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

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.

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.

Pauli-limit upper critical field of high-temperature superconductor La1.84Sr0.16CuO4

The upper critical field of a cuprate high-temperature superconductor, La_1.84Sr_0.16CuO₄, was investigated by high-frequency self-resonant contactless electrical conductivity measurements in magnetic fields up to 102 T. An irreversible transition was observed at 85 T (T = 4.2 K), defined as the upper critical field. The temperature-dependent upper critical field was argued on the basis of the Werthamer-Helfand-Hohenberg theory. The Pauli-limiting pair-breaking process with a small contribution of the spin-orbit coupling explained the first-order phase transition exhibiting a hysteresis observed at low temperatures.

Stabilization of three-dimensional charge order in YBa2Cu3O6+x via epitaxial growth

Incommensurate charge order (CO) has been identified as the leading competitor of high-temperature superconductivity in all major families of layered copper oxides, but the perplexing variety of CO states in different cuprates has confounded investigations of its impact on the transport and thermodynamic properties. The three-dimensional (3D) CO observed in YBa₂Cu₃O_6+x in high magnetic fields is of particular interest, because quantum transport measurements have revealed detailed information about the corresponding Fermi surface. Here we use resonant X-ray scattering to demonstrate 3D-CO in underdoped YBa₂Cu₃O_6+x films grown epitaxially on SrTiO₃ in the absence of magnetic fields. The resonance profiles indicate that Cu sites in the charge-reservoir layers participate in the CO state, and thus efficiently transmit CO correlations between adjacent CuO₂ bilayer units. The results offer fresh perspectives for experiments elucidating the influence of 3D-CO on the electronic properties of cuprates without the need to apply high magnetic fields.

In many cuprates the high temperature superconducting state competes with a charge ordered phase that has been difficult to investigate in detail. Here the authors show three-dimensional charge order can be stabilized in YBCO films and studied without using the high magnetic fields that are necessary in the bulk material.

Electron Doping of the Parent Cuprate La_{2}CuO_{4} without Cation Substitution

In the cuprates, carrier doping of the Mott insulating parent state is necessary to realize superconductivity as well as a number of other exotic states involving charge or spin density waves. Cation substitution is the primary method for doping carriers into these compounds, and is the only known method for electron doping in these materials. Here, we report electron doping without cation substitution in epitaxially stabilized thin films of La_{2}CuO_{4} grown via molecular-beam epitaxy. We use angle-resolved photoemission spectroscopy to directly measure their electronic structure and conclusively determine that these compounds are electron doped with a carrier concentration of 0.09±0.02 e^{-}/Cu. We propose that intrinsic defects, most likely oxygen vacancies, are the sources of doped electrons in these materials. Our results suggest a new approach to electron doping in the cuprates, one which could lead to a more detailed experimental understanding of their properties.

Long-range charge-density-wave proximity effect at cuprate/manganate interfaces

The interplay between charge density waves (CDWs) and high-temperature superconductivity is currently under intense investigation. Experimental research on this issue is difficult because CDW formation in bulk copper oxides is strongly influenced by random disorder, and a long-range-ordered CDW state in high magnetic fields is difficult to access with spectroscopic and diffraction probes. Here we use resonant X-ray scattering in zero magnetic field to show that interfaces with the metallic ferromagnet La2/3Ca1/3MnO3 greatly enhance CDW formation in the optimally doped high-temperature superconductor YBa2Cu3O6+δ (δ ∼ 1), and that this effect persists over several tens of nanometres. The wavevector of the incommensurate CDW serves as an internal calibration standard of the charge carrier concentration, which allows us to rule out any significant influence of oxygen non-stoichiometry, and to attribute the observed phenomenon to a genuine electronic proximity effect. Long-range proximity effects induced by heterointerfaces thus offer a powerful method to stabilize the charge-density-wave state in the cuprates and, more generally, to manipulate the interplay between different collective phenomena in metal oxides.

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.

Frustrated magnets in high magnetic fields-selected examples

An indispensable parameter to study strongly correlated electron systems is the magnetic field. Application of high magnetic fields allows the investigation, modification and control of different states of matter. Specifically for magnetic materials experimental tools applied in such fields are essential for understanding their fundamental properties. Here, we focus on selected high-field studies of frustrated magnetic materials that have been shown to host a broad range of fascinating new and exotic phases. We will give brief insights into the influence of geometrical frustration on the critical behavior of triangular-lattice antiferromagnets, the accurate determination of exchange constants in the high-field saturated state by use of electron spin resonance measurements, and the coupling of magnetic degrees of freedom to the lattice evidenced by ultrasound experiments. The latter technique as well allowed new, partially metastable phases in strong magnetic fields to be revealed.

