σ'(T) and pseudogap ∆*(T) in Y0.95Pr0.05Ba2Cu3O7-δ single crystal with critical temperature Тс = 85.2 K (at P = 0) was investigated. The application of pressure leads to the increase in Tc with dTc/dP = +1.82 K∙GPa-1 while the resistance decreases as dlnρ(100 K)/dP = -(10.5 ± 0.2) %∙GPa-1. Regardless of the pressure, in the temperature interval from Tc to T0 (~88 K at P = 0) the behaviour of σ'(T) is well described by the Aslamazov - Larkin (AL - 3D) fluctuation theory, and above the T0 by the Lawrence - Doniach theory (LD). The Maki-Thompson (MT - 2D) fluctuation contribution is not observed. This indicates the presence of structural defects in the sample induced by Pr. Here it is determined for the first time that when the pressure is applied to the Y1-xPrxBa2Cu3O7-δ single crystal, the pseudogap increases as dlnΔ*/dP = 0.17 GPa-1.

Anomalies in the pseudogap phase of the cuprates: competing ground states and the role of umklapp scattering

Over the past two decades, advances in computational algorithms have revealed a curious property of the two-dimensional Hubbard model (and related theories) with hole doping: the presence of close-in-energy competing ground states that display very different physical properties. On the one hand, there is a complicated state exhibiting intertwined spin, charge, and pair density wave orders. We call this 'type A'. On the other hand, there is a uniform d-wave superconducting state that we denote as 'type B'. We advocate, with the support of both microscopic theoretical calculations and experimental data, dividing the high-temperature cuprate superconductors into two corresponding families, whose properties reflect either the type A or type B ground states at low temperatures. We review the anomalous properties of the pseudogap phase that led us to this picture, and present a modern perspective on the role that umklapp scattering plays in these phenomena in the type B materials. This reflects a consistent framework that has emerged over the last decade, in which Mott correlations at weak coupling drive the formation of the pseudogap. We discuss this development, recent theory and experiments, and open issues.

Spectral functions of Sr2IrO4: theory versus experiment

The spin-orbit Mott insulator Sr₂IrO₄ has attracted a lot of interest in recent years from theory and experiment due to its close connection to isostructural high-temperature copper oxide superconductors. Despite not being superconductive, its spectral features closely resemble those of the cuprates, including Fermi surface and pseudogap properties. In this article, we review and extend recent work in the theoretical description of the spectral function of pure and electron-doped Sr₂IrO₄ based on a cluster extension of dynamical mean-field theory ('oriented-cluster DMFT') and compare it to available angle-resolved photoemission data. Current theories provide surprisingly good agreement for pure and electron-doped Sr₂IrO₄, both in the paramagnetic and antiferromagnetic phases. Most notably, one obtains simple explanations for the experimentally observed steep feature around the M point and the pseudo-gap-like spectral feature in electron-doped Sr₂IrO₄.

Tc and Other Cuprate Properties in Relation to Planar Charges as Measured by NMR

Nuclear magnetic resonance (NMR) in cuprate research is a prominent bulk local probe of magnetic properties. NMR also, as was shown over the last years, actually provides a quantitative measure of local charges in the CuO 2 plane. This has led to fundamental insights, e.g., that the maximum T c is determined by the sharing of the parent planar hole between Cu and O. Using bonding orbital hole contents on planar Cu and O measured by NMR, instead of the total doping x, the thus defined two-dimensional cuprate phase diagram reveals significant differences between the various cuprate materials. Even more importantly, the reflected differences in material chemistry appear to set a number of electronic properties as we discuss here, for undoped, underdoped and optimally doped cuprates. These relations should advise attempts at a theoretical understanding of cuprate physics as well as inspire material chemists towards new high- T c materials. Probing planar charges, NMR is also sensitive to charge variations or ordering phenomena in the CuO 2 plane. Thereby, local charge order on planar O in optimally doped YBCO could recently be proven. Charge density variations seen by NMR in both planar bonding orbitals with amplitudes between 1% to 5% appear to be omnipresent in the doped CuO 2 plane, i.e., not limited to underdoped cuprates and low temperatures.

