Destruction of the Fermi surface in underdoped high-Tc superconductors

Emergent normal fluid in the superconducting ground state of overdoped cuprates

The microscopic mechanism for the disappearance of superconductivity in overdoped cuprates is still under heated debate. Here we use scanning tunneling spectroscopy to investigate the evolution of quasiparticle interference phenomenon in Bi2Sr2CuO6+δ over a wide range of hole densities. We find that when the system enters the overdoped regime, a peculiar quasiparticle interference wavevector with arc-like pattern starts to emerge even at zero bias, and its intensity grows with increasing doping level. Its energy dispersion is incompatible with the octet model for d-wave superconductivity, but is highly consistent with the scattering interference of gapless normal carriers. The gapless quasiparticles are mainly located near the antinodes and are independent of temperature, consistent with the disorder scattering mechanism. We propose that a branch of normal fluid emerges from the pair-breaking scattering between flat antinodal bands in the quantum ground state, which is the primary cause for the reduction of superfluid density and suppression of superconductivity in overdoped cuprates.

SdH Oscillations from the Dirac Surface State in the Fermi-Arc Antiferromagnet NdBi

The recent progress in CuMnAs and Mn3X (X = Sn, Ge, Pt) shows that antiferromagnets (AFMs) provide a promising platform for advanced spintronics device innovations. Most recently, a switchable Fermi-arc is discovered by the ARPES technique in antiferromagnet NdBi, but the knowledge about electron-transport property and the manipulability of the magnetic structure in NdBi is still vacant to date. In this study, SdH oscillations are successfully verified from the Dirac surface states (SSs) with 2-dimensionality and nonzero Berry phase. Particularly, it is observed that the spin-flop transition only appears when the external magnetical field is applied along [001] direction, and features obvious hysteresis for the first time in NdBi, which provides a powerful handle for adjusting the spin texture in NdBi. Crucially, the DFT shows the Dirac cone and the Fermi arc strongly depend on the high-order magnetic structure of NdBi and further reveals the orbital magnetic moment of Nd plays a crucial role in fostering the peculiar SSs, leading to unveil the mystery of the band-splitting effect and to manipulate the electronic transport, high-effectively, in the thin film works in NdBi. It is believed that this study provides important guidance for the development of new antiferromagnet-based spintronics devices based on cutting-edge rare-earth monopnictides.

Density of States and Spectral Function of a Superconductor out of a Quantum-Critical Metal

We analyze the validity of a quasiparticle description of a superconducting state above a metallic quantum-critical point (QCP). A normal state at a QCP is a non-Fermi liquid with no coherent quasiparticles. A superconducting order gaps out low-energy excitations, except for a sliver of states for non-s-wave gap symmetry, and at a first glance, restores coherent quasiparticle behavior. We argue that this does not necessarily hold as the fermionic self-energy may remain singular above the gap edge. This singularity gives rise to markedly non-BCS behavior of the density of states and to the appearance of a nondispersing mode at the gap edge in the spectral function. We analyze the set of quantum-critical models with an effective dynamical four-fermion interaction V(Ω)∝1/Ω^{γ}, where Ω is a frequency of a boson, which mediates the interaction. We show that coherent quasiparticle behavior in a superconducting state holds for γ<1/2, but breaks down for larger γ. We discuss signatures of quasiparticle breakdown and compare our results with the photoemission data for Bi2201 and Bi2212.

Unveiling phase diagram of the lightly doped high-Tc cuprate superconductors with disorder removed

The currently established electronic phase diagram of cuprates is based on a study of single- and double-layered compounds. These CuO₂ planes, however, are directly contacted with dopant layers, thus inevitably disordered with an inhomogeneous electronic state. Here, we solve this issue by investigating a 6-layered Ba₂Ca₅Cu₆O₁₂(F,O)₂ with inner CuO₂ layers, which are clean with the extremely low disorder, by angle-resolved photoemission spectroscopy (ARPES) and quantum oscillation measurements. We find a tiny Fermi pocket with a doping level less than 1% to exhibit well-defined quasiparticle peaks which surprisingly lack the polaronic feature. This provides the first evidence that the slightest amount of carriers is enough to turn a Mott insulating state into a metallic state with long-lived quasiparticles. By tuning hole carriers, we also find an unexpected phase transition from the superconducting to metallic states at 4%. Our results are distinct from the nodal liquid state with polaronic features proposed as an anomaly of the heavily underdoped cuprates.

Atomic-scale interpretation of the quantum oscillations in cuprate superconductors

Cuprate superconductors display unusual features in bothkspace and real space as the superconductivity is suppressed-a broken Fermi surface, charge density wave, and pseudogap. Contrarily, recent transport measurements on cuprates under high magnetic fields report quantum oscillations (QOs), which imply rather a usual Fermi liquid behavior. To settle the disagreement, we investigated Bi₂Sr₂CaCu₂O_8+δunder a magnetic field in an atomic scale. A particle-hole (p-h) asymmetrically dispersing density of states (DOSs) modulation was found at the vortices on a slightly underdoped sample, while on a highly underdoped sample, no trace of the vortex was found even at 13 T. However, a similar p-h asymmetric DOS modulation persisted in almost an entire field of view. From this observation, we infer an alternative explanation of the QO results by providing a unifying picture where the aforementioned seemingly conflicting evidence from angle-resolved photoemission spectroscopy, spectroscopic imaging scanning tunneling microscopy, and magneto-transport measurements can be understood solely in terms of the DOS modulations.

