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In various "strange" metals, electrons undergo Planckian dissipation, a strong and anomalous scattering that grows linearly with temperature, in contrast to the quadratic temperature dependence expected from the standard theory of metals. In some cuprates and pnictides, a linear dependence of the resistivity on magnetic field has also been considered anomalous - possibly an additional facet of Planckian dissipation. Here we show that the resistivity of the cuprate strange metals Nd-LSCO and LSCO is quantitatively consistent with the standard Boltzmann theory of electron motion in a magnetic field, in all aspects - field strength, field direction, temperature, and disorder level. The linear field dependence is found to be simply the consequence of scattering rate anisotropy. We conclude that Planckian dissipation is anomalous in its temperature dependence but not in its field dependence. The scattering rate in these cuprates does not depend on field, which means their Planckian dissipation is robust against fields up to at least 85 T.

We report thermopower measurements under hydrostatic pressure on the cuprate superconductor La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ (Nd-LSCO), at low-temperature in the normal state accessed by suppressing superconductivity with a magnetic field up to $H = 31$ T. Using a newly developed AC thermopower measurement technique suitable for high pressure and high field, we track the pressure evolution of the Seebeck coefficient $S$. At ambient pressure and low temperature, $S/T$ was recently found to suddenly increase in Nd-LSCO at the pseudogap critical doping $p^{\star} = 0.23$, consistent with a drop in carrier density $n$ from $n = 1 + p$ above $p^{\star}$ to $n = p$ below. Under a pressure of 2.0 GPa, we observe that this jump in $S/T$ is suppressed. This confirms a previous pressure study based on electrical resistivity and Hall effect which found $dp^{\star}/dP \simeq - 0.01$ holes/GPa, thereby reinforcing the interpretation that this effect is driven by the pressure-induced shift of the van Hove point. It implies that the pseudogap only exists when the Fermi surface is hole-like, which puts strong constraints on theories of the pseudogap phase. We also report thermopower measurements on Nd-LSCO and La$_{1.8-x}$Eu$_{0.2}$Sr$_x$CuO$_4$ in the charge density-wave phase near $p \sim 1/8$, which reveals a weakening of this phase under pressure., Comment: 9 pages, 5 figures

The Seebeck coefficient (thermopower) $S$ of the cuprate superconductor La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ was measured across its doping phase diagram (from $p = 0.12$ to $p = 0.25$), at various temperatures down to $T \simeq 2$ K, in the normal state accessed by suppressing superconductivity with a magnetic field up to $H = 37.5$ T. The magnitude of $S/T$ in the $T=0$ limit is found to suddenly increase, by a factor $\simeq 5$, when the doping is reduced below $p^{\star} = 0.23$, the critical doping for the onset of the pseudogap phase. This confirms that the pseudogap phase causes a large reduction of the carrier density $n$, consistent with a drop from $n = 1 + p$ above $p^{\star}$ to $n = p$ below $p^{\star}$, as previously inferred from measurements of the Hall coefficient, resistivity and thermal conductivity. When the doping is reduced below $p = 0.19$, a qualitative change is observed whereby $S/T$ decreases as $T \to 0$, eventually to reach negative values at $T=0$. In prior work on other cuprates, negative values of $S/T$ at $T \to 0$ were shown to result from a reconstruction of the Fermi surface caused by charge-density-wave (CDW) order. We therefore identify $p_{\rm CDW} \simeq 0.19$ as the critical doping beyond which there is no CDW-induced Fermi surface reconstruction. The fact that $p_{\rm CDW}$ is well separated from $p^{\star}$ reveals that there is a doping range below $p^{\star}$ where the transport signatures of the pseudogap phase are unaffected by CDW correlations, as previously found in YBa$_2$Cu$_3$O$_y$ and La$_{2-x}$Sr$_x$CuO$_4$., Comment: Present version includes a comparison with new x-ray data on Nd-LSCO by Gupta et al., arXiv:2012.08450. 13 pages, 12 figures, includes SM file