Effect of annealing on a pseudogap state in untwinned YBa2Cu3O7-δ single crystals

The effect of annealing both in the oxygen atmosphere and at room temperatures on physical properties such as the pseudogap (Δ*(T)) and excess conductivity (σ'(T)) of untwined YBa2Cu3O7-δ (YBCO) single crystal with a small deviation from oxygen stoichiometry is studied. It was revealed that as the charge carrier density, nf, increases, Тс also slightly increases, whereas the temperature of the pseudogap opening, T*, decreases noticeably, which is consistent with the phase diagram (PD) of cuprates. The excess conductivity in the vicinity of Tc is represented by the Aslamazov-Larkin and Hikami-Larkin fluctuation theories, illustrating the three-dimensional to two-dimensional (i.e. 3D-2D) crossover with an increase in temperature. The crossover temperature T0 determines the coherence length along the c axis is ξc(0) = 0.86 Å, that is 2.6 times larger than for optimally doped YBCO single crystals with defects. Taking into account the short coherence length in high-temperature superconductors, in the model of free charge carriers the phase relaxation time of fluctuating Cooper pairs is determined, τφ (100 K) = (4.55 ± 0.4) · 10-13 s, which is slightly (1.2 times) larger than in well-structured YBCO films, and as in films, does not depend on nf. It is shown that Δ*(T) at different annealing stages practically does not change its shape. As in the well-structured YBCO films, Δ*(T) demonstrates maximum at Tpair~124 K which depends weakly on nf. However, the maximum value of Δ*(Tpair) increases with increasing nf, as it follows from the PD of cuprates. Comparing the experimental data with the Peters-Bauer theory we estimated the density of local pairs ≈ 0.3 near Tc that is a common value for high-temperature superconductors.

Electrically controlled nuclear polarization of individual atoms

Nuclear spins serve as sensitive probes in chemistry¹ and materials science² and are promising candidates for quantum information processing^3-6. NMR, the resonant control of nuclear spins, is a powerful tool for probing local magnetic environments in condensed matter systems, which range from magnetic ordering in high-temperature superconductors^7,8 and spin liquids⁹ to quantum magnetism in nanomagnets^10,11. Increasing the sensitivity of NMR to the single-atom scale is challenging as it requires a strong polarization of nuclear spins, well in excess of the low polarizations obtained at thermal equilibrium, as well as driving and detecting them individually^4,5,12. Strong nuclear spin polarization, known as hyperpolarization, can be achieved through hyperfine coupling with electron spins². The fundamental mechanism is the conservation of angular momentum: an electron spin flips and a nuclear spin flops. The nuclear hyperpolarization enables applications such as in vivo magnetic resonance imaging using nanoparticles¹³, and is harnessed for spin-based quantum information processing in quantum dots¹⁴ and doped silicon^15-17. Here we polarize the nuclear spins of individual copper atoms on a surface using a spin-polarized current in a scanning tunnelling microscope. By employing the electron-nuclear flip-flop hyperfine interaction, the spin angular momentum is transferred from tunnelling electrons to the nucleus of individual Cu atoms. The direction and magnitude of the nuclear polarization is controlled by the direction and amplitude of the current. The nuclear polarization permits the detection of the NMR of individual Cu atoms, which is used to sense the local magnetic environment of the Cu electron spin.

Origin of the Fermi arcs in cuprates: a dual role of quasiparticle and pair excitations

Angle resolved photoemission spectroscopy (ARPES) mesurements in cuprates have given key information on the temperature and angle dependence of the gap (d-wave order parameter, Fermi arcs and pseudogap). We show that these features can be understood in terms of a Bose condensation of interacting pairons (preformed hole pairs which form in their local antiferromagnetic environment). Starting from the basic properties of the pairon wavefunction, we derive the corresponding k-space spectral function. The latter explains the variation of the ARPES spectra as a function of temperature and angle up to T ^*, the onset temperature of pairon formation. While Bose excitations dominate at the antinode, the fermion excitations dominate around the nodal direction, giving rise to the Fermi arcs at finite temperature. This dual role is the key feature distinguishing cuprate from conventional superconductivity.

Pseudo-spin skyrmions in the phase diagram of cuprate superconductors

Topological states of matter are at the root of some of the most fascinating phenomena in condensed matter physics. Here we argue that skyrmions in the pseudo-spin space related to an emerging SU(2) symmetry enlighten many mysterious properties of the pseudogap phase in under-doped cuprates. We detail the role of the SU(2) symmetry in controlling the phase diagram of the cuprates, in particular how a cascade of phase transitions explains the arising of the pseudogap, superconducting and charge modulation phases seen at low temperature. We specify the structure of the charge modulations inside the vortex core below T _c, as well as in a wide temperature region above T _c, which is a signature of the skyrmion topological structure. We argue that the underlying SU(2) symmetry is the main structure controlling the emergent complexity of excitations at the pseudogap scale T ^*. The theory yields a gapping of a large part of the anti-nodal region of the Brillouin zone, along with q  =  0 phase transitions, of both nematic and loop currents characters.