Observations of Nematicity, Dopants, and Zero-Bias Conductance Peaks for the Ca0.9La0.1FeAs2 Superconductor

Ca_1-xLa_xFeAs₂ (CLFA112) belongs to a new family of Fe-based superconductors (FeSCs) and has a unique crystal structure featuring an arsenic zigzag chain layer, which has been proposed to be a possible two-dimensional topological insulator. This suggests that CLFA112 is a potential topological superconductor-a platform to realize Majorana fermions. Up to now, even a clear superconducting (SC) gap in CLFA112 has never been observed, and the SC properties of CLFA112 remain largely elusive. In this letter, we report the results of an atomic-scale investigation of the electronic structure of CLFA112 crystals using low-temperature scanning tunneling microscopy (STM). We revealed four different types of surfaces exhibiting distinct electronic properties, with all surfaces displaying dominating 2 × 1 surface reconstructions. On a Ca/La layer on top of an FeAs layer, a clear SC gap of ~12 mV was observed only at the crevices (vacancies) where the FeAs layer can be directly accessed. Remarkably, the FeAs termination layer displayed a dispersing nematic modulation both in real and q space. We also present peculiar zero-bias conductance peaks for the very As chain layer that is believed to exhibit a topological edge state as well as the influence of La dopants on the As chain layer.

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}.

Fermi Surface Expansion above Critical Temperature in a Hund Ferromagnet

Using a cluster extension of the dynamical mean-field theory, we show that strongly correlated metals subject to Hund's physics exhibit significant electronic structure modulations above magnetic transition temperatures. In particular, in a ferromagnet having a large local moment due to Hund's coupling (Hund's ferromagnet), the Fermi surface expands even above the Curie temperature (T_{C}) as if a spin polarization occurred. Behind this phenomenon, effective "Hund's physics" works in momentum space, originating from ferromagnetic fluctuations in the strong-coupling regime. The resulting significantly momentum-dependent (spatially nonlocal) electron correlations induce an electronic structure reconstruction involving a Fermi surface volume change and a redistribution of the momentum-space occupation. Our finding will give a deeper insight into the physics of Hund's ferromagnets 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.

Emergence of Fermi arcs due to magnetic splitting in an antiferromagnet

The Fermi surface plays an important role in controlling the electronic, transport and thermodynamic properties of materials. As the Fermi surface consists of closed contours in the momentum space for well-defined energy bands, disconnected sections known as Fermi arcs can be signatures of unusual electronic states, such as a pseudogap¹. Another way to obtain Fermi arcs is to break either the time-reversal symmetry² or the inversion symmetry³ of a three-dimensional Dirac semimetal, which results in formation of pairs of Weyl nodes that have opposite chirality⁴, and their projections are connected by Fermi arcs at the bulk boundary^3,5-12. Here, we present experimental evidence that pairs of hole- and electron-like Fermi arcs emerge below the Neel temperature (T_N) in the antiferromagnetic state of cubic NdBi due to a new magnetic splitting effect. The observed magnetic splitting is unusual, as it creates bands of opposing curvature, which change with temperature and follow the antiferromagnetic order parameter. This is different from previous theoretically considered^13,14 and experimentally reported cases^15,16 of magnetic splitting, such as traditional Zeeman and Rashba, in which the curvature of the bands is preserved. Therefore, our findings demonstrate a type of magnetic band splitting in the presence of a long-range antiferromagnetic order that is not readily explained by existing theoretical ideas.

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.

Optical manipulation of electronic dimensionality in a quantum material

Exotic phenomena can be achieved in quantum materials by confining electronic states into two dimensions. For example, relativistic fermions are realized in a single layer of carbon atoms¹, the quantized Hall effect can result from two-dimensional (2D) systems^2,3, and the superconducting transition temperature can be considerably increased in a one-atomic-layer material^4,5. Ordinarily, a 2D electronic system can be obtained by exfoliating the layered materials, growing monolayer materials on substrates, or establishing interfaces between different materials. Here we use femtosecond infrared laser pulses to invert the periodic lattice distortion sectionally in a three-dimensional (3D) charge density wave material (1T-TiSe₂), creating macroscopic domain walls of transient 2D ordered electronic states with unusual properties. The corresponding ultrafast electronic and lattice dynamics are captured by time-resolved and angle-resolved photoemission spectroscopy⁶ and ultrafast electron diffraction at energies of the order of megaelectronvolts⁷. Moreover, in the photoinduced 2D domain wall near the surface we identify a phase with enhanced density of states and signatures of potential opening of an energy gap near the Fermi energy. Such optical modulation of atomic motion is an alternative path towards realizing 2D electronic states and will be a useful platform upon which novel phases in quantum materials may be discovered.

