Metal-insulator quantum critical point beneath the high Tc superconducting dome

Direct measurement of the evolution of magnetism and superconductivity toward the quantum critical point

Nontrivial quantum states can be realized in the vicinity of the quantum critical point (QCP) in many strongly correlated electron systems. In particular, an emergence of unconventional superconductivity around the QCP strongly suggests that the quantum critical fluctuations play a central role in the superconducting pairing mechanism. However, a clear signature of the direct coupling between the superconducting pairing states and the quantum criticality has not yet been elucidated by the microscopic probes. Herein, we present muon spin rotation/relaxation and neutron diffraction measurements in the superconducting dome of CeCo(In1 - xZnx)5. It was found that a magnetically ordered state develops at x≥ 0.03, coexisting with the superconductivity. The magnitude of the ordered magnetic moment is continuously reduced with decreasing x, and it disappears below x∼ 0.03, indicating a second-order phase transition and the presence of the QCP at this critical Zn concentration. Furthermore, the magnetic penetration depth diverges toward the QCP. These facts provide evidence for the intimate coupling between quantum criticality and Cooper pairing.

Unusual Pressure-Induced Quantum Phase Transition from Superconducting to Charge-Density Wave State in Rare-Earth-Based Heusler LuPd_{2}In Compound

We investigate the pressure effects on the electronic structures and phonon properties of rare-earth-based cubic-Heusler compound LuPd_{2}In, on the basis of ab initio density functional theory. We find the occurrence of intriguing phase transition from the superconducting (SC) to charge-density wave (CDW) state under pressure (P), which is quite unusual in that the pressure is detrimental to the CDW state in usual systems. The SC transition temperature T_{C} of LuPd_{2}In increases first with increasing pressure, up to P_{C}≈28  GPa, above which a quantum phase transition into the CDW state takes place. This extraordinary transition originates from the occurrence of phonon softening instability at a special q=M in the Brillouin zone. We thus propose that LuPd_{2}In is a quite unique material, in which the CDW quantum critical point is realized under the SC dome by applying the pressure.

Extent of Fermi-surface reconstruction in the high-temperature superconductor HgBa2CuO4+δ

High magnetic fields have revealed a surprisingly small Fermi surface in underdoped cuprates, possibly resulting from Fermi-surface reconstruction due to an order parameter that breaks translational symmetry of the crystal lattice. A crucial issue concerns the doping extent of such a state and its relationship to the principal pseudogap and superconducting phases. We employ pulsed magnetic-field measurements on the cuprate [Formula: see text]Cu[Formula: see text] to identify signatures of Fermi-surface reconstruction from a sign change of the Hall effect and a peak in the temperature-dependent planar resistivity. We trace the termination of Fermi-surface reconstruction to two hole concentrations where the superconducting upper critical fields are found to be enhanced. One of these points is associated with the pseudogap endpoint near optimal doping. These results connect the Fermi-surface reconstruction to both superconductivity and the pseudogap phenomena.

Unusual Interplay between Superconductivity and Field-Induced Charge Order in YBa_{2}Cu_{3}O_{y}

We present a detailed study of the temperature (T) and magnetic field (H) dependence of the electronic density of states (DOS) at the Fermi level, as deduced from specific heat and Knight shift measurements in underdoped YBa_{2}Cu_{3}O_{y}. We find that the DOS becomes field independent above a characteristic field H_{DOS}, and that the H_{DOS}(T) line displays an unusual inflection near the onset of the long-range 3D charge-density wave order. The unusual S shape of H_{DOS}(T) is suggestive of two mutually exclusive orders that eventually establish a form of cooperation in order to coexist at low T. On theoretical grounds, such a collaboration could result from the stabilization of a pair-density wave state, which calls for further investigation in this region of the phase diagram.