Five transport coefficients of the cuprate superconductor Bi$_2$Sr$_{2-x}$La$_x$CuO$_{6+\delta}$ were measured in the normal state down to low temperature, reached by applying a magnetic field (up to 66T) large enough to suppress superconductivity. The electrical resistivity, Hall coefficient, thermal conductivity, Seebeck coefficient and thermal Hall conductivity were measured in two overdoped single crystals, with La concentration $x = 0.2$ ($T_{\rm c}=18$K) and $x = 0.0$ ($T_{\rm c}=10$K). The samples have dopings $p$ very close to the critical doping $p^{\star}$ where the pseudogap phase ends. The resistivity displays a linear dependence on temperature whose slope is consistent with Planckian dissipation. The Hall number $n_{\rm H}$ decreases with reduced $p$, consistent with a drop in carrier density from $n = 1+p$ above $p^{\star}$ to $n=p$ below $p^{\star}$. This drop in $n_{\rm H}$ is concomitant with a sharp drop in the density of states inferred from prior NMR Knight shift measurements. The thermal conductivity satisfies the Wiedemann-Franz law, showing that the pseudogap phase at $T = 0$ is a metal whose fermionic excitations carry heat and charge as do conventional electrons. The Seebeck coefficient diverges logarithmically at low temperature, a signature of quantum criticality. The thermal Hall conductivity becomes negative at low temperature, showing that phonons are chiral in the pseudogap phase. Given the observation of these same properties in other, very different cuprates, our study provides strong evidence for the universality of these five signatures of the pseudogap phase and its critical point., Comment: Added references

The heat carriers responsible for the unexpectedly large thermal Hall conductivity of the cuprate Mott insulator La$_2$CuO$_4$ were recently shown to be phonons. However, the mechanism by which phonons in cuprates acquire chirality in a magnetic field is still unknown. Here, we report a similar thermal Hall conductivity in two cuprate Mott insulators with significantly different crystal structures and magnetic orders - Nd$_2$CuO$_4$ and Sr$_2$CuO$_2$Cl$_2$ - and show that two potential mechanisms can be excluded - the scattering of phonons by rare-earth impurities and by structural domains. Our comparative study further reveals that orthorhombicity, apical oxygens, the tilting of oxygen octahedra and the canting of spins out of the CuO$_2$ planes are not essential to the mechanism of chirality. Our findings point to a chiral mechanism coming from a coupling of acoustic phonons to the intrinsic excitations of the CuO$_2$ planes., Comment: 29 pages, 8 figures

A key unexplained feature of cuprate superconductors is the upturn in their normal state electrical resistivity $\rho(T)$ seen at low temperature inside the pseudogap phase. We examined this issue via measurements of the thermal conductivity $\kappa(T)$ down to 50 mK and in fields up to 17 T on the cuprate La$_{2-x}$Sr$_x$CuO$_4$ at dopings $p = 0.13$, 0.136, 0.143 and 0.18. At $p$ = 0.136, 0.143, and 0.18, we observe an initial increase of the electronic thermal conductivity $\kappa_0/T$ as a function of field, as expected in a $d$-wave superconductor. For $p$ = 0.136 and 0.143, further increasing the field then leads to a decrease of $\kappa_0/T$, which correlates with the onset of spin density-wave order as observed in neutron scattering experiments on the same samples. This decrease of $\kappa_0/T$ with field is imposed by the Wiedemann-Franz law and the high value of the resistivity in the high-field normal state of these samples. Our study therefore provides a direct link between magnetism and the resistivity upturn in the pseudogap phase of cuprates. We discuss this scenario in the broader context of other cuprates., Comment: 10 pages, 7 Figures, includes Supplementary Material

The nature of the pseudogap phase of cuprates remains a major puzzle. Although there are indications that this phase breaks various symmetries, there is no consensus on its fundamental nature. Although Fermi-surface, transport and thermodynamic signatures of the pseudogap phase are reminiscent of a transition into a phase with antiferromagnetic order, there is no evidence for an associated long-range magnetic order. Here we report measurements of the thermal Hall conductivity $\kappa_{\rm xy}$ in the normal state of four different cuprates (Nd-LSCO, Eu-LSCO, LSCO, and Bi2201) and show that a large negative $\kappa_{\rm xy}$ signal is a property of the pseudogap phase, appearing with the onset of that phase at the critical doping $p^*$. Since it is not due to charge carriers -- as it persists when the material becomes an insulator, at low doping -- or magnons -- as it exists in the absence of magnetic order -- or phonons -- since skew scattering is very weak, we attribute this $\kappa_{\rm xy}$ signal to exotic neutral excitations, presumably with spin chirality. The thermal Hall conductivity in the pseudogap phase of cuprates is reminiscent of that found in insulators with spin-liquid states. In the Mott insulator LCO, it attains the highest known magnitude of any insulator., Comment: 4 figures + 5 supplemental figures