Fermi surface in La-based cuprate superconductors from Compton scattering imaging

Compton scattering provides invaluable information on the underlying Fermi surface (FS) and is a powerful tool complementary to angle-resolved photoemission spectroscopy and quantum oscillation measurements. Here we perform high-resolution Compton scattering measurements for La_2−xSr_xCuO₄ with x = 0.08 (T_c = 20 K) at 300 K and 150 K, and image the momentum distribution function in the two-dimensional Brillouin zone. We find that the observed images cannot be reconciled with the conventional hole-like FS believed so far. Instead, our data imply that the FS is strongly deformed by the underlying nematicity in each CuO₂ plane, but the bulk FSs recover the fourfold symmetry. We also find an unusually strong temperature dependence of the momentum distribution function, which may originate from the pseudogap formation in the presence of the reconstructed FSs due to the underlying nematicity. Additional measurements for x = 0.15 and 0.30 at 300 K suggest similar FS deformation with weaker nematicity, which nearly vanishes at x = 0.30.

Compton scattering provides information on the Fermi surface (FS) hence very useful to understand the electronic structure of high temperature superconductors. Here, Yamase et al. perform Compton scattering measurements on La_2−xSr_xCuO₄ samples and observe deformed FS in CuO₂ plane due to nematicity but recovering fourfold symmetry in bulk FS.

Observation of small Fermi pockets protected by clean CuO2 sheets of a high-T c superconductor

In cuprate superconductors with high critical transition temperature (T _c), light hole-doping to the parent compound, which is an antiferromagnetic Mott insulator, has been predicted to lead to the formation of small Fermi pockets. These pockets, however, have not been observed. Here, we investigate the electronic structure of the five-layered Ba₂Ca₄Cu₅O₁₀(F,O)₂, which has inner copper oxide (CuO₂) planes with extremely low disorder, and find small Fermi pockets centered at (π/2, π/2) of the Brillouin zone by angle-resolved photoemission spectroscopy and quantum oscillation measurements. The d-wave superconducting gap opens along the pocket, revealing the coexistence between superconductivity and antiferromagnetic ordering in the same CuO₂ sheet. These data further indicate that superconductivity can occur without contribution from the antinodal region around (π, 0), which is shared by other competing excitations.

Calculations of quantum oscillations in cuprate superconductors considering the pseudogap

The observations of quantum oscillations frequencies in overdoped cuprates were in agreement with a charge density contained in a cylindrical Fermi surface but the measured frequencies of underdoped compounds were much smaller than expected. This was attributed to a topological transition into small pockets of Fermi surface associated with the existence of charge density waves. On the other hand, spectroscopic measurements suggested that the large two-dimensional Fermi surface changes continuously into a set of four disconnected arcs. Here we take into account the effect of the pseudogap that limits the availablek-space area where the Landau levels are developed on the Luttinger theorem and obtain the correct total carrier densities. The calculations show how the disconnected arcs evolve into a closed Fermi surface reconciling the experiments.

ARPES studies on new types of electron-doped cuprate superconductors

For more than thirty years since the discovery of superconductivity in cuprates, it has been widely agreed that the superconductivity is realized by doping a charge-transfer insulator with charge carriers through chemical substitution. For electron-doped cuprates, however, the recent development of reduction annealing methods has enabled superconductivity for a very small amount of or even without chemical substitution. In this article, we review recent angle-resolved photoemission spectroscopy studies on the new types of electron-doped cuprates with particular emphasis on the effect of reduction annealing. The presented results provide us with renewed insight into the phase diagram and the nature of the pseudogap not only on the electron-doped side but also in the entire doping range including hole doping.

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.

Photoemission perspective on pseudogap, superconducting fluctuations, and charge order in cuprates: a review of recent progress

In the course of seeking the microscopic mechanism of superconductivity in cuprate high temperature superconductors, the pseudogap phase- the very abnormal 'normal' state on the hole-doped side- has proven to be as big of a quandary as superconductivity itself. Angle-resolved photoemission spectroscopy (ARPES) is a powerful tool for assessing the momentum-dependent phenomenology of the pseudogap, and recent technological developments have permitted a more detailed understanding. This report reviews recent progress in understanding the relationship between superconductivity and the pseudogap, the Fermi arc phenomena, and the relationship between charge order and pseudogap from the perspective of ARPES measurements.

Quantum oscillations in a biaxial pair density wave state

At higher temperatures, and in high magnetic fields at low temperatures, an extraordinary and unidentified electronic phase, dubbed the “pseudogap,” appears in lightly hole-doped cuprates. At high fields and low temperatures, the pseudogap phase supports quantum oscillations that have resisted quantitative theoretical explanation since their discovery, and it also exhibits an unidentified density wave state. Although the latter has typically been referred to as a “charge” density wave because of the observed charge density modulations, theory indicates that it could actually be an electron-pair density wave (PDW) state. Here we demonstrate theoretically that a biaxial PDW state with 8a periodicity may provide a compelling quantitative explanation for much of the observed quantum oscillation data.