Correlation-Driven Lifshitz Transition at the Emergence of the Pseudogap Phase in the Two-Dimensional Hubbard Model

We study the relationship between the pseudogap and Fermi-surface topology in the two-dimensional Hubbard model by means of the cellular dynamical mean-field theory. We find two possible mean-field metallic solutions on a broad range of interactions, doping, and frustration: a conventional renormalized metal and an unconventional pseudogap metal. At half filling, the conventional metal is more stable and displays an interaction-driven Mott metal-insulator transition. However, for large interactions and small doping, a region that is relevant for cuprates, the pseudogap phase becomes the ground state. By increasing doping, we show that a first-order transition from the pseudogap to the conventional metal is tied to a change of the Fermi surface from hole- to electronlike, unveiling a correlation-driven mechanism for a Lifshitz transition. This explains the puzzling link between the pseudogap phase and Fermi surface topology that has been pointed out in recent experiments.

Spin susceptibility of charge-ordered YBa2Cu3O y across the upper critical field

The value of the upper critical field H_c2, a fundamental characteristic of the superconducting state, has been subject to strong controversy in high-T_c copper oxides. Since the issue has been tackled almost exclusively by macroscopic techniques so far, there is a clear need for local-probe measurements. Here, we use ¹⁷O NMR to measure the spin susceptibility [Formula: see text] of the CuO₂ planes at low temperature in charge-ordered YBa₂Cu₃O _y We find that [Formula: see text] increases (most likely linearly) with magnetic field H and saturates above field values ranging from 20 T to 40 T. This result is consistent with the lowest H_c2 values claimed previously and with the interpretation that the charge density wave (CDW) reduces H_c2 in underdoped YBa₂Cu₃O _y Furthermore, the absence of marked deviation in [Formula: see text] at the onset of long-range CDW order indicates that this [Formula: see text] reduction and the Fermi-surface reconstruction are primarily rooted in the short-range CDW order already present in zero field, not in the field-induced long-range CDW order. Above [Formula: see text], the relatively low values of [Formula: see text] at [Formula: see text] K show that the pseudogap is a ground-state property, independent of the superconducting gap.

Review of pseudogaps in strongly interacting Fermi gases

A central challenge in modern condensed matter physics is developing the tools for understanding nontrivial yet unordered states of matter. One important idea to emerge in this context is that of a 'pseudogap': the fact that under appropriate circumstances the normal state displays a suppression of the single particle spectral density near the Fermi level, reminiscent of the gaps seen in ordered states of matter. While these concepts arose in a solid state context, they are now being explored in cold gases. This article reviews the current experimental and theoretical understanding of the normal state of strongly interacting Fermi gases, with particular focus on the phenomonology which is traditionally associated with the pseudogap.

Contrasting Phenomenology of NMR Shifts in Cuprate Superconductors

Nuclear magnetic resonance (NMR) shifts, if stripped of their uncertainties, must hold key information about the electronic fluid in the cuprates. The early shift interpretation that favored a single-fluid scenario will be reviewed, as well as recent experiments that reported its failure. Thereafter, based on literature shift data for planar Cu, a contrasting shift phenomenology for cuprate superconductors is developed, which is very different from the early view while being in agreement with all published data. For example, it will be shown that the hyperfine scenario used up to now is inadequate as a large isotropic shift component is discovered. Furthermore, the changes of the temperature dependences of the shifts above and below the superconducting transitions temperature proceed according to a few rules that were not discussed before. It appears that there can be substantial spin shift at the lowest temperature if the magnetic field is perpendicular to the CuO 2 plane, which points to a localization of spin in the 3 d ( x 2 − y 2 ) orbital. A simple model is presented based on the most fundamental findings. The analysis must have new consequences for theory of the cuprates.