Emergence of Quantum Critical Behavior in Metallic Quantum-Well States of Strongly Correlated Oxides

Controlling quantum critical phenomena in strongly correlated electron systems, which emerge in the neighborhood of a quantum phase transition, is a major challenge in modern condensed matter physics. Quantum critical phenomena are generated from the delicate balance between long-range order and its quantum fluctuation. So far, the nature of quantum phase transitions has been investigated by changing a limited number of external parameters such as pressure and magnetic field. We propose a new approach for investigating quantum criticality by changing the strength of quantum fluctuation that is controlled by the dimensional crossover in metallic quantum well (QW) structures of strongly correlated oxides. With reducing layer thickness to the critical thickness of metal-insulator transition, crossover from a Fermi liquid to a non-Fermi liquid has clearly been observed in the metallic QW of SrVO₃ by in situ angle-resolved photoemission spectroscopy. Non-Fermi liquid behavior with the critical exponent α = 1 is found to emerge in the two-dimensional limit of the metallic QW states, indicating that a quantum critical point exists in the neighborhood of the thickness-dependent Mott transition. These results suggest that artificial QW structures provide a unique platform for investigating novel quantum phenomena in strongly correlated oxides in a controllable fashion.

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.

Critical Behavior in Doping-Driven Metal-Insulator Transition on Single-Crystalline Organic Mott-FET

We present the carrier transport properties in the vicinity of a doping-driven Mott transition observed at a field-effect transistor (FET) channel using a single crystal of the typical two-dimensional organic Mott insulator κ-(BEDT-TTF)₂CuN(CN)₂Cl (κ-Cl). The FET shows a continuous metal-insulator transition (MIT) as electrostatic doping proceeds. The phase transition appears to involve two-step crossovers, one in Hall measurement and the other in conductivity measurement. The crossover in conductivity occurs around the conductance quantum e²/h, and hence is not associated with "bad metal" behavior, which is in stark contrast to the MIT in half-filled organic Mott insulators or that in doped inorganic Mott insulators. Through in-depth scaling analysis of the conductivity, it is found that the above carrier transport properties in the vicinity of the MIT can be described by a high-temperature Mott quantum critical crossover, which is theoretically argued to be a ubiquitous feature of various types of Mott transitions.

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.

Single reconstructed Fermi surface pocket in an underdoped single-layer cuprate superconductor

The observation of a reconstructed Fermi surface via quantum oscillations in hole-doped cuprates opened a path towards identifying broken symmetry states in the pseudogap regime. However, such an identification has remained inconclusive due to the multi-frequency quantum oscillation spectra and complications accounting for bilayer effects in most studies. We overcome these impediments with high-resolution measurements on the structurally simpler cuprate HgBa₂CuO_4+δ (Hg1201), which features one CuO₂ plane per primitive unit cell. We find only a single oscillatory component with no signatures of magnetic breakdown tunnelling to additional orbits. Therefore, the Fermi surface comprises a single quasi-two-dimensional pocket. Quantitative modelling of these results indicates that a biaxial charge density wave within each CuO₂ plane is responsible for the reconstruction and rules out criss-crossed charge stripes between layers as a viable alternative in Hg1201. Lastly, we determine that the characteristic gap between reconstructed pockets is a significant fraction of the pseudogap energy.

The identification of broken symmetry states in underdoped cuprate superconductors via quantum oscillation measurements remains inconclusive. Here, Chan et al. report the reconstructed Fermi surface of HgBa₂CuO_4+δ comprises only a single pocket indicating a biaxial charge-density-wave order within each CuO₂ plane.

Superconductivity and Charge Density Wave in ZrTe3-xSex

Charge density wave (CDW), the periodic modulation of the electronic charge density, will open a gap on the Fermi surface that commonly leads to decreased or vanishing conductivity. On the other hand superconductivity, a commonly believed competing order, features a Fermi surface gap that results in infinite conductivity. Here we report that superconductivity emerges upon Se doping in CDW conductor ZrTe₃ when the long range CDW order is gradually suppressed. Superconducting critical temperature T_c(x) in ZrTe_3−xSe_x (0 ≤ x ≤ 0.1) increases up to 4 K plateau for 0.04 ≤ x ≤ 0.07. Further increase in Se content results in diminishing T_c and filametary superconductivity. The CDW modes from Raman spectra are observed in x = 0.04 and 0.1 crystals, where signature of ZrTe₃ CDW order in resistivity vanishes. The electronic-scattering for high T_c crystals is dominated by local CDW fluctuations at high temperatures, the resistivity is linear up to highest measured T = 300 K and contributes to substantial in-plane anisotropy.