The thermal conductivity $\kappa$ of the cuprate superconductor La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ was measured down to 50 mK in seven crystals with doping from $p=0.12$ to $p=0.24$, both in the superconducting state and in the magnetic field-induced normal state. We obtain the electronic residual linear term $\kappa_0/T$ as $T \to 0$ across the pseudogap critical point $p^{\star}= 0.23$. In the normal state, we observe an abrupt drop in $\kappa_0/T$ upon crossing below $p^{\star}$, consistent with a drop in carrier density $n$ from $1 + p$ to $p$, the signature of the pseudogap phase inferred from the Hall coefficient. A similar drop in $\kappa_0/T$ is observed at $H=0$, showing that the pseudogap critical point and its signatures are unaffected by the magnetic field. In the normal state, the Wiedemann-Franz law, $\kappa_0/T=L_0/\rho(0)$, is obeyed at all dopings, including at the critical point where the electrical resistivity $\rho(T)$ is $T$-linear down to $T \to 0$. We conclude that the non-superconducting ground state of the pseudogap phase at $T=0$ is a metal whose fermionic excitations carry heat and charge as conventional electrons do., Comment: 10 pages, including Supplementary Material

The three central phenomena of cuprate superconductors are linked by a common doping $p^{\star}$, where the enigmatic pseudogap phase ends, around which the superconducting phase forms a dome, and at which the resistivity exhibits an anomalous linear dependence on temperature as $T \to 0$. However, the fundamental nature of $p^{\star}$ remains unclear, in particular whether it marks a true quantum phase transition. We have measured 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 across $p^{\star}$. As a function of doping, we find that the electronic term $C_{\rm el}$ is strongly peaked at $p^{\star}$, where it exhibits a $-T$log$T$ dependence as $T \to 0$. These are the classic signatures of a quantum critical point, as observed in heavy-fermion and iron-based superconductors where their antiferromagnetic phase ends. We conclude that the pseudogap phase of cuprates ends at a quantum critical point, whose associated fluctuations are most likely involved in the $d$-wave pairing and the anomalous scattering., Comment: Includes Supplementary Information

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 $p^*$ $\leq$ $p_{FS}$. We derive this result from high-magnetic-field transport measurements in La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ 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., Comment: 15 pages, 5 figures, 7 supplemental figures

The thermal conductivity $\kappa$ of the Kondo insulator SmB$_6$ was measured at low temperature, down to 70 mK, in magnetic fields up to 15 T, on single crystals grown using both the floating-zone and the flux methods. The residual linear term $\kappa_0/T$ at $T \to 0$ is found to be zero in all samples, for all magnetic fields, in agreement with previous studies. There is therefore no clear evidence of fermionic heat carriers. In contrast to some prior data, we observe a large enhancement of $\kappa(T)$ with increasing field. The effect of field is anisotropic, depending on the relative orientation of field and heat current (parallel or perpendicular), and with respect to the cubic crystal structure. We interpret our data in terms of heat transport predominantly by phonons, which are scattered by magnetic impurities., Comment: publish version

The Seebeck coefficient $S$ of the cuprate YBa$_{2}$Cu$_{3}$O$_{y}$ was measured in magnetic fields large enough to suppress superconductivity, at hole dopings $p = 0.11$ and $p = 0.12$, for heat currents along the $a$ and $b$ directions of the orthorhombic crystal structure. For both directions, $S/T$ decreases and becomes negative at low temperature, a signature that the Fermi surface undergoes a reconstruction due to broken translational symmetry. Above a clear threshold field, a strong new feature appears in $S_{\rm b}$, for conduction along the $b$ axis only. We attribute this feature to the onset of 3D-coherent unidirectional charge-density-wave modulations seen by x-ray diffraction, also along the $b$ axis only. Because these modulations have a sharp onset temperature well below the temperature where $S/T$ starts to drop towards negative values, we infer that they are not the cause of Fermi-surface reconstruction. Instead, the reconstruction must be caused by the quasi-2D bidirectional modulations that develop at significantly higher temperature., Comment: 7 pages, 5 figures