Study of spinel LiTi2O4 superconductors via near-infrared reflection experiments

We present an optical study on high-quality and single-phase LiTi₂O₄ (LTO) superconductor thin films grown on MgAl₂O₄ substrates by pulsed laser deposition. The near infrared (NIR) reflectivity is measured for samples with (001) and (111) lattice orientations. The temperature-induced metal-superconductor transition can be observed, and the superconducting transition temperature can be measured for both samples. We find that the NIR reflection experiment can reflect rightly the basic features of LTO superconductor thin films. Furthermore, the results obtained from this simple optical measurement suggest that the photo-induced electronic localization effect can be present in LTO thin films in a metallic state. Such information cannot be obtained directly from conventional transport and magneto-transport measurements. These interesting and important findings demonstrate that the NIR reflection experiment is a powerful optical technique for contactless characterizations and investigations of superconductor materials.

Simulation of the NMR response in the pseudogap regime of the cuprates

The pseudogap in the cuprate high-temperature superconductors was discovered as a suppression of the Knight shift and spin relaxation time measured in nuclear magnetic resonance (NMR) experiments. However, theoretical understanding of this suppression in terms of the magnetic susceptiblility of correlated itinerant fermion systems was so far lacking. Here we study the temperature and doping evolution of these quantities on the two-dimensional Hubbard model using cluster dynamical mean field theory. We recover the suppression of the Knight shift and the linear-in-T spin echo decay that increases with doping. The relaxation rate shows a marked increase as T is lowered but no indication of a pseudogap on the Cu site, and a clear downturn on the O site, consistent with experimental results on single layer materials but different from double layer materials. The consistency of these results with experiment suggests that the pseudogap is well described by strong short-range correlation effects.

Superconductivity Emerging from an Electronic Phase Separation in the Charge Ordered Phase of RbFe_{2}As_{2}

^{75}As, ^{87}Rb, and ^{85}Rb nuclear quadrupole resonance (NQR) and ^{87}Rb nuclear magnetic resonance measurements in a RbFe_{2}As_{2} iron-based superconductor are presented. We observe a marked broadening of the ^{75}As NQR spectrum below T_{0}≃140  K which is associated with the onset of a charge order in the FeAs planes. Below T_{0} we observe a power-law decrease in the ^{75}As nuclear spin-lattice relaxation rate down to T^{*}≃20  K. Below T^{*} the nuclei start to probe different dynamics owing to the different local electronic configurations induced by the charge order. A fraction of the nuclei probes spin dynamics associated with electrons approaching a localization while another fraction probes activated dynamics possibly associated with a pseudogap. These different trends are discussed in light of an orbital selective behavior expected for the electronic correlations.

Optical studies of high-temperature superconducting cuprates

The optical studies of high-temperature superconducting cuprates (HTSC) are reviewed. From the doping dependence of room temperature spectra, a dramatic change of the electronic state from a Mott (charge transfer) insulator to a Fermi liquid has been revealed. Additionally, the unusual 2D nature of the electronic state has been found. The temperature dependence of the optical spectra provided a rich source of information on the pseudogap, superconducting gap, Josephson plasmon, transverse Josephson plasma mode and precursory superconductivity. Among these issues, Josephson plasmons and transverse Josephson plasma mode were experimentally discovered by optical measurements, and thus are unique to HTSC. The effect of the spin/charge stripe order is also unique to HTSC, reflecting the conducting nature of the stripe order in this system. The pair-breaking due to the stripe order seems stronger in the out-of-plane direction than in the in-plane one.

Charge orders, magnetism and pairings in the cuprate superconductors

We review the recent developments in the field of cuprate superconductors with special focus on the recently observed charge order in the underdoped compounds. We introduce new theoretical developments following the study of the antiferromagnetic quantum critical point in two dimensions, in which preemptive orders in both charge and superconducting (SC) sectors emerge, that are in turn related by an SU(2) symmetry. We consider the implications of this proliferation of orders in the underdoped region, and provide a study of the type of fluctuations which characterize the SU(2) symmetry. We identify an intermediate energy scale where the SC fluctuations are dominant and argue that they are unstable towards the formation of a resonant excitonic state at the pseudogap temperature T (*). We discuss the implications of this scenario for a few key experiments.

Pairing in a dry Fermi sea

In the traditional Bardeen–Cooper–Schrieffer theory of superconductivity, the amplitude for the propagation of a pair of electrons with momentum k and −k has a log singularity as the temperature decreases. This so-called Cooper instability arises from the presence of an electron Fermi sea. It means that an attractive interaction, no matter how weak, will eventually lead to a pairing instability. However, in the pseudogap regime of the cuprate superconductors, where parts of the Fermi surface are destroyed, this log singularity is suppressed, raising the question of how pairing occurs in the absence of a Fermi sea. Here we report Hubbard model numerical results and the analysis of angular-resolved photoemission experiments on a cuprate superconductor. In contrast to the traditional theory, we find that in the pseudogap regime the pairing instability arises from an increase in the strength of the spin–fluctuation pairing interaction as the temperature decreases rather than the Cooper log instability.