Commensurate antiferromagnetic excitations as a signature of the pseudogap in the tetragonal high-Tc cuprate HgBa2CuO(4+δ)

Antiferromagnetic correlations have been argued to be the cause of the d-wave superconductivity and the pseudogap phenomena exhibited by the cuprates. Although the antiferromagnetic response in the pseudogap state has been reported for a number of compounds, there exists no information for structurally simple HgBa₂CuO_4+δ. Here we report neutron-scattering results for HgBa₂CuO_4+δ (superconducting transition temperature T_c≈71 K, pseudogap temperature T*≈305 K) that demonstrate the absence of the two most prominent features of the magnetic excitation spectrum of the cuprates: the X-shaped ‘hourglass' response and the resonance mode in the superconducting state. Instead, the response is Y-shaped, gapped and significantly enhanced below T*, and hence a prominent signature of the pseudogap state.

In the cuprates, antiferromagnetic correlations might be the cause of the pseudogap phenomenon. Here the authors use neutron scattering on the tetragonal cuprate HgBa₂CuO_4+δ revealing commensurate antiferromagnetic excitations as a signature of the pseudogap state.

Quantum Critical Origin of the Superconducting Dome in SrTiO_{3}

We expand the well-known notion that quantum criticality can induce superconductivity by proposing a concrete mechanism for superconductivity due to quantum ferroelectric fluctuations. To this end, we investigate the origin of superconductivity in doped SrTiO_{3} using a combination of density functional and strong coupling theories within the framework of quantum criticality. Our density functional calculations of the ferroelectric soft mode frequency as a function of doping reveal a crossover related to quantum paraelectricity at a doping level coincident with the experimentally observed top of the superconducting dome. Thus, we suggest a model in which the soft mode fluctuations provide the pairing interaction for superconductivity carriers. Within our model, the low doping limit of the superconducting dome is explained by the emergence of the Fermi surface, and the high doping limit by departure from the quantum critical regime. We predict that the highest critical temperature will increase and shift to lower carrier doping with increasing ^{18}O isotope substitution, a scenario that is experimentally verifiable. Our model is applicable to other quantum paraelectrics, such as KTaO_{3}.

Evidence for a small hole pocket in the Fermi surface of underdoped YBa2Cu3Oy

In underdoped cuprate superconductors, the Fermi surface undergoes a reconstruction that produces a small electron pocket, but whether there is another, as yet, undetected portion to the Fermi surface is unknown. Establishing the complete topology of the Fermi surface is key to identifying the mechanism responsible for its reconstruction. Here we report evidence for a second Fermi pocket in underdoped YBa2Cu3Oy, detected as a small quantum oscillation frequency in the thermoelectric response and in the c-axis resistance. The field-angle dependence of the frequency shows that it is a distinct Fermi surface, and the normal-state thermopower requires it to be a hole pocket. A Fermi surface consisting of one electron pocket and two hole pockets with the measured areas and masses is consistent with a Fermi-surface reconstruction by the charge-density-wave order observed in YBa2Cu3Oy, provided other parts of the reconstructed Fermi surface are removed by a separate mechanism, possibly the pseudogap.

Anomalous critical fields in quantum critical superconductors

Fluctuations around an antiferromagnetic quantum critical point (QCP) are believed to lead to unconventional superconductivity and in some cases to high-temperature superconductivity. However, the exact mechanism by which this occurs remains poorly understood. The iron-pnictide superconductor BaFe₂(As_1−xP_x)₂ is perhaps the clearest example to date of a high-temperature quantum critical superconductor, and so it is a particularly suitable system to study how the quantum critical fluctuations affect the superconducting state. Here we show that the proximity of the QCP yields unexpected anomalies in the superconducting critical fields. We find that both the lower and upper critical fields do not follow the behaviour, predicted by conventional theory, resulting from the observed mass enhancement near the QCP. Our results imply that the energy of superconducting vortices is enhanced, possibly due to a microscopic mixing of antiferromagnetism and superconductivity, suggesting that a highly unusual vortex state is realized in quantum critical superconductors.