There has been growing speculation that a pair density wave state is a key component of the phenomenology of the pseudogap phase in the cuprates. Recently, direct evidence for such a state has emerged from an analysis of scanning tunneling microscopy data in halos around the vortex cores. By extrapolation, these vortex halos would then overlap at a magnetic-field scale where quantum oscillations have been observed. Here, we show that a biaxial pair density wave state gives a unique description of the quantum oscillation data, bolstering the case that the pseudogap phase in the cuprates may be a pair density wave state.

Collapse of superconductivity in cuprates via ultrafast quenching of phase coherence

The possibility of driving phase transitions in low-density condensates through the loss of phase coherence alone has far-reaching implications for the study of quantum phases of matter. This has inspired the development of tools to control and explore the collective properties of condensate phases via phase fluctuations. Electrically gated oxide interfaces^1,2, ultracold Fermi atoms^3,4 and cuprate superconductors^5,6, which are characterized by an intrinsically small phase stiffness, are paradigmatic examples where these tools are having a dramatic impact. Here we use light pulses shorter than the internal thermalization time to drive and probe the phase fragility of the Bi₂Sr₂CaCu₂O_8+δ cuprate superconductor, completely melting the superconducting condensate without affecting the pairing strength. The resulting ultrafast dynamics of phase fluctuations and charge excitations are captured and disentangled by time-resolved photoemission spectroscopy. This work demonstrates the dominant role of phase coherence in the superconductor-to-normal state phase transition and offers a benchmark for non-equilibrium spectroscopic investigations of the cuprate phase diagram.

Charge Order and Superconductivity in Underdoped YBa_{2}Cu_{3}O_{7-δ} under Pressure

In underdoped cuprates, an incommensurate charge density wave (CDW) order is known to coexist with superconductivity. A dip in T_{c} at the hole doping level where the CDW is strongest (n_{p}≃0.12) suggests that CDW order may suppress superconductivity. We investigate the interplay of charge order with superconductivity in underdoped YBa_{2}Cu_{3}O_{7-δ} by measuring the temperature dependence of the Hall coefficient R_{H}(T) at high magnetic field and at high hydrostatic pressure. We find that, although pressure increases T_{c} by up to 10 K at 2.6 GPa, it has very little effect on R_{H}(T). This suggests that pressure, at these levels, only weakly affects the CDW and that the increase in T_{c} with pressure cannot be attributed to a suppression of the CDW. We argue, therefore, that the dip in T_{c} at n_{p}≃0.12 at ambient pressure is probably not caused by the CDW formation.

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.

Evidence for Weakly Correlated Oxygen Holes in the Highest-T_{c} Cuprate Superconductor HgBa_{2}Ca_{2}Cu_{3}O_{8+δ}

We study the electronic structure of HgBa_{2}Ca_{2}Cu_{3}O_{8+δ} (Hg1223; T_{c}=134  K) using photoemission spectroscopy (PES) and x-ray absorption spectroscopy (XAS). Resonant valence band PES across the O K edge and Cu L edge identifies correlation satellites originating in O 2p and Cu 3d two-hole final states, respectively. Analyses using the experimental O 2p and Cu 3d partial density of states show quantitatively different on-site Coulomb energy for the Cu site (U_{dd}=6.5±0.5  eV) and O site (U_{pp}=1.0±0.5  eV). Cu_{2}O_{7}-cluster calculations with nonlocal screening explain the Cu 2p core level PES and Cu L-edge XAS spectra, confirm the U_{dd} and U_{pp} values, and provide evidence for the Zhang-Rice singlet state in Hg1223. In contrast to other hole-doped cuprates and 3d-transition metal oxides, the present results indicate weakly correlated oxygen holes in Hg1223.

Bi-2212/1T-TaS2 Van der Waals junctions: Interplay of proximity induced high-T c superconductivity and CDW order

Understanding the coexistence, competition and/or cooperation between superconductivity and charge density waves (CDWs) in the transition metal dichalcogenides (TMDs) is an elusive goal which, when realized, promises to reveal fundamental information on this important class of materials. Here, we use four-terminal current-voltage measurements to study the Van der Waals interface between freshly exfoliated flakes of the high-T_c superconductor, Bi-2212, and the CDW-dominated TMD layered material, 1T-TaS₂. For highly transparent barriers, there is a pronounced Andreev reflection feature providing evidence for proximity-induced high-T_c superconductivity in 1T-TaS₂ with a surprisingly large energy gap (~20 meV) equal to half that of intrinsic Bi-2212 (~40 meV). Our systematic study using conductance spectroscopy of junctions with different transparencies also reveals the presence of two separate boson modes, each associated with a “dip-hump” structure. We infer that the proximity-induced high-T_c superconductivity in the 1T-TaS₂ is driven by coupling to the metastable metallic phase coexisting within the Mott commensurate CDW (CCDW) phase and associated with a concomitant change of the CCDW order parameter in the interfacial region.