Pairing interaction appears at room temperature in traditional superconductors with a Cooper instability in the Fermi sea. Here, Maier et al. report that in the pseudogap phase of cuprate, where this instability is absent, superconductivity arises from an increase in the strength of the spin fluctuation pairing interaction as the temperature decreases.

Unconventional High-Energy-State Contribution to the Cooper Pairing in the Underdoped Copper-Oxide Superconductor HgBa_{2}Ca_{2}Cu_{3}O_{8+δ}

We study the temperature-dependent electronic B_{1g} Raman response of a slightly underdoped single crystal HgBa_{2}Ca_{2}Cu_{3}O_{8+δ} with a superconducting critical temperature T_{c}=122  K. Our main finding is that the superconducting pair-breaking peak is associated with a dip on its higher-energy side, disappearing together at T_{c}. This result reveals a key aspect of the unconventional pairing mechanism: spectral weight lost in the dip is transferred to the pair-breaking peak at lower energies. This conclusion is supported by cellular dynamical mean-field theory on the Hubbard model, which is able to reproduce all the main features of the B_{1g} Raman response and explain the peak-dip behavior in terms of a nontrivial relationship between the superconducting gap and the pseudogap.

Unusual spin dynamics in topological insulators

The dynamic spin susceptibility (DSS) has a ubiquitous Lorentzian form around the Zeeman energy in conventional materials with weak spin orbit coupling, whose spectral width characterizes the spin relaxation rate. We show that DSS has an unusual non-Lorentzian form in topological insulators, which are characterized by strong SOC, and the anisotropy of the DSS reveals the orientation of the underlying spin texture of topological states. At zero temperature, the high frequency part of DSS is universal and increases in certain directions as ω^d−1 with d = 2 and 3 for surface states and Weyl semimetals, respectively, while for helical edge states, the interactions renormalize the exponent as d = 2K − 1 with K the Luttinger-liquid parameter. As a result, spin relaxation rate cannot be deduced from the DSS in contrast to the case of usual metals, which follows from the strongly entangled spin and charge degrees of freedom in these systems.

Collapse of the normal-state pseudogap at a Lifshitz transition in the Bi(2)Sr(2)CaCu(2)O(8+δ) cuprate superconductor

We report a fine tuned doping study of strongly overdoped Bi_{2}Sr_{2}CaCu_{2}O_{8+δ} single crystals using electronic Raman scattering. Combined with theoretical calculations, we show that the doping, at which the normal-state pseudogap closes, coincides with a Lifshitz quantum phase transition where the active holelike Fermi surface becomes electronlike. This conclusion suggests that the microscopic cause of the pseudogap is sensitive to the Fermi surface topology. Furthermore, we find that the superconducting transition temperature is unaffected by this transition, demonstrating that their origins are different on the overdoped side.

A model of magneto-electric multipoles

A long-known Hamiltonian of electrons with entangled spin and orbital degrees of freedom is re-examined as a model of magneto-electric multipoles (MEs). In the model, a magnetic charge and simple quantum rotator are tightly locked in action, some might say they are enslaved entities. It is shown that MEs almost perfectly accord with those inferred from an analysis of magnetic neutron diffraction data on a ceramic superconductor (YBCO) in the pseudo-gap phase. Nigh on perfection between Stone's model and inferred MEs is achieved by addition to the original model of a crystal-field potential appropriate for the magnetic space group used in the published data analysis. An impression of thermal properties of multipoles is sought from a molecular-field model.

Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy

The pseudogap regime of high-temperature cuprates harbours diverse manifestations of electronic ordering whose exact nature and universality remain debated. Here, we show that the short-ranged charge order recently reported in the normal state of YBa2Cu3Oy corresponds to a truly static modulation of the charge density. We also show that this modulation impacts on most electronic properties, that it appears jointly with intra-unit-cell nematic, but not magnetic, order, and that it exhibits differences with the charge density wave observed at lower temperatures in high magnetic fields. These observations prove mostly universal, they place new constraints on the origin of the charge density wave and they reveal that the charge modulation is pinned by native defects. Similarities with results in layered metals such as NbSe2, in which defects nucleate halos of incipient charge density wave at temperatures above the ordering transition, raise the possibility that order-parameter fluctuations, but no static order, would be observed in the normal state of most cuprates if disorder were absent.

