The quasi-two-dimensional metal Sr2RuO4 is one of the best characterized unconventional superconductors, yet the nature of its superconducting order parameter is still under debate1–3. This ...information is crucial to determine the pairing mechanism of Cooper pairs. Here we use ultrasound velocity to probe the superconducting state of Sr2RuO4. This thermodynamic probe is sensitive to the symmetry of the material, and therefore, it can help in identifying the symmetry of the superconducting order parameter4,5. Indeed, we observe a sharp jump in the shear elastic constant c66 as the temperature is increased across the superconducting transition. This directly implies that the superconducting order parameter is of a two-component nature. On the basis of symmetry arguments and given the other known properties of Sr2RuO4 (refs. 6–8), we discuss which states are compatible with this requirement and propose that the two-component order parameter {dxz; dyz} is the most likely candidate.Ultrasound experiments show that the superconducting order parameter in strontium ruthenate must have two components.
The nature of the pseudogap phase of cuprates remains a major puzzle1,2. One of its signatures is a large negative thermal Hall conductivity3, whose origin is as yet unknown. This is observed even in ...the undoped Mott insulator La2CuO4, in which the charge carriers are localized and therefore cannot be responsible. Here, we show that the thermal Hall conductivity of La2CuO4 is roughly isotropic; that is, for heat transport parallel and normal to the CuO2 planes, it is nearly the same. This shows that the Hall response must come from phonons, as they are the only heat carriers that are able to move with the same ease both normal and parallel to the planes4. For doping levels higher than the critical doping level at which the pseudogap phase ends, both La1.6−xNd0.4SrxCuO4 and La1.8−xEu0.2SrxCuO4 show no thermal Hall signal for a heat current normal to the planes, which establishes that phonons have zero Hall response outside the pseudogap phase. Inside the pseudogap phase, the phonons must become chiral to generate the Hall response, but the mechanism by which this happens remains to be identified. It must be intrinsic (from a coupling of phonons to their electronic environment) rather than extrinsic (from structural defects or impurities), as these are the same on both sides of critical doping.Thermal transport measurements show that there is a thermal Hall effect in the out-of-plane direction in two cuprates in the pseudogap regime. This indicates that phonons are carrying the heat and that they have a handedness of unknown origin.
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 nature
. 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 lacking
. Here we report measurements of the thermal Hall conductivity (in the x-y plane, κ
) in the normal state of four different cuprates-La
Nd
Sr
CuO
, La
Eu
Sr
CuO
, La
Sr
CuO
and Bi
Sr
La
CuO
. We show that a large negative κ
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 κ
has the largest reported magnitude of any insulator so far
. Because this negative κ
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 states
, pointing to neutral excitations with spin chirality
in the pseudogap phase of cuprates.
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 diagram
. 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 range
that includes p*. As a function of doping, we find that C
/T is strongly peaked at p* (where C
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 point
, as observed in heavy-fermion
and iron-based
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.
The perfectly linear temperature dependence of the electrical resistivity observed as T → 0 in a variety of metals close to a quantum critical point1–4 is a major puzzle of condensed-matter physics5. ...Here we show that T-linear resistivity as T → 0 is a generic property of cuprates, associated with a universal scattering rate. We measured the low-temperature resistivity of the bilayer cuprate Bi2Sr2CaCu2O8+δ and found that it exhibits a T-linear dependence with the same slope as in the single-layer cuprates Bi2Sr2CuO6+δ (ref. 6), La1.6−xNd0.4SrxCuO4 (ref. 7) and La2−xSrxCuO4 (ref. 8), despite their very different Fermi surfaces and structural, superconducting and magnetic properties. We then show that the T-linear coefficient (per CuO2 plane), A1□, is given by the universal relation A1□TF = h/2e2, where e is the electron charge, h is the Planck constant and TF is the Fermi temperature. This relation, obtained by assuming that the scattering rate 1/τ of charge carriers reaches the Planckian limit9,10, whereby ħ/τ = kBT, works not only for hole-doped cuprates6–8,11,12 but also for electron-doped cuprates13,14, despite the different nature of their quantum critical point and strength of their electron correlations.
The thermal conductivityκof the quasi-2D organic spin-liquid candidateEtMe3SbPd(dmit)22(dmit-131) was measured at low temperatures, down to 0.07 K. We observe a vanishingly small residual linear ...termκ0/T, inκ/TvsTasT→0. This shows that the low-energy excitations responsible for the sizable residual linear termγin the specific heatC, seen inC/TvsTasT→0, are localized. We conclude that there are no mobile gapless excitations in this spin-liquid candidate, in contrast with a prior study of dmit-131 that reported a largeκ0/T value , Science 328, 1246 (2010). Our study shows that dmit-131 is in fact similar toκ−(BEDT−TTF)2Cu2(CN)3, another quasi-2D organic spin-liquid candidate where a vanishingly smallκ0/Tand a sizableγare seen. We attribute heat conduction in these organic insulators without magnetic order to phonons undergoing strong spin-phonon scattering, as observed in several other spin-liquid materials.
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.
We report the observation of Shubnikov-de Haas oscillations in the underdoped cuprate superconductor YBa2Cu4O8 (Y124). For fields aligned along the c axis, the frequency of the oscillations is ...660+/-30 T, which corresponds to approximately 2.4% of the total area of the first Brillouin zone. The effective mass of the quasiparticles on this orbit is measured to be 2.7+/-0.3 times the free electron mass. Both the frequency and mass are comparable to those recently observed for ortho-II YBa2Cu3O6.5 (Y123-II). We show that although small Fermi surface pockets may be expected from band-structure calculations in Y123-II, no such pockets are predicted for Y124. Our results therefore imply that these small pockets are a generic feature of the copper oxide plane in underdoped cuprates.
Fermi-liquid theory (the standard model of metals) has been challenged by the discovery of anomalous properties in an increasingly large number of metals. The anomalies often occur near a quantum ...critical point-a continuous phase transition in the limit of absolute zero, typically between magnetically ordered and paramagnetic phases. Although not understood in detail, unusual behaviour in the vicinity of such quantum critical points was anticipated nearly three decades ago by theories going beyond the standard model. Here we report electrical resistivity measurements of the 3d metal MnSi, indicating an unexpected breakdown of the Fermi-liquid model-not in a narrow crossover region close to a quantum critical point where it is normally expected to fail, but over a wide region of the phase diagram near a first-order magnetic transition. In this regime, corrections to the Fermi-liquid model are expected to be small. The range in pressure, temperature and applied magnetic field over which we observe an anomalous temperature dependence of the electrical resistivity in MnSi is not consistent with the crossover behaviour widely seen in quantum critical systems. This may suggest the emergence of a well defined but enigmatic quantum phase of matter.
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