Superconductivity in the iron pnictides is believed to be related to quantum critical fluctuations. Putzke et al. observe unexpected anomalies in the critical fields of BaFe₂(As_1−xP_x)₂ that emerge close to its magnetic critical point, which they argue is a generic feature of quantum critical superconductivity.

Normal-state nodal electronic structure in underdoped high-Tc copper oxides

An outstanding problem in the field of high-transition-temperature (high-Tc) superconductivity is the identification of the normal state out of which superconductivity emerges in the mysterious underdoped regime. The normal state uncomplicated by thermal fluctuations can be studied using applied magnetic fields that are sufficiently strong to suppress long-range superconductivity at low temperatures. Proposals in which the normal ground state is characterized by small Fermi surface pockets that exist in the absence of symmetry breaking have been superseded by models based on the existence of a superlattice that breaks the translational symmetry of the underlying lattice. Recently, a charge superlattice model that positions a small electron-like Fermi pocket in the vicinity of the nodes (where the superconducting gap is minimum) has been proposed as a replacement for the prevalent superlattice models that position the Fermi pocket in the vicinity of the pseudogap at the antinodes (where the superconducting gap is maximum). Although some ingredients of symmetry breaking have been recently revealed by crystallographic studies, their relevance to the electronic structure remains unresolved. Here we report angle-resolved quantum oscillation measurements in the underdoped copper oxide YBa2Cu3O6 + x. These measurements reveal a normal ground state comprising electron-like Fermi surface pockets located in the vicinity of the nodes, and also point to an underlying superlattice structure of low frequency and long wavelength with features in common with the charge order identified recently by complementary spectroscopic techniques.

Emerging superconductivity hidden beneath charge-transfer insulators

In many of today's most interesting materials, strong interactions prevail upon the magnetic moments, the electrons, and the crystal lattice, forming strong links between these different aspects of the system. Particularly, in two-dimensional cuprates, where copper is either five- or six-fold coordinated, superconductivity is commonly induced by chemical doping which is deemed to be mandatory by destruction of long-range antiferromagnetic order of 3d⁹ Cu²⁺ moments. Here we show that superconductivity can be induced in Pr₂CuO₄, where copper is four-fold coordinated. We induced this novel quantum state of Pr₂CuO₄ by realizing pristine square-planar coordinated copper in the copper-oxygen planes, thus, resulting in critical superconducting temperatures even higher than by chemical doping. Our results demonstrate new degrees of freedom, i.e., coordination of copper, for the manipulation of magnetic and superconducting order parameters in quantum materials.

Fermi-liquid computation of the phase diagram of high-Tc cuprate superconductors with an orbital antiferromagnetic pseudogap

A 4-parameter Fermi-liquid calculation of the high-Tc cuprate phase diagram is reported. Simultaneously accounted for are the special doping densities of 5% and 16%, the d-wave functional form of the (orbital antiferromagnetic) pseudogap, the measured Tc, superconducting gap, pseudogap and superfluid density as a function of doping, the particle-hole doping asymmetry and the half-filling spin wave velocity.

Direct measurement of the upper critical field in cuprate superconductors

In the quest to increase the critical temperature Tc of cuprate superconductors, it is essential to identify the factors that limit the strength of superconductivity. The upper critical field Hc2 is a fundamental measure of that strength, yet there is no agreement on its magnitude and doping dependence in cuprate superconductors. Here we show that the thermal conductivity can be used to directly detect Hc2 in the cuprates YBa2Cu3Oy, YBa2Cu4O8 and Tl2Ba2CuO6+δ, allowing us to map out Hc2 across the doping phase diagram. It exhibits two peaks, each located at a critical point where the Fermi surface of YBa2Cu3Oy is known to undergo a transformation. Below the higher critical point, the condensation energy, obtained directly from Hc2, suffers a sudden 20-fold collapse. This reveals that phase competition-associated with Fermi-surface reconstruction and charge-density-wave order-is a key limiting factor in the superconductivity of cuprates.

