Superconductivity in (Ba,K)SbO3.

(Ba,K)BiO3 constitute an interesting class of superconductors, where the remarkably high superconducting transition temperature Tc of 30 K arises in proximity to charge density wave order. However, the precise mechanism behind these phases remains unclear. Here, enabled by high-pressure synthesis, we report superconductivity in (Ba,K)SbO3 with a positive oxygen-metal charge transfer energy in contrast to (Ba,K)BiO3. The parent compound BaSbO3-δ shows a larger charge density wave gap compared to BaBiO3. As the charge density wave order is suppressed via potassium substitution up to 65%, superconductivity emerges, rising up to Tc = 15 K. This value is lower than the maximum Tc of (Ba,K)BiO3, but higher by more than a factor of two at comparable potassium concentrations. The discovery of an enhanced charge density wave gap and superconductivity in (Ba,K)SbO3 indicates that strong oxygen-metal covalency may be more essential than the sign of the charge transfer energy in the main-group perovskite superconductors.

Change of carrier density at the pseudogap critical point of a cuprate superconductor.

The pseudogap is a partial gap in the electronic density of states that opens in the normal (non-superconducting) state of cuprate superconductors and whose origin is a long-standing puzzle. Its connection to the Mott insulator phase at low doping (hole concentration, p) remains ambiguous and its relation to the charge order that reconstructs the Fermi surface at intermediate doping is still unclear. Here we use measurements of the Hall coefficient in magnetic fields up to 88 tesla to show that Fermi-surface reconstruction by charge order in the cuprate YBa2Cu3Oy ends sharply at a critical doping p = 0.16 that is distinctly lower than the pseudogap critical point p* = 0.19 (ref. 11). This shows that the pseudogap and charge order are separate phenomena. We find that the change in carrier density n from n = 1 + p in the conventional metal at high doping (ref. 12) to n = p at low doping (ref. 13) starts at the pseudogap critical point. This shows that the pseudogap and the antiferromagnetic Mott insulator are linked.

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.

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

The value of the upper critical field Hc2, a fundamental characteristic of the superconducting state, has been subject to strong controversy in high-Tc 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 Hc2 values claimed previously and with the interpretation that the charge density wave (CDW) reduces Hc2 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.

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].

Bounding the pseudogap with a line of phase transitions in YBa2Cu3O6+δ.

Close to optimal doping, the copper oxide superconductors show 'strange metal' behaviour, suggestive of strong fluctuations associated with a quantum critical point. Such a critical point requires a line of classical phase transitions terminating at zero temperature near optimal doping inside the superconducting 'dome'. The underdoped region of the temperature-doping phase diagram from which superconductivity emerges is referred to as the 'pseudogap' because evidence exists for partial gapping of the conduction electrons, but so far there is no compelling thermodynamic evidence as to whether the pseudogap is a distinct phase or a continuous evolution of physical properties on cooling. Here we report that the pseudogap in YBa2Cu3O6+δ is a distinct phase, bounded by a line of phase transitions. The doping dependence of this line is such that it terminates at zero temperature inside the superconducting dome. From this we conclude that quantum criticality drives the strange metallic behaviour and therefore superconductivity in the copper oxide superconductors.

Ideal charge-density-wave order in the high-field state of superconducting YBCO.

The existence of charge-density-wave (CDW) correlations in cuprate superconductors has now been established. However, the nature of the CDW ground state has remained uncertain because disorder and the presence of superconductivity typically limit the CDW correlation lengths to only a dozen unit cells or less. Here we explore the field-induced 3D CDW correlations in extremely pure detwinned crystals of YBa2Cu3O2 (YBCO) ortho-II and ortho-VIII at magnetic fields in excess of the resistive upper critical field ([Formula: see text]) where superconductivity is heavily suppressed. We observe that the 3D CDW is unidirectional and possesses a long in-plane correlation length as well as significant correlations between neighboring CuO2 planes. It is significant that we observe only a single sharply defined transition at a critical field proportional to [Formula: see text], given that the field range used in this investigation overlaps with other high-field experiments including quantum oscillation measurements. The correlation volume is at least two to three orders of magnitude larger than that of the zero-field CDW. This is by far the largest CDW correlation volume observed in any cuprate crystal and so is presumably representative of the high-field ground state of an "ideal" disorder-free cuprate.