Anomalous thermal diffusivity in underdoped YBa2Cu3O6+x

The thermal diffusivity in the [Formula: see text] plane of underdoped YBCO crystals is measured by means of a local optical technique in the temperature range of 25-300 K. The phase delay between a point heat source and a set of detection points around it allows for high-resolution measurement of the thermal diffusivity and its in-plane anisotropy. Although the magnitude of the diffusivity may suggest that it originates from phonons, its anisotropy is comparable with reported values of the electrical resistivity anisotropy. Furthermore, the anisotropy drops sharply below the charge order transition, again similar to the electrical resistivity anisotropy. Both of these observations suggest that the thermal diffusivity has pronounced electronic as well as phononic character. At the same time, the small electrical and thermal conductivities at high temperatures imply that neither well-defined electron nor phonon quasiparticles are present in this material. We interpret our results through a strongly interacting incoherent electron-phonon "soup" picture characterized by a diffusion constant [Formula: see text], where [Formula: see text] is the soup velocity, and scattering of both electrons and phonons saturates a quantum thermal relaxation time [Formula: see text].

Enhancement of the Superconducting Gap by Nesting in CaKFe_{4}As_{4}: A New High Temperature Superconductor

We use high resolution angle resolved photoemission spectroscopy and density functional theory with measured crystal structure parameters to study the electronic properties of CaKFe_{4}As_{4}. In contrast to the related CaFe_{2}As_{2} compounds, CaKFe_{4}As_{4} has a high T_{c} of 35 K at stochiometric composition. This presents a unique opportunity to study the properties of high temperature superconductivity in the iron arsenides in the absence of doping or substitution. The Fermi surface consists of several hole and electron pockets that have a range of diameters. We find that the values of the superconducting gap are nearly isotropic (within the explored portions of the Brillouin zone), but are significantly different for each of the Fermi surface (FS) sheets. Most importantly, we find that the momentum dependence of the gap magnitude plotted across the entire Brillouin zone displays a strong deviation from the simple cos(k_{x})cos(k_{y}) functional form of the gap function, proposed by the scenario of Cooper pairing driven by a short range antiferromagnetic exchange interaction. Instead, the maximum value of the gap is observed on FS sheets that are closest to the ideal nesting condition, in contrast to previous observations in other ferropnictides. These results provide strong support for the multiband character of superconductivity in CaKFe_{4}As_{4}, in which Cooper pairing forms on the electron and the hole bands interacting via a dominant interband repulsive interaction, enhanced by band nesting.

Proving Nontrivial Topology of Pure Bismuth by Quantum Confinement

The topology of pure Bi is controversial because of its very small (∼10  meV) band gap. Here we perform high-resolution angle-resolved photoelectron spectroscopy measurements systematically on 14-202 bilayer Bi films. Using high-quality films, we succeed in observing quantized bulk bands with energy separations down to ∼10  meV. Detailed analyses on the phase shift of the confined wave functions precisely determine the surface and bulk electronic structures, which unambiguously show nontrivial topology. The present results not only prove the fundamental property of Bi but also introduce a capability of the quantum-confinement approach.

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.

Evolution of electron Fermi surface with doping in cobaltates

The notion of the electron Fermi surface is one of the characteristic concepts in the field of condensed matter physics, and it plays a crucial role in the understanding of the physical properties of doped Mott insulators. Based on the t-J model, we study the nature of the electron Fermi surface in the cobaltates, and qualitatively reproduce the essential feature of the evolution of the electron Fermi surface with doping. It is shown that the underlying hexagonal electron Fermi surface obeys Luttinger's theorem. The theory also predicts a Fermi-arc phenomenon at the low-doped regime, where the region of the hexagonal electron Fermi surface along the [Formula: see text]-K direction is suppressed by the electron self-energy, and then six disconnected Fermi arcs located at the region of the hexagonal electron Fermi surface along the [Formula: see text]-M direction emerge. However, this Fermi-arc phenomenon at the low-doped regime weakens with the increase of doping.

Electron-hole doping asymmetry of Fermi surface reconstructed in a simple Mott insulator

It is widely recognized that the effect of doping into a Mott insulator is complicated and unpredictable, as can be seen by examining the Hall coefficient in high T_c cuprates. The doping effect, including the electron–hole doping asymmetry, may be more straightforward in doped organic Mott insulators owing to their simple electronic structures. Here we investigate the doping asymmetry of an organic Mott insulator by carrying out electric-double-layer transistor measurements and using cluster perturbation theory. The calculations predict that strongly anisotropic suppression of the spectral weight results in the Fermi arc state under hole doping, while a relatively uniform spectral weight results in the emergence of a non-interacting-like Fermi surface (FS) in the electron-doped state. In accordance with the calculations, the experimentally observed Hall coefficients and resistivity anisotropy correspond to the pocket formed by the Fermi arcs under hole doping and to the non-interacting FS under electron doping.