From quantum matter to high-temperature superconductivity in copper oxides

The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the 'normal' state at elevated temperatures.

Pseudogap in cuprates in the loop-current ordered state

Scanning tunneling microscopy (STM) has revealed that the magnitude of the pseudo-gap in under-doped cuprates varies spatially and is correlated with disorder. The loop-current order, characterized by the anapole vector Ω, discovered in under-doped cuprates occurs in the same region of the temperature and doping as the pseudo gap observed in STM and ARPES experiments. Since translational symmetry remains unchanged in the pure limit, no gap occurs at the chemical potential. On the other hand for disorder coupling linearly to the different possible orientations of Ω, there can only be a finite temperature dependent static correlation length for the loop-current state at any temperature. This leads to formation of domains of the ordered state with different orientation and magnitude of Ω in each. For the characteristic size of the domains much larger than the Fermi-vectors [Formula: see text], the boundary of the domains leads to forward scattering of the Fermions. Such forward scattering is shown to push states near the chemical potential to energies both above and below it leading to a pseudo-gap with an angular dependence which is maximum in the [Formula: see text] directions because the single-particle energies are degenerate in these directions for all domains. The magnitude of the average gap systematically increases with the square of the average loop order parameter measured by polarized neutron scattering. This result is tested. A unique result of the gap due to forward scattering is the lack of a bump in the density of states at the 'edge' of the pseudo-gap so that the depletion of states near the chemical potential is recovered only in integration up to the edge of the band. This is also in agreement with a variety of experiments. Some predictions for further experiments are provided. Due to the finite correlation length, low frequency excitations are expected at long wavelength at all temperatures in the 'ordered' phase. Such fluctuations motionally average over the shifts in frequencies of local probes such as NMR and muon resonance expected for a truly static order.

NMR study of the superconducting gap variation near the Mott transition in Cs₃C₆₀

Former extensive studies of superconductivity in the A3C60 compounds, where A is an alkali metal, have led one to consider that Bardeen-Cooper-Schrieffer electron-phonon pairing prevails in those compounds, though the incidence of electronic Coulomb repulsion has been highly debated. The discovery of two isomeric fulleride compounds Cs3C60 which exhibit a transition with pressure from a Mott insulator (MI) to a superconducting (SC) state clearly reopens that question. Using pressure (p) as a single control parameter of the C60 balls lattice spacing, one can now study the progressive evolution of the SC properties when the electronic correlations are increased towards the critical pressure p(c) of the Mott transition. We have used 13C and 133Cs NMR measurements on the cubic phase A15-Cs3C60 just above p(c)=5.0(3) kbar, where the SC transition temperature Tc displays a dome shape with decreasing cell volume. From the T dependence below T(c) of the nuclear spin lattice relaxation rate (T1)(-1) we determine the electronic excitations in the SC state, that is 2Δ, the gap value. The latter is found to be largely enhanced with respect to the Bardeen-Cooper-Schrieffer value established in the case of dense A3C60 compounds. It even increases slightly with decreasing p towards p(c), where T(c) decreases on the SC dome, so that 2Δ/k(B)T(c) increases regularly upon approaching the Mott transition. These results bring clear evidence that the increasing correlations near the Mott transition are not significantly detrimental to superconductivity. They rather suggest that repulsive electron interactions might even reinforce elecron-phonon superconductivity, being then partly responsible for the large T(c) values, as proposed by theoretical models taking the electronic correlations as a key ingredient.

Emergence of charge order from the vortex state of a high-temperature superconductor

Evidence is mounting that charge order competes with superconductivity in high Tc cuprates. Whether this has any relationship to the pairing mechanism is unknown as neither the universality of the competition nor its microscopic nature has been established. Here, we show using nuclear magnetic resonance that charge order in YBa2Cu3Oy has maximum strength inside the superconducting dome, similar to compounds of the La2-x(Sr,Ba)xCuO4 family. In YBa2Cu3Oy, this occurs at doping levels of p=0.11-0.12. We further show that the overlap of halos of incipient charge order around vortex cores, similar to those visualised in Bi2Sr2CaCu2O8+δ, can explain the threshold magnetic field at which long-range charge order emerges. These results reveal universal features of a competition in which charge order and superconductivity appear as joint instabilities of the same normal state, whose relative balance can be field-tuned in the vortex state.