Influence of Spin-Orbit Coupling in Iron-Based Superconductors.

We report on the influence of spin-orbit coupling (SOC) in Fe-based superconductors via application of circularly polarized spin and angle-resolved photoemission spectroscopy. We combine this technique in representative members of both the Fe-pnictides (LiFeAs) and Fe-chalcogenides (FeSe) with tight-binding calculations to establish an ubiquitous modification of the electronic structure in these materials imbued by SOC. At low energy, the influence of SOC is found to be concentrated on the hole pockets, where the largest superconducting gaps are typically found. This effect varies substantively with the k_{z} dispersion, and in FeSe we find SOC to be comparable to the energy scale of orbital order. These results contest descriptions of superconductivity in these materials in terms of pure spin-singlet eigenstates, raising questions regarding the possible pairing mechanisms and role of SOC therein.

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.

Logarithmic Upturn in Low-Temperature Electronic Transport as a Signature of d-Wave Order in Cuprate Superconductors.

In cuprate superconductors, high magnetic fields have been used extensively to suppress superconductivity and expose the underlying normal state. Early measurements revealed insulatinglike behavior in underdoped material versus temperature T, in which resistivity increases on cooling with a puzzling log(1/T) form. We instead use microwave measurements of flux-flow resistivity in YBa_{2}Cu_{3}O_{6+y} and Tl_{2}Ba_{2}CuO_{6+δ} to study charge transport deep inside the superconducting phase, in the low-temperature and low-field regime. Here, the transition from metallic low-temperature resistivity (dρ/dT>0) to a log(1/T) upturn persists throughout the superconducting doping range, including a regime at high carrier dopings in which the field-revealed normal-state resistivity is Fermi-liquid-like. The log(1/T) form is thus likely a signature of d-wave superconducting order, and the field-revealed normal state's log(1/T) resistivity may indicate the free-flux-flow regime of a phase-disordered d-wave superconductor.

Teaching critical thinking.

The ability to make decisions based on data, with its inherent uncertainties and variability, is a complex and vital skill in the modern world. The need for such quantitative critical thinking occurs in many different contexts, and although it is an important goal of education, that goal is seldom being achieved. We argue that the key element for developing this ability is repeated practice in making decisions based on data, with feedback on those decisions. We demonstrate a structure for providing suitable practice that can be applied in any instructional setting that involves the acquisition of data and relating that data to scientific models. This study reports the results of applying that structure in an introductory physics laboratory course. Students in an experimental condition were repeatedly instructed to make and act on quantitative comparisons between datasets, and between data and models, an approach that is common to all science disciplines. These instructions were slowly faded across the course. After the instructions had been removed, students in the experimental condition were 12 times more likely to spontaneously propose or make changes to improve their experimental methods than a control group, who performed traditional experimental activities. The students in the experimental condition were also four times more likely to identify and explain a limitation of a physical model using their data. Students in the experimental condition also showed much more sophisticated reasoning about their data. These differences between the groups were seen to persist into a subsequent course taken the following year.

Orbital symmetry of charge-density-wave order in La1.875Ba0.125CuO4 and YBa2Cu3O6.67.

Recent theories of charge-density-wave (CDW) order in high-temperature superconductors have predicted a primarily d CDW orbital symmetry. Here, we report on the orbital symmetry of CDW order in the canonical cuprate superconductors La1.875Ba0.125CuO4 (LBCO) and YBa2Cu3O6.67 (YBCO), using resonant soft X-ray scattering and a model mapped to the CDW orbital symmetry. From measurements sensitive to the O sublattice, we conclude that LBCO has predominantly s' CDW orbital symmetry, in contrast to the d orbital symmetry recently reported in other cuprates. Furthermore, we show for YBCO that the CDW orbital symmetry differs along the a and b crystal axes and that these both differ from LBCO. This work highlights CDW orbital symmetry as an additional key property that distinguishes the different cuprate families. We discuss how the CDW symmetry may be related to the '1/8-anomaly' and to static spin ordering.

Quasiparticle Scattering off Defects and Possible Bound States in Charge-Ordered YBa_{2}Cu_{3}O_{y}.