Electron or hole doping in a Mott insulator leads to superconductivity, with the mechanism obscured by multi-orbital Fermi surface reconstructions. Here, Kawasugi et al. report doping dependent Hall coefficients and resistivity anisotropy of an organic Mott insulator, revealing doping asymmetry of reconstructed Fermi surface of a single electronic orbital.

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.

Self-energy behavior away from the Fermi surface in doped Mott insulators

We analyze self-energies of electrons away from the Fermi surface in doped Mott insulators using the dynamical cluster approximation to the Hubbard model. For large onsite repulsion, U, and hole doping, the magnitude of the self-energy for imaginary frequencies at the top of the band ([Formula: see text]) is enhanced with respect to the self-energy magnitude at the bottom of the band ([Formula: see text]). The self-energy behavior at these two [Formula: see text]-points is switched for electron doping. Although the hybridization is much larger for (0, 0) than for [Formula: see text], we demonstrate that this is not the origin of this difference. Isolated clusters under a downward shift of the chemical potential, [Formula: see text], at half-filling reproduce the overall self-energy behavior at (0, 0) and [Formula: see text] found in low hole doped embedded clusters. This happens although there is no change in the electronic structure of the isolated clusters. Our analysis shows that a downward shift of the chemical potential which weakly hole dopes the Mott insulator can lead to a large enhancement of the [Formula: see text] self-energy for imaginary frequencies which is not associated with electronic correlation effects, even in embedded clusters. Interpretations of the strength of electronic correlations based on self-energies for imaginary frequencies are, in general, misleading for states away from the Fermi surface.

Giant phonon anomaly associated with superconducting fluctuations in the pseudogap phase of cuprates

The pseudogap in underdoped cuprates leads to significant changes in the electronic structure, and was later found to be accompanied by anomalous fluctuations of superconductivity and certain lattice phonons. Here we propose that the Fermi surface breakup due to the pseudogap, leads to a breakup of the pairing order into two weakly coupled sub-band amplitudes, and a concomitant low energy Leggett mode due to phase fluctuations between them. This increases the temperature range of superconducting fluctuations containing an overdamped Leggett mode. In this range inter-sub-band phonons show strong damping due to resonant scattering into an intermediate state with a pair of overdamped Leggett modes. In the ordered state, the Leggett mode develops a finite energy, changing the anomalous phonon damping into an anomaly in the dispersion. This proposal explains the intrinsic connection between the anomalous pseudogap phase, enhanced superconducting fluctuations and giant anomalies in the phonon spectra.

The emergence of a giant phonon anomaly in the pseudogap phase of underdoped cuprate superconductors has been assumed to be a consequence of instability towards a charge density wave state. Here, the authors present a theory suggesting the anomaly arises due to large superconducting fluctuations.

Quasi-particles ultrafastly releasing kink bosons to form Fermi arcs in a cuprate superconductor

In a conventional framework, superconductivity is lost at a critical temperature (T_c) because, at higher temperatures, gluing bosons can no longer bind two electrons into a Cooper pair. In high-T_c cuprates, it is still unknown how superconductivity vanishes at T_c. We provide evidence that the so-called ≲70-meV kink bosons that dress the quasi-particle excitations are playing a key role in the loss of superconductivity in a cuprate. We irradiated a 170-fs laser pulse on Bi₂Sr₂CaCu₂O_8+δ and monitored the responses of the superconducting gap and dressed quasi-particles by time- and angle-resolved photoemission spectroscopy. We observe an ultrafast loss of superconducting gap near the d-wave node, or light-induced Fermi arcs, which is accompanied by spectral broadenings and weight redistributions occurring within the kink binding energy. We discuss that the underlying mechanism of the spectral broadening that induce the Fermi arc is the undressing of quasi-particles from the kink bosons. The loss mechanism is beyond the conventional framework, and can accept the unconventional phenomena such as the signatures of Cooper pairs remaining at temperatures above T_c.

Collapse of the Mott Gap and Emergence of a Nodal Liquid in Lightly Doped Sr(2)IrO(4)

We report angle resolved photoemission experiments on the electron doped Heisenberg antiferromagnet (Sr(1-x)La(x))(2)IrO(4). For a doping level of x=0.05, we find an unusual metallic state with coherent nodal excitations and an antinodal pseudogap bearing strong similarities with underdoped cuprates. This state emerges from a rapid collapse of the Mott gap with doping resulting in a large underlying Fermi surface that is backfolded by a (π,π) reciprocal lattice vector which we attribute to the intrinsic structural distortion of Sr(2)IrO(4).

