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 C_el/T is strongly peaked at p* (where C_el 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^3-5, 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.

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.

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}.

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.

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.

Universal heat conduction in the iron arsenide superconductor KFe2As2: evidence of a d-wave state

The thermal conductivity κ of the iron arsenide superconductor KFe2As2 was measured down to 50 mK for a heat current parallel and perpendicular to the tetragonal c axis. A residual linear term at T→0, κ(0)/T is observed for both current directions, confirming the presence of nodes in the superconducting gap. Our value of κ(0)/T in the plane is equal to that reported by Dong et al. [Phys. Rev. Lett. 104, 087005 (2010)] for a sample whose residual resistivity ρ(0) was 10 times larger. This independence of κ(0)/T on impurity scattering is the signature of universal heat transport, a property of superconducting states with symmetry-imposed line nodes. This argues against an s-wave state with accidental nodes. It favors instead a d-wave state, an assignment consistent with five additional properties: the magnitude of the critical scattering rate Γ(c) for suppressing T(c) to zero; the magnitude of κ(0)/T, and its dependence on current direction and on magnetic field; the temperature dependence of κ(T).

The metallic transport of (TMTSF)2X organic conductors close to the superconducting phase

Comparing resistivity data of the quasi-one-dimensional superconductors (TMTSF)2PF6 and (TMTSF)2ClO4 along the least conducting c(⋆)-axis and along the high conductivity a-axis as a function of temperature and pressure, a low temperature regime is observed in which a unique scattering time governs the transport along both directions of these anisotropic conductors. However, the pressure dependence of the anisotropy implies a large pressure dependence of the interlayer coupling. This is in agreement with the results of first-principles density functional theory calculations implying methyl group hyperconjugation in the TMTSF molecule. In this low temperature regime, both materials exhibit for ρ(c) a temperature dependence aT + bT(2). Taking into account the strong pressure dependence of the anisotropy, the T-linear ρ(c) is found to correlate with the suppression of the superconducting Tc, in close analogy with ρ(a) data. This work reveals the domain of existence of the three-dimensional coherent regime in the generic (TMTSF)2X phase diagram and provides further support for the correlation between T-linear resistivity and superconductivity in non-conventional superconductors.

Doping dependence of heat transport in the iron-arsenide superconductor Ba(Fe(1-x)Co(x))2As2: from isotropic to a strongly k-dependent gap structure

The temperature and magnetic field dependence of the in-plane thermal conductivity kappa of the iron-arsenide superconductor Ba(Fe(1-x)Co(x))2As2 was measured down to T approximately 50 mK and up to H = 15 T as a function of Co concentration x in the range 0.048 < or = x < or = 0.114. At H = 0, a negligible residual linear term in kappa/T as T-->0 at all x shows that the superconducting gap has no nodes in the ab plane anywhere in the phase diagram. However, while the slow H dependence of kappa(H) at T-->0 in the underdoped regime is consistent with a superconducting gap that is large everywhere on the Fermi surface, the rapid increase in kappa(H) observed in the overdoped regime shows that the gap acquires a deep minimum somewhere on the Fermi surface. Outside the antiferromagnetic-orthorhombic phase, the superconducting gap structure has a strongly k-dependent amplitude.

Small Fermi surface pockets in underdoped high temperature superconductors: observation of Shubnikov-de Haas oscillations in YBa2Cu4O8

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 breakdown in the paramagnetic phase of a pure metal

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.