We report the NMR observation of a skewed distribution of ^{17}O Knight shifts when a magnetic field quenches superconductivity and induces long-range charge-density-wave (CDW) order in YBa_{2}Cu_{3}O_{y}. This distribution is explained by an inhomogeneous pattern of the local density of states N(E_{F}) arising from quasiparticle scattering off, yet unidentified, defects in the CDW state. We argue that the effect is most likely related to the formation of quasiparticle bound states, as is known to occur, under specific circumstances, in some metals and superconductors (but not in the CDW state, in general, except for very few cases in 1D materials). These observations should provide insight into the microscopic nature of the CDW, especially regarding the reconstructed band structure and the sensitivity to disorder.

Crossover from Collective to Incoherent Spin Excitations in Superconducting Cuprates Probed by Detuned Resonant Inelastic X-Ray Scattering.

Spin excitations in the overdoped high temperature superconductors Tl_{2}Ba_{2}CuO_{6+δ} and (Bi,Pb)_{2}(Sr,La)_{2}CuO_{6+δ} were investigated by resonant inelastic x-ray scattering (RIXS) as functions of doping and detuning of the incoming photon energy above the Cu-L_{3} absorption peak. The RIXS spectra at optimal doping are dominated by a paramagnon feature with peak energy independent of photon energy, similar to prior results on underdoped cuprates. Beyond optimal doping, the RIXS data indicate a sharp crossover to a regime with a strong contribution from incoherent particle-hole excitations whose maximum shows a fluorescencelike shift upon detuning. The spectra of both compound families are closely similar, and their salient features are reproduced by exact-diagonalization calculations of the single-band Hubbard model on a finite cluster. The results are discussed in the light of recent transport experiments indicating a quantum phase transition near optimal doping.

Magnetic-field-induced charge-stripe order in the high-temperature superconductor YBa2Cu3Oy.

Electronic charges introduced in copper-oxide (CuO(2)) planes generate high-transition-temperature (T(c)) superconductivity but, under special circumstances, they can also order into filaments called stripes. Whether an underlying tendency towards charge order is present in all copper oxides and whether this has any relationship with superconductivity are, however, two highly controversial issues. To uncover underlying electronic order, magnetic fields strong enough to destabilize superconductivity can be used. Such experiments, including quantum oscillations in YBa(2)Cu(3)O(y) (an extremely clean copper oxide in which charge order has not until now been observed) have suggested that superconductivity competes with spin, rather than charge, order. Here we report nuclear magnetic resonance measurements showing that high magnetic fields actually induce charge order, without spin order, in the CuO(2) planes of YBa(2)Cu(3)O(y). The observed static, unidirectional, modulation of the charge density breaks translational symmetry, thus explaining quantum oscillation results, and we argue that it is most probably the same 4a-periodic modulation as in stripe-ordered copper oxides. That it develops only when superconductivity fades away and near the same 1/8 hole doping as in La(2-x)Ba(x)CuO(4) (ref. 1) suggests that charge order, although visibly pinned by CuO chains in YBa(2)Cu(3)O(y), is an intrinsic propensity of the superconducting planes of high-T(c) copper oxides.

Symmetry of charge order in cuprates.

Charge-ordered ground states permeate the phenomenology of 3d-based transition metal oxides, and more generally represent a distinctive hallmark of strongly correlated states of matter. The recent discovery of charge order in various cuprate families has fuelled new interest into the role played by this incipient broken symmetry within the complex phase diagram of high-T(c) superconductors. Here, we use resonant X-ray scattering to resolve the main characteristics of the charge-modulated state in two cuprate families: Bi2Sr(2-x)La(x)CuO(6+δ) (Bi2201) and YBa2Cu3O(6+y) (YBCO). We detect no signatures of spatial modulations along the nodal direction in Bi2201, thus clarifying the inter-unit-cell momentum structure of charge order. We also resolve the intra-unit-cell symmetry of the charge-ordered state, which is revealed to be best represented by a bond order with modulated charges on the O-2p orbitals and a prominent d-wave character. These results provide insights into the origin and microscopic description of charge order in cuprates, and its interplay with superconductivity.

Thermal Conductivity of the Iron-Based Superconductor FeSe: Nodeless Gap with a Strong Two-Band Character.