Evidence for superconductivity in Li-decorated monolayer graphene

Monolayer graphene exhibits many spectacular electronic properties, with superconductivity being arguably the most notable exception. It was theoretically proposed that superconductivity might be induced by enhancing the electron-phonon coupling through the decoration of graphene with an alkali adatom superlattice [Profeta G, Calandra M, Mauri F (2012) Nat Phys 8(2):131-134]. Although experiments have shown an adatom-induced enhancement of the electron-phonon coupling, superconductivity has never been observed. Using angle-resolved photoemission spectroscopy (ARPES), we show that lithium deposited on graphene at low temperature strongly modifies the phonon density of states, leading to an enhancement of the electron-phonon coupling of up to λ ≃ 0.58. On part of the graphene-derived π*-band Fermi surface, we then observe the opening of a Δ ≃ 0.9-meV temperature-dependent pairing gap. This result suggests for the first time, to our knowledge, that Li-decorated monolayer graphene is indeed superconducting, with Tc ≃ 5.9 K.

Quasiparticle dynamics across the full Brillouin zone of Bi2Sr2CaCu2O8+δ traced with ultrafast time and angle-resolved photoemission spectroscopy

A hallmark in the cuprate family of high-temperature superconductors is the nodal-antinodal dichotomy. In this regard, angle-resolved photoemission spectroscopy (ARPES) has proven especially powerful, providing band structure information directly in energy-momentum space. Time-resolved ARPES (trARPES) holds great promise of adding ultrafast temporal information, in an attempt to identify different interaction channels in the time domain. Previous studies of the cuprates using trARPES were handicapped by the low probing energy, which significantly limits the accessible momentum space. Using 20.15 eV, 12 fs pulses, we show for the first time the evolution of quasiparticles in the antinodal region of Bi2Sr2CaCu2O8+δ and demonstrate that non-monotonic relaxation dynamics dominates above a certain fluence threshold. The dynamics is heavily influenced by transient modification of the electron-phonon interaction and phase space restrictions, in stark contrast to the monotonic relaxation in the nodal and off-nodal regions.

Point nodes persisting far beyond Tc in Bi2212

In contrast to a complex feature of antinodal state, suffering from competing orders, the pairing gap of cuprates is obtained in the nodal region, which therefore holds the key to the superconducting mechanism. One of the biggest question is whether the point nodal state as a hallmark of d-wave pairing collapses at T_c like the BCS-type superconductors, or it instead survives above T_c turning into the preformed pair state. A difficulty in this issue comes from the small magnitude of the nodal gap, which has been preventing experimentalists from solving it. Here we use a laser ARPES capable of ultrahigh-energy resolution, and detect the point nodes surviving far beyond T_c in Bi2212. By tracking the temperature evolution of spectra, we reveal that the superconductivity occurs when the pair-breaking rate is suppressed smaller than the single-particle scattering rate on cooling, which governs the value of T_c in cuprates.

The pairing gap of the high-T_c cuprates has been expected to close at the transition temperature, similarly to the case of conventional superconductors. Here the authors perform ARPES measurements on Bi2212, and reveal a point nodal gap formation beyond T_c, characterized in terms of three parameters.

Phase diagram of cuprate high-temperature superconductors described by a field theory based on anharmonic oxygen degrees of freedom

In high temperature superconductors, although some phenomena such as the Mott transition (MT) at low doping are clearly driven by electron correlations, recent experimental data imply that anharmonic oxygen degrees of freedom-characteristic of perovskite materials-are playing a significant role. A key test of the role of anharmonic oxygen is to reproduce the complex cuprate phase diagram from a simple model. Here, we show that a field theory based on nonlinear coupling to anharmonic oxygens, parametrized from ab initio calculations, quantitatively reproduces the cuprate phase diagram for dopings above the MT. Pairing is mediated by renormalized oxygen vibrations transmuted into excitations of the pseudogap. The observed strong dependence of gap to transition temperature ratio on Tc also emerges from this field theory. This work suggests that including vibrational degrees of freedom is key to developing a complete understanding of the cuprates.

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.

Fermi arcs vs. Fermi pockets in electron-doped perovskite iridates

We report on an angle resolved photoemission (ARPES) study of bulk electron-doped perovskite iridate, (Sr_1−xLa_x)₃Ir₂O₇. Fermi surface pockets are observed with a total electron count in keeping with that expected from La substitution. Depending on the energy and polarization of the incident photons, these pockets show up in the form of disconnected “Fermi arcs”, reminiscent of those reported recently in surface electron-doped Sr₂IrO₄. Our observed spectral variation is consistent with the coexistence of an electronic supermodulation with structural distortion in the system.

Coherent quasiparticles with a small fermi surface in lightly doped Sr(3)Ir(2)O(7)

We characterize the electron doping evolution of (Sr_{1-x}La_{x})_{3}Ir_{2}O_{7} by means of angle-resolved photoemission. Concomitant with the metal insulator transition around x≈0.05 we find the emergence of coherent quasiparticle states forming a closed small Fermi surface of volume 3x/2, where x is the independently measured La concentration. The quasiparticle weight Z remains large along the entire Fermi surface, consistent with the moderate renormalization of the low-energy dispersion, and no pseudogap is observed. This indicates a conventional, weakly correlated Fermi liquid state with a momentum independent residue Z≈0.5 in lightly doped Sr_{3}Ir_{2}O_{7}.