Absence of static loop-current magnetism at the apical oxygen site in HgBa2CuO4+δ from NMR

The simple structure of HgBa(2)CuO(4+δ) (Hg1201) is ideal among cuprates for study of the pseudogap phase as a broken symmetry state. We have performed (17)O nuclear magnetic resonance on an underdoped Hg1201 crystal with a transition temperature of 74 K to look for circulating loop currents proposed theoretically and inferred from neutron scattering. The narrow spectra preclude static local fields in the pseudogap phase at the apical site, suggesting that the moments observed with neutrons are fluctuating. The nuclear magnetic resonance frequency shifts are consistent with a dipolar field from the Cu(2+) site.

Universal sheet resistance and revised phase diagram of the cuprate high-temperature superconductors

Upon introducing charge carriers into the copper-oxygen sheets of the enigmatic lamellar cuprates, the ground state evolves from an insulator to a superconductor and eventually to a seemingly conventional metal (a Fermi liquid). Much has remained elusive about the nature of this evolution and about the peculiar metallic state at intermediate hole-carrier concentrations (p). The planar resistivity of this unconventional metal exhibits a linear temperature dependence (ρ ∝ T) that is disrupted upon cooling toward the superconducting state by the opening of a partial gap (the pseudogap) on the Fermi surface. Here, we first demonstrate for the quintessential compound HgBa2CuO4+δ a dramatic switch from linear to purely quadratic (Fermi liquid-like, ρ ∝ T(2)) resistive behavior in the pseudogap regime. Despite the considerable variation in crystal structures and disorder among different compounds, our result together with prior work gives insight into the p-T phase diagram and reveals the fundamental resistance per copper-oxygen sheet in both linear (ρ = A1T) and quadratic (ρ = A2T(2)) regimes, with A1 ∝ A2 ∝ 1/p. Theoretical models can now be benchmarked against this remarkably simple universal behavior. Deviations from this underlying behavior can be expected to lead to new insight into the nonuniversal features exhibited by certain compounds.

New insights into the phase diagram of the copper oxide superconductors from electronic Raman scattering

The mechanism of unconventional superconductivity is still unknown despite over 25 years passing since the discovery of high-T(c) cuprate superconductors by Bednorz and Muller (1986 Z. Phys. B 64 189). Here, we explore the cuprate phase diagram by electronic Raman spectroscopy and shed light on the superconducting state in hole-doped curates, namely, how superconductivity and the critical temperature T(c) are affected by the pseudogap.

Towards resolution of the Fermi surface in underdoped high-Tc superconductors

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 in Fermi velocity measured by quantum oscillations, which is found to be associated with the nodal density of states observed in angular resolved photoemission, the persistence of quantum oscillations down to low fields in the vortex state, the small value of density of states from heat capacity and the multiple frequency quantum oscillation pattern consistent with nodal magnetic breakdown of bilayer-split pockets. A nodal Fermi surface pocket is further consistent with the observation of a density of states at the Fermi level concentrated at the nodes in photoemission experiments, and the antinodal pseudogap observed by photoemission, optical conductivity, nuclear magnetic resonance (NMR) Knight shift, as well as other complementary diffraction, transport and thermodynamic measurements. One of the possibilities considered is that the small Fermi surface pockets observed at high magnetic fields can be understood in terms of Fermi surface reconstruction by a form of small wavevector charge order, observed over long lengthscales in experiments such as NMR and x-ray scattering, potentially accompanied by an additional mechanism to gap the antinodal density of states.

Pseudogap temperature as a Widom line in doped Mott insulators

The pseudogap refers to an enigmatic state of matter with unusual physical properties found below a characteristic temperature T* in hole-doped high-temperature superconductors. Determining T* is critical for understanding this state. Here we study the simplest model of correlated electron systems, the Hubbard model, with cluster dynamical mean-field theory to find out whether the pseudogap can occur solely because of strong coupling physics and short nonlocal correlations. We find that the pseudogap characteristic temperature T* is a sharp crossover between different dynamical regimes along a line of thermodynamic anomalies that appears above a first-order phase transition, the Widom line. The Widom line emanating from the critical endpoint of a first-order transition is thus the organizing principle for the pseudogap phase diagram of the cuprates. No additional broken symmetry is necessary to explain the phenomenon. Broken symmetry states appear in the pseudogap and not the other way around.