Revisiting the vortex-core tunnelling spectroscopy in YBa2Cu3O7-δ

The observation by scanning tunnelling spectroscopy of Abrikosov vortex cores in the high-temperature superconductor YBa2Cu3O7-δ (Y123) has revealed a robust pair of electron-hole symmetric states at finite subgap energy. Their interpretation remains an open question because theory predicts a different signature in the vortex cores, characterized by a strong zero-bias conductance peak. Here, we present scanning tunnelling spectroscopy data on very homogeneous Y123 at 0.4 K revealing that the subgap features do not belong to vortices: they are actually observed everywhere along the surface with high spatial and energy reproducibility, even in the absence of magnetic field. Detailed analysis and modelling show that these states remain unpaired in the superconducting phase and belong to an incoherent channel, which contributes to the tunnelling signal in parallel with the superconducting density of states.

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.

Three-dimensional charge density wave order in YBa2Cu3O6.67 at high magnetic fields

Charge density wave (CDW) correlations have been shown to universally exist in cuprate superconductors. However, their nature at high fields inferred from nuclear magnetic resonance is distinct from that measured with x-ray scattering at zero and low fields. We combined a pulsed magnet with an x-ray free-electron laser to characterize the CDW in YBa2Cu3O6.67 via x-ray scattering in fields of up to 28 tesla. While the zero-field CDW order, which develops at temperatures below ~150 kelvin, is essentially two dimensional, at lower temperature and beyond 15 tesla, another three-dimensionally ordered CDW emerges. The field-induced CDW appears around the zero-field superconducting transition temperature; in contrast, the incommensurate in-plane ordering vector is field-independent. This implies that the two forms of CDW and high-temperature superconductivity are intimately linked.

Fragile charge order in the nonsuperconducting ground state of the underdoped high-temperature superconductors

The normal state in the hole underdoped copper oxide superconductors has proven to be a source of mystery for decades. The measurement of a small Fermi surface by quantum oscillations on suppression of superconductivity by high applied magnetic fields, together with complementary spectroscopic measurements in the hole underdoped copper oxide superconductors, point to a nodal electron pocket from charge order in YBa2Cu3(6+δ). Here, we report quantum oscillation measurements in the closely related stoichiometric material YBa2Cu4O8, which reveals similar Fermi surface properties to YBa2Cu3(6+δ), despite the nonobservation of charge order signatures in the same spectroscopic techniques, such as X-ray diffraction, that revealed signatures of charge order in YBa2Cu3(6+δ). Fermi surface reconstruction in YBa2Cu4O8 is suggested to occur from magnetic field enhancement of charge order that is rendered fragile in zero magnetic fields because of its potential unconventional nature and/or its occurrence as a subsidiary to more robust underlying electronic correlations.

Nodal bilayer-splitting controlled by spin-orbit interactions in underdoped high-Tc cuprates

The highest superconducting transition temperatures in the cuprates are achieved in bilayer and trilayer systems, highlighting the importance of interlayer interactions for high Tc. It has been argued that interlayer hybridization vanishes along the nodal directions by way of a specific pattern of orbital overlap. Recent quantum oscillation measurements in bilayer cuprates have provided evidence for a residual bilayer-splitting at the nodes that is sufficiently small to enable magnetic breakdown tunneling at the nodes. Here we show that several key features of the experimental data can be understood in terms of weak spin-orbit interactions naturally present in bilayer systems, whose primary effect is to cause the magnetic breakdown to be accompanied by a spin flip. These features can now be understood to include the equidistant set of three quantum oscillation frequencies, the asymmetry of the quantum oscillation amplitudes in c-axis transport compared to ab-plane transport, and the anomalous magnetic field angle dependence of the amplitude of the side frequencies suggestive of small effective g-factors. We suggest that spin-orbit interactions in bilayer systems can further affect the structure of the nodal quasiparticle spectrum in the superconducting phase. PACS numbers: 71.45.Lr, 71.20.Ps, 71.18.+y.

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.