The thermal conductivity κ of the iron-based superconductor FeSe was measured at temperatures down to 75 mK in magnetic fields up to 17 T. In a zero magnetic field, the electronic residual linear term in the T=0 K limit, κ_{0}/T, is vanishingly small. The application of a magnetic field B causes an exponential increase in κ_{0}/T initially. Those two observations show that there are no zero-energy quasiparticles that carry heat and therefore no nodes in the superconducting gap of FeSe. The full field dependence of κ_{0}/T has the classic two-step shape of a two-band superconductor: a first rise at very low field, with a characteristic field B^{⋆}≪B_{c2}, and then a second rise up to the upper critical field B_{c2}. This shows that the superconducting gap is very small (but finite) on one of the pockets in the Fermi surface of FeSe. We estimate that the minimum value of the gap, Δ_{min}, is an order of magnitude smaller than the maximum value, Δ_{max}.

Broken rotational symmetry in the pseudogap phase of a high-T(c) superconductor.

The nature of the pseudogap phase is a central problem in the effort to understand the high-transition-temperature (high-T(c)) copper oxide superconductors. A fundamental question is what symmetries are broken when the pseudogap phase sets in, which occurs when the temperature decreases below a value T*. There is evidence from measurements of both polarized neutron diffraction and the polar Kerr effect that time-reversal symmetry is broken, but at temperatures that differ significantly from one another. Broken rotational symmetry was detected from both resistivity measurements and inelastic neutron scattering at low doping, and from scanning tunnelling spectroscopy at low temperature, but showed no clear relation to T*. Here we report the observation of a large in-plane anisotropy of the Nernst effect in YBa(2)Cu(3)O(y) that sets in precisely at T* throughout the doping phase diagram. We show that the CuO chains of the orthorhombic lattice are not responsible for this anisotropy, which is therefore an intrinsic property of the CuO(2) planes. We conclude that the pseudogap phase is an electronic state that strongly breaks four-fold rotational symmetry. This narrows the range of possible states considerably, pointing to stripe or nematic order.

Impact of quenched oxygen disorder on charge density wave order in YBa2Cu3O6+x.

The competition between superconductivity and charge density wave (CDW) order in underdoped cuprates has now been widely reported, but the role of disorder in this competition has yet to be fully resolved. A central question is whether disorder sets the length scale of the CDW order, for instance by pinning charge density fluctuations or disrupting an otherwise long-range order. Using resonant soft x-ray scattering, we investigate the sensitivity of CDW order in YBa2Cu3O6+x (YBCO) to varying levels of oxygen disorder. We find that quench cooling YBCO6.67 (YBCO6.75) crystals to destroy their o-V and o-VIII (o-III) chains decreases the intensity of the CDW superlattice peak by a factor of 1.9 (1.3), but has little effect on the CDW correlation length, incommensurability, and temperature dependence. This reveals that while quenched oxygen disorder influences the CDW order parameter, the spatial extent of the CDW order is insensitive to the level of quenched oxygen disorder and may instead be a consequence of competition with superconductivity.

A multi-component Fermi surface in the vortex state of an underdoped high-Tc superconductor.

To understand the origin of superconductivity, it is crucial to ascertain the nature and origin of the primary carriers available to participate in pairing. Recent quantum oscillation experiments on high-transition-temperature (high-T(c)) copper oxide superconductors have revealed the existence of a Fermi surface akin to that in normal metals, comprising fermionic carriers that undergo orbital quantization. The unexpectedly small size of the observed carrier pocket, however, leaves open a variety of possibilities for the existence or form of any underlying magnetic order, and its relation to d-wave superconductivity. Here we report experiments on quantum oscillations in the magnetization (the de Haas-van Alphen effect) in superconducting YBa(2)Cu(3)O(6.51) that reveal more than one carrier pocket. In particular, we find evidence for the existence of a much larger pocket of heavier mass carriers playing a thermodynamically dominant role in this hole-doped superconductor. Importantly, characteristics of the multiple pockets within this more complete Fermi surface impose constraints on the wavevector of any underlying order and the location of the carriers in momentum space. These constraints enable us to construct a possible density-wave model with spiral or related modulated magnetic order, consistent with experimental observations.