Momentum-dependent charge correlations in YBa2Cu3O6+δ superconductors probed by resonant X-ray scattering: evidence for three competing phases

We use resonant x-ray scattering to determine the momentum-dependent charge correlations in YBa(2)Cu(3) O(6.55) samples with highly ordered chain arrays of oxygen acceptors (ortho-II structure). The results reveal nearly critical, biaxial charge density wave (CDW) correlations at in-plane wave vectors (0.315, 0) and (0, 0.325). The corresponding scattering intensity exhibits a strong uniaxial anisotropy. The CDW amplitude and correlation length are enhanced as superconductivity is weakened by an external magnetic field. Analogous experiments are carried out on a YBa(2)Cu(3)O(6.6) crystal with a dilute concentration of spinless (Zn) impurities, which had earlier been shown to nucleate incommensurate magnetic order. Compared to pristine crystals with the same doping level, the CDW amplitude and correlation length are found to be strongly reduced. These results indicate a three-phase competition between spin-modulated, charge-modulated, and superconducting states in underdoped YBa(2)Cu(3)O(6+δ).

Phase competition in trisected superconducting dome

A detailed phenomenology of low energy excitations is a crucial starting point for microscopic understanding of complex materials, such as the cuprate high-temperature superconductors. Because of its unique momentum-space discrimination, angle-resolved photoemission spectroscopy (ARPES) is ideally suited for this task in the cuprates, where emergent phases, particularly superconductivity and the pseudogap, have anisotropic gap structure in momentum space. We present a comprehensive doping- and temperature-dependence ARPES study of spectral gaps in Bi(2)Sr(2)CaCu(2)O(8+δ), covering much of the superconducting portion of the phase diagram. In the ground state, abrupt changes in near-nodal gap phenomenology give spectroscopic evidence for two potential quantum critical points, p = 0.19 for the pseudogap phase and p = 0.076 for another competing phase. Temperature dependence reveals that the pseudogap is not static below T(c) and exists p > 0.19 at higher temperatures. Our data imply a revised phase diagram that reconciles conflicting reports about the endpoint of the pseudogap in the literature, incorporates phase competition between the superconducting gap and pseudogap, and highlights distinct physics at the edge of the superconducting dome.

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.

Cyclotron motion in the vicinity of a Lifshitz transition in graphite

Graphite, a model (semi)metal with trigonally warped bands, is investigated with a magnetoabsorption experiment and viewed as an electronic system in the vicinity of the Lifshitz transition. A characteristic pattern of up to 20 cyclotron resonance harmonics has been observed. This large number of resonances, their relative strengths and characteristic shapes trace the universal properties of the electronic states near a separatrix in momentum space. Quantum-mechanical perturbative methods with respect to the trigonal warping term hardly describe the data which are, on the other hand, fairly well reproduced within a quasiclassical approach and conventional band structure model. Trigonal symmetry is preserved in graphite in contrast to a similar system, bilayer graphene.

Measurement of magnetic susceptibility in pulsed magnetic fields using a proximity detector oscillator

We present a novel susceptometer with a particularly small spatial footprint and no moving parts. The susceptometer is suitable for use in systems with limited space where magnetic measurements may not have been previously possible, such as in pressure cells and rotators, as well as in extremely high pulsed fields. The susceptometer is based on the proximity detector oscillator, which has a broad dynamic resonant frequency range and has so far been used predominantly for transport measurements. We show that for insulating samples, the resonance frequency behavior as a function of field consists of a magnetoresistive and an inductive component, originating, respectively, from the sensor coil and the sample. The response of the coil is modeled, and upon subtraction of the magnetoresistive component the dynamic magnetic susceptibility and magnetization can be extracted. We successfully measure the magnetization of the organic molecular magnets Cu(H(2)O)(5)(VOF(4))(H(2)O) and [Cu(HF(2))(pyz)(2)]BF(4) in pulsed magnetic fields and by comparing the results to that from a traditional extraction susceptometer confirm that the new system can be used to measure and observe magnetic susceptibilities and phase transitions.