A phenomenological theory of the anomalous pseudogap phase in underdoped cuprates

The theoretical description of the anomalous properties of the pseudogap phase in the underdoped region of the cuprate phase diagram lags behind the progress in spectroscopic and other experiments. A phenomenological ansatz, based on analogies to the approach to Mott localization at weak coupling in lower dimensional systems, has been proposed by Yang et al (2006 Phys. Rev. B 73 174501). This ansatz has had success in describing a range of experiments. The motivation underlying this ansatz is described and the comparisons with experiment are reviewed. Implications for a more microscopic theory are discussed together with the relation to theories that start directly from microscopic strongly coupled Hamiltonians.

Mottness collapse and T-linear resistivity in cuprate superconductors

Central to the normal state of cuprate high-temperature superconductors is the collapse of the pseudo-gap, briefly reviewed here, at a critical point and the subsequent onset of the strange metal characterized by a resistivity that scales linearly with temperature. A possible clue to the resolution of this problem is the inter-relation between two facts: (i) a robust theory of T-linear resistivity resulting from quantum criticality requires an additional length scale outside the standard one-parameter scaling scenario and (ii) breaking the Landau correspondence between the Fermi gas and an interacting system with short-range repulsions requires non-fermionic degrees. We show that a low-energy theory of the Hubbard model that correctly incorporates dynamical spectral weight transfer has the extra degrees of freedom needed to describe this physics. The degrees of freedom that mix into the lower band as a result of dynamical spectral weight transfer are shown to either decouple beyond a critical doping, thereby signalling Mottness collapse, or unbind above a critical temperature, yielding strange metal behaviour characterized by T-linear resistivity.

Evidence of a precursor superconducting phase at temperatures as high as 180 K in RBa2Cu3O(7-δ) (R=Y, Gd, Eu) superconducting crystals from infrared spectroscopy

We show that a multilayer analysis of the infrared c-axis response of RBa2Cu3O(7-δ) (R=Y, Gd, Eu) provides important new information about the anomalous normal-state properties of underdoped cuprate high temperature superconductors. In addition to competing correlations which give rise to a pseudogap that depletes the low-energy electronic states below T*≫T(c), it enables us to identify the onset of a precursor superconducting state below T(ons)>T(c). We map out the doping phase diagram of T(ons) which reaches a maximum of 180 K at strong underdoping and present magnetic field dependent data which confirm our conclusions.

Evidence for two electronic components in high-temperature superconductivity from NMR

A new analysis of (63)Cu and (17)O NMR shift data on La(1.85)Sr(0.15)CuO(4) is reported that supports earlier work arguing for a two-component description of La(1.85)Sr(0.15)CuO(4), but conflicts with the widely held view that the cuprates are a one-component system. The data are analyzed in terms of two components A and B with susceptibilities χ(AA), χ(AB)(= χ(BA)) and χ(BB). We find that above T(c), χ(AB) and χ(BB) are independent of temperature and obtain for the first time the temperature dependence of all three susceptibilities above T(c) as well as the complete temperature dependence of χ(AA)+χ(AB) and χ(AB)+χ(BB) below T(c). The form of the results agrees with that recently proposed by Barzykin and Pines.

Lack of evidence for orbital-current effects in the high-temperature Y2Ba4Cu7O15-delta superconductor using 89Y nuclear magnetic resonance

We have performed NMR measurements at the Y site on a c-axis-oriented powder sample of the cuprate superconductor Y2Ba4Cu7O15-delta to search for the possible orbital-current phase. The temperature dependence of the Y linewidth and relaxation behavior in the normal-conducting phase were studied down to 100 K. These measurements give upper limits for a static magnetic field and the amplitude of a fluctuating magnetic field at the Y site of < or approximately 0.15 and < or approximately 0.7 mT, respectively. These values provide significant constraints on possible static or quasistatic orbital currents.

75As NMR studies of superconducting LaFeAsO0.9F0.1

We have performed 75As nuclear magnetic resonance measurements on aligned powders of the new LaFeAsO0.9F0.1 superconductor. In the normal state, we find a strong temperature dependence of the spin shift and Korringa behavior of the spin lattice relaxation rate. In the superconducting state, we find evidence for line nodes in the superconducting gap and spin-singlet pairing. Our measurements reveal a strong anisotropy of the spin lattice relaxation rate, which suggests that superconducting vortices contribute to the relaxation rate when the field is parallel to the c axis but not for the perpendicular direction.