We use the Nernst effect to delineate the boundary of the pseudogap phase in the temperature-doping phase diagram of cuprate superconductors. New data for the Nernst coefficient $\nu(T)$ of YBa$_{2}$Cu$_{3}$O$_{y}$ (YBCO), La$_{1.8-x}$Eu$_{0.2}$Sr$_x$CuO$_4$ (Eu-LSCO) and La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$ (Nd-LSCO) are presented and compared with previous data including La$_{2-x}$Sr$_x$CuO$_4$ (LSCO). The temperature $T_\nu$ at which $\nu/T$ deviates from its high-temperature behaviour is found to coincide with the temperature at which the resistivity deviates from its linear-$T$ dependence, which we take as the definition of the pseudogap temperature $T^\star$- in agreement with gap opening detected in ARPES data. We track $T^\star$ as a function of doping and find that it decreases linearly vs $p$ in all four materials, having the same value in the three LSCO-based cuprates, irrespective of their different crystal structures. At low $p$, $T^\star$ is higher than the onset temperature of the various orders observed in underdoped cuprates, suggesting that these orders are secondary instabilities of the pseudogap phase. A linear extrapolation of $T^\star(p)$ to $p=0$ yields $T^\star(p\to 0)\simeq T_N(0)$, the N\'eel temperature for the onset of antiferromagnetic order at $p=0$, suggesting that there is a link between pseudogap and antiferromagnetism. With increasing $p$, $T^\star(p)$ extrapolates linearly to zero at $p\simeq p_{\rm c2}$, the critical doping below which superconductivity emerges at high doping, suggesting that the conditions which favour pseudogap formation also favour pairing. We also use the Nernst effect to investigate how far superconducting fluctuations extend above $T_{\rm c}$, as a function of doping, and find that a narrow fluctuation regime tracks $T_{\rm c}$, and not $T^\star$. This confirms that the pseudogap phase is not a form of precursor superconductivity., Comment: 24 pages and 26 figures including Appendix

The electrical resistivity $\rho$ and Hall coefficient R$_H$ of the tetragonal single-layer cuprate Nd-LSCO were measured in magnetic fields up to $H = 37.5$ T, large enough to access the normal state at $T \to 0$, for closely spaced dopings $p$ across the pseudogap critical point at $p^\star = 0.235$. Below $p^\star$, both coefficients exhibit an upturn at low temperature, which gets more pronounced with decreasing $p$. Taken together, these upturns show that the normal-state carrier density $n$ at $T = 0$ drops upon entering the pseudogap phase. Quantitatively, it goes from $n = 1 + p$ at $p = 0.24$ to $n = p$ at $p = 0.20$. By contrast, the mobility does not change appreciably, as revealed by the magneto-resistance. The transition has a width in doping and some internal structure, whereby R$_H$ responds more slowly than $\rho$ to the opening of the pseudogap. We attribute this difference to a Fermi surface that supports both hole-like and electron-like carriers in the interval $0.2 < p < p^\star$, with compensating contributions to R$_H$. Our data are in excellent agreement with recent high-field data on YBCO and LSCO. The quantitative consistency across three different cuprates shows that a drop in carrier density from $1 + p$ to $p$ is a universal signature of the pseudogap transition at $T=0$. We discuss the implication of these findings for the nature of the pseudogap phase., Comment: 11 pages, 12 figures

Superconductivity in cuprates peaks in the doping regime between a metal at high p and an insulator at low p. Understanding how the material evolves from metal to insulator is a fundamental and open question. Early studies in high magnetic fields revealed that below some critical doping an insulator-like upturn appears in the resistivity of cuprates at low temperature, but its origin has remained a puzzle. Here we propose that this 'metal-to-insulator crossover' is due to a drop in carrier density n associated with the onset of the pseudogap phase at a critical doping p*. We use high-field resistivity measurements on LSCO to show that the upturns are quantitatively consistent with a drop from n=1+p above p* to n=p below p*, in agreement with high-field Hall data in YBCO. We demonstrate how previously reported upturns in the resistivity of LSCO, YBCO and Nd-LSCO are explained by the same universal mechanism: a drop in carrier density by 1.0 hole per Cu atom., Comment: 16 pages, 4 figures, Supplementary material (12 pages, 7 figures)

