Giant thermal Hall conductivity in the pseudogap phase of cuprate superconductors.

The nature of the pseudogap phase of the copper oxides ('cuprates') remains a puzzle. Although there are indications that this phase breaks various symmetries, there is no consensus on its fundamental nature1. Fermi-surface, transport and thermodynamic signatures of the pseudogap phase are reminiscent of a transition into a phase with antiferromagnetic order, but evidence for an associated long-range magnetic order is still lacking2. Here we report measurements of the thermal Hall conductivity (in the x-y plane, κxy) in the normal state of four different cuprates-La1.6-xNd0.4SrxCuO4, La1.8-xEu0.2SrxCuO4, La2-xSrxCuO4 and Bi2Sr2-xLaxCuO6+δ. We show that a large negative κxy signal is a property of the pseudogap phase, appearing at its critical hole doping, p*. It is also a property of the Mott insulator at p ≈ 0, where κxy has the largest reported magnitude of any insulator so far3. Because this negative κxy signal grows as the system becomes increasingly insulating electrically, it cannot be attributed to conventional mobile charge carriers. Nor is it due to magnons, because it exists in the absence of magnetic order. Our observation is reminiscent of the thermal Hall conductivity of insulators with spin-liquid states4-6, pointing to neutral excitations with spin chirality7 in the pseudogap phase of cuprates.

Thermodynamic signatures of quantum criticality in cuprate superconductors.

The three central phenomena of cuprate (copper oxide) superconductors are linked by a common doping level p*-at which the enigmatic pseudogap phase ends and the resistivity exhibits an anomalous linear dependence on temperature, and around which the superconducting phase forms a dome-shaped area in the phase diagram1. However, the fundamental nature of p* remains unclear, in particular regarding whether it marks a true quantum phase transition. Here we measure the specific heat C of the cuprates Eu-LSCO and Nd-LSCO at low temperature in magnetic fields large enough to suppress superconductivity, over a wide doping range2 that includes p*. As a function of doping, we find that Cel/T is strongly peaked at p* (where Cel is the electronic contribution to C) and exhibits a log(1/T) dependence as temperature T tends to zero. These are the classic thermodynamic signatures of a quantum critical point3-5, as observed in heavy-fermion6 and iron-based7 superconductors at the point where their antiferromagnetic phase comes to an end. We conclude that the pseudogap phase of cuprates ends at a quantum critical point, the associated fluctuations of which are probably involved in d-wave pairing and the anomalous scattering of charge carriers.

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.

Quasiparticle mass enhancement close to the quantum critical point in BaFe2(As(1-x)P(x))2.

We report a combined study of the specific heat and de Haas-van Alphen effect in the iron-pnictide superconductor BaFe2(As(1-x)P(x))2. Our data when combined with results for the magnetic penetration depth give compelling evidence for the existence of a quantum critical point close to x=0.30 which affects the majority of the Fermi surface by enhancing the quasiparticle mass. The results show that the sharp peak in the inverse superfluid density seen in this system results from a strong increase in the quasiparticle mass at the quantum critical point.

Pseudogap phase of cuprate superconductors confined by Fermi surface topology.

The properties of cuprate high-temperature superconductors are largely shaped by competing phases whose nature is often a mystery. Chiefly among them is the pseudogap phase, which sets in at a doping p* that is material-dependent. What determines p* is currently an open question. Here we show that the pseudogap cannot open on an electron-like Fermi surface, and can only exist below the doping p FS at which the large Fermi surface goes from hole-like to electron-like, so that p* ≤ p FS. We derive this result from high-magnetic-field transport measurements in La1.6-x Nd0.4Sr x CuO4 under pressure, which reveal a large and unexpected shift of p* with pressure, driven by a corresponding shift in p FS. This necessary condition for pseudogap formation, imposed by details of the Fermi surface, is a strong constraint for theories of the pseudogap phase. Our finding that p* can be tuned with a modest pressure opens a new route for experimental studies of the pseudogap.

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-x)P(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.