Pseudogap in cuprates driven by D-wave flux-phase order proximity effects: a theoretical analysis from Raman and ARPES experiments

One of the puzzling characteristics of the pseudogap phase of high-Tc cuprates is the nodal-antinodal dichotomy. While the nodal quasiparticles have a Fermi liquid behaviour, the antinodal ones show non-Fermi liquid features and an associated pseudogap. Angle-resolved photoemission spectroscopy and electronic Raman scattering are two valuable tools which have shown universal features which are rather material-independent, and presumably intrinsic to the pseudogap phase. The doping and temperature dependence of the Fermi arcs and the pseudogap observed by photoemission near the antinode correlates with the non-Fermi liquid behaviour observed by Raman for the B(1g) mode. In contrast, and similar to the nodal quasiparticles detected by photoemission, the Raman B(2g) mode shows Fermi liquid features. We show that these two experiments can be analysed, in the context of the t-J model, by self-energy effects in the proximity to a D-wave flux-phase order instability. This approach supports a crossover origin for the pseudogap, and a scenario of two competing phases. The B(2g) mode shows, in an underdoped case, a depletion at intermediate energy which has attracted renewed interest. We study this depletion and discuss its origin and relation with the pseudogap.

Time-resolved photoemission apparatus achieving sub-20-meV energy resolution and high stability

The paper describes a time- and angle-resolved photoemission apparatus consisting of a hemispherical analyzer and a pulsed laser source. We demonstrate 1.48-eV pump and 5.92-eV probe measurements at the ⩾10.5-meV and ⩾240-fs resolutions by use of fairly monochromatic 170-fs pulses delivered from a regeneratively amplified Ti:sapphire laser system operating typically at 250 kHz. The apparatus is capable to resolve the optically filled superconducting peak in the unoccupied states of a cuprate superconductor, Bi2Sr2CaCu2O(8 + δ). A dataset recorded on Bi(111) surface is also presented. Technical descriptions include the followings: A simple procedure to fine-tune the spatio-temporal overlap of the pump-and-probe beams and their diameters; achieving a long-term stability of the system that enables a normalization-free dataset acquisition; changing the repetition rate by utilizing acoustic optical modulator and frequency-division circuit.

Single-band model of resonant inelastic x-ray scattering by quasiparticles in high-T(c) cuprate superconductors

We show that a simple model of noninteracting quasiparticles accurately describes resonant inelastic x-ray scattering (RIXS) experiments in the hole-doped cuprate superconductors. Band structure alone yields signatures previously attributed to collective magnetic modes, such as the dispersing peaks and nontrivial polarization dependence found in several experiments. We conclude that RIXS data can be explained without positing the existence of magnetic excitations that persist with increasing doping. In so doing we develop a formalism for RIXS in itinerant electron systems that accounts for the positively charged core hole exactly and discover a mechanism by which the core hole produces polarization dependence mimicking that of a magnetic system.

Simultaneous transitions in cuprate momentum-space topology and electronic symmetry breaking

The existence of electronic symmetry breaking in the underdoped cuprates and its disappearance with increased hole density p are now widely reported. However, the relation between this transition and the momentum-space (k-space) electronic structure underpinning the superconductivity has not yet been established. Here, we visualize the Q = 0 (intra-unit-cell) and Q ≠ 0 (density-wave) broken-symmetry states, simultaneously with the coherent k-space topology, for Bi₂Sr₂CaCu₂O(8+δ) samples spanning the phase diagram 0.06 ≤ p ≤ 0.23. We show that the electronic symmetry-breaking tendencies weaken with increasing p and disappear close to a critical doping p(c) = 0.19. Concomitantly, the coherent k-space topology undergoes an abrupt transition, from arcs to closed contours, at the same p(c). These data reveal that the k-space topology transformation in cuprates is linked intimately with the disappearance of the electronic symmetry breaking at a concealed critical point.

Anisotropic breakdown of Fermi liquid quasiparticle excitations in overdoped La₂-xSrxCuO₄

High-temperature superconductivity emerges from an un-conventional metallic state. This has stimulated strong efforts to understand exactly how Fermi liquids breakdown and evolve into an un-conventional metal. A fundamental question is how Fermi liquid quasiparticle excitations break down in momentum space. Here we show, using angle-resolved photoemission spectroscopy, that the Fermi liquid quasiparticle excitations of the overdoped superconducting cuprate La1.77Sr0.23CuO4 is highly anisotropic in momentum space. The quasiparticle scattering and residue behave differently along the Fermi surface and hence the Kadowaki-Wood's relation is not obeyed. This kind of Fermi liquid breakdown may apply to a wide range of strongly correlated metal systems where spin fluctuations are present.