Near doping-independent pocket area from an antinodal Fermi surface instability in underdoped high temperature superconductors

Fermi surface models applied to the underdoped cuprates predict the small pocket area to be strongly dependent on doping whereas quantum oscillations in YBa(2)Cu(3)O(6+x) find precisely the opposite to be true--seemingly at odds with the Luttinger volume. We show that such behavior can be explained by an incommensurate antinodal Fermi surface nesting-type instability--further explaining the doping-dependent superstructures seen in cuprates using scanning tunneling microscopy. We develop a Fermi surface reconstruction scheme involving orthogonal density waves in two dimensions and show that their incommensurate behavior requires momentum-dependent coupling. A cooperative modulation of the charge and bond strength is therefore suggested.

Coexistence of bulk superconductivity and charge density wave in CuxZrTe3

We report the coexistence of bulk superconductivity with T(c)=3.8  K and charge density wave (CDW) in Cu intercalated quasi-two-dimensional crystals of ZrTe(3). The Cu intercalation results in the expansion of the unit cell orthogonal to the Zr-Zr metal chains and partial filling of CDW energy gap. We present anisotropic parameters of the superconducting state. We also show that the contribution of CDW to the scattering mechanism is anisotropic in the a-b plane. The dominant scattering mechanism in the normal state for both ZrTe(3) and Cu(0.05)ZrTe(3) along the b axis is the electron-electron umklapp scattering.

Protected nodal electron pocket from multiple-Q ordering in underdoped high temperature superconductors

A multiple wave vector (Q) reconstruction of the Fermi surface is shown to yield a profoundly different electronic structure to that characteristic of single wave vector reconstruction, despite their proximity in energy. We consider the specific case in which ordering is generated by Q(x)=[2πa,0] and Q(y)=[0,2πb] (in which a=b=1/4)-similar to those identified in neutron diffraction and scanning tunneling microscopy experiments-and more generally show that an isolated pocket adjacent to the nodal point k(nodal)=[±π/2,±π/2] is a protected feature of such a multiple-Q model, potentially corresponding to the nodal "Fermi arcs" observed in photoemission and the small size of the electronic heat capacity found in high magnetic fields-importantly, containing electron carriers which can yield negative Hall and Seebeck coefficients observed in high magnetic fields.

Quantum oscillations in the high-Tc cuprates

We review recent progress in the study of quantum oscillations as a tool for uniquely probing low-energy electronic excitations in high-T(c) cuprate superconductors. Quantum oscillations in the underdoped cuprates reveal that a close correspondence with Landau Fermi-liquid behaviour persists in the accessed regions of the phase diagram, where small pockets are observed. Quantum oscillation results are viewed in the context of momentum-resolved probes such as photoemission, and evidence examined from complementary experiments for potential explanations for the transformation from a large Fermi surface into small sections. Indications from quantum oscillation measurements of a low-energy Fermi surface instability at low dopings under the superconducting dome at the metal-insulator transition are reviewed, and potential implications for enhanced superconducting temperatures are discussed.

Energy-dependent enhancement of the electron-coupling spectrum of the underdoped Bi2Sr2CaCu2O(8+δ) superconductor

We have determined the electron-coupling spectrum of superconducting Bi2Sr2CaCu2O(8+δ) from high-resolution angle-resolved photoemission spectra by two deconvolution-free robust methods. As hole concentration decreases, the coupling spectral weight at low energies ≲15  meV shows a twofold and nearly band-independent enhancement, while that around ∼65  meV increases moderately, and that in ≳130  meV decreases leading to a crossover of dominant coupling excitation between them. Our results suggest the competition among multiple screening effects, and provide important clues to the source of sufficiently strong low-energy coupling, λ(LE)≈1, in an underdoped system.