Field-induced density wave in the heavy-fermion compound CeRhIn₅

Strong electron correlations lead to a variety of distinct ground states, such as magnetism, charge order or superconductivity. Understanding the competitive or cooperative interplay between neighbouring phases is an outstanding challenge in physics. CeRhIn₅ is a prototypical example of a heavy-fermion superconductor: it orders anti-ferromagnetically below 3.8 K, and moderate hydrostatic pressure suppresses the anti-ferromagnetic order inducing unconventional superconductivity. Here we show evidence for a phase transition to a state akin to a density wave (DW) under high magnetic fields (>27 T) in high-quality single crystal microstructures of CeRhIn₅. The DW is signalled by a hysteretic anomaly in the in-plane resistivity accompanied by non-linear electrical transport, yet remarkably thermodynamic measurements suggest that the phase transition involves only small portions of the Fermi surface. Such a subtle order might be a common feature among correlated electron systems, reminiscent of the similarly subtle charge DW state in 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.

Two-component energy spectrum of cuprates in the pseudogap phase and its evolution with temperature and at charge ordering

In the search for mechanisms of high-temperature superconductivity it is critical to know the electronic spectrum in the pseudogap phase from which superconductivity evolves. The lack of angle-resolved photoemission data for every cuprate family precludes an agreement as to its structure, doping and temperature dependence and the role of charge ordering. Here we show that, in the entire Fermi-liquid-like regime that is ubiquitous in underdoped cuprates, the spectrum consists of holes on the Fermi arcs and an electronic pocket. We argue that experiments on the Hall coefficient identify the latter as a permanent feature at doped hole concentration x > 0.08-0.10, in contrast to the idea of the Fermi surface reconstruction via charge ordering. The longstanding issue of the origin of the negative Hall coefficient in YBCO and Hg1201 at low temperature is resolved: the electronic contribution prevails as mobility of the latter (evaluated by the Dingle temperature) becomes temperature independent, while the mobility of holes scattered by the short-wavelength charge density waves decreases.

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.

Physics, emergence, and the connectome

Experience with complex systems more primitive than the brain teaches important lessons about big data in biology. Chief among them is that physical laws, relationships among measured things that are always true, emerge out of chaos, not the other way around. Correct prediction (as opposed to incorrect prediction) from large data sets requires understanding of these laws. The reason is that the same processes that make them also make the system wildly error-intolerant if the errors are too large. This instability routinely causes computer simulations of even primitive systems to fail by enabling mistakes to cascade into ever worsening falsehoods. The more complex and sophisticated the system is, the more intolerant to errors it becomes.

Charge order and its connection with Fermi-liquid charge transport in a pristine high-T(c) cuprate

Electronic inhomogeneity appears to be an inherent characteristic of the enigmatic cuprate superconductors. Here we report the observation of charge-density-wave correlations in the model cuprate superconductor HgBa2CuO(4+δ) (T(c)=72 K) via bulk Cu L3-edge-resonant X-ray scattering. At the measured hole-doping level, both the short-range charge modulations and Fermi-liquid transport appear below the same temperature of about 200 K. Our result points to a unifying picture in which these two phenomena are preceded at the higher pseudogap temperature by q=0 magnetic order and the build-up of significant dynamic antiferromagnetic correlations. The magnitude of the charge modulation wave vector is consistent with the size of the electron pocket implied by quantum oscillation and Hall effect measurements for HgBa2CuO(4+δ) and with corresponding results for YBa2Cu3O(6+δ), which indicates that charge-density-wave correlations are universally responsible for the low-temperature quantum oscillation phenomenon.

Connecting high-field quantum oscillations to zero-field electron spectral functions in the underdoped cuprates

The nature of the pseudogap regime of cuprate superconductors at low hole density remains unresolved. It has a number of seemingly distinct experimental signatures: a suppression of the paramagnetic spin susceptibility at high temperatures, low-energy electronic excitations that extend over arcs in the Brillouin zone, X-ray detection of charge-density wave order at intermediate temperatures and quantum oscillations at high magnetic fields and low temperatures. Here we show that a model of competing charge-density wave and superconducting orders provides a unified description of the intermediate and low-temperature regimes. We treat quantum oscillations at high field beyond semiclassical approximations, and find clear and robust signatures of an electron pocket compatible with existing observations; we also predict oscillations due to additional hole pockets. In the zero-field and intermediate temperature regime, we compute the electronic spectrum in the presence of thermally fluctuating charge-density and superconducting orders. Our results are compatible with experimental trends.