Close to a zero temperature transition between ordered and disordered electronic phases, quantum fluctuations can lead to a strong enhancement of the electron mass and to the emergence of competing phases such as superconductivity. A correlation between the existence of such a quantum phase transition and superconductivity is quite well established in some heavy fermion and iron-based superconductors and there have been suggestions that high temperature superconductivity in the copper oxide materials (cuprates) may also be driven by the same mechanism. Close to optimal doping, where the superconducting transition temperature $T_c$ is maximum in the cuprates, two different phases are known to compete with superconductivity: a poorly understood pseudogap phase and a charge ordered phase. Recent experiments have shown a strong increase in quasiparticle mass $m^*$ in the cuprate YBa$_2$Cu$_3$O$_{7-\delta}$ as optimal doping is approached suggesting that quantum fluctuations of the charge ordered phase may be responsible for the high-$T_c$ superconductivity. We have tested the robustness of this correlation between $m^*$ and $T_c$ by performing quantum oscillation studies on the stoichiometric compound YBa$_2$Cu$_4$O$_8$ under hydrostatic pressure. In contrast to the results for YBa$_2$Cu$_3$O$_{7-\delta}$, we find that in YBa$_2$Cu$_4$O$_8$ the mass decreases as $T_c$ increases under pressure. This inverse correlation between $m^*$ and $T_c$ suggests that quantum fluctuations of the charge order enhance $m^*$ but do not enhance $T_c$., Comment: 11 pages includes supplementary information

The Seebeck coefficient $S$ of the cuprate superconductor La$ _{2-x} $Sr$_{x} $CuO$ _{4}$ (LSCO) was measured in magnetic fields large enough to access the normal state at low temperatures, for a range of Sr concentrations from $x = 0.07$ to $x = 0.15$. For $x = 0.11$, 0.12, 0.125 and 0.13, $S/T$ decreases upon cooling to become negative at low temperatures. The same behavior is observed in the Hall coefficient $R_{H}(T)$. In analogy with other hole-doped cuprates at similar hole concentrations $p$, the negative $S$ and $R_{H}$ show that the Fermi surface of LSCO undergoes a reconstruction caused by the onset of charge-density-wave modulations. Such modulations have indeed been detected in LSCO by X-ray diffraction in precisely the same doping range. Our data show that in LSCO this Fermi-surface reconstruction is confined to $0.085 < p < 0.15$. We argue that in the field-induced normal state of LSCO, charge-density-wave order ends at a critical doping $p_{\rm CDW} = 0.15 \pm 0.005$, well below the pseudogap critical doping $p^\star \simeq 0.19$.

The pseudogap is a central puzzle of cuprate superconductors. Its connection to the Mott insulator at low doping $p$ remains ambiguous and its relation to the charge order that reconstructs the Fermi surface at intermediate $p$ is still unclear. Here we use measurements of the Hall coefficient in magnetic fields up to 88 T to show that Fermi-surface reconstruction by charge order in YBa$_2$Cu$_3$O$_y$ ends sharply at a critical doping $p = 0.16$, distinctly lower than the pseudogap critical point at $p^* = 0.19$. This shows that pseudogap and charge order are separate phenomena. We then find that the change of carrier density from $n = 1 + p$ in the conventional metal at high p to $n = p$ at low $p$ - a signature of the lightly doped cuprates - starts at $p^*$. This shows that pseudogap and antiferromagnetic Mott insulator are linked.

Quantum oscillations and negative Hall and Seebeck coefficients at low temperature and high magnetic field have shown the Fermi surface of underdoped cuprates to contain a small closed electron pocket. It is thought to result from a reconstruction by charge order, but whether it is the order seen by NMR and ultrasound above a threshold field or the short-range modulations seen by X-ray diffraction in zero field is unclear. Here we use measurements of the thermal Hall conductivity in YBCO to show that Fermi-surface reconstruction occurs only above a sharply defined onset field, equal to the transition field seen in ultrasound. This reveals that electrons do not experience long-range broken translational symmetry in the zero-field ground state, and hence in zero field there is no quantum critical point for the onset of charge order as a function of doping., Comment: 20 pages and 5 figures in Main text + 9 pages and 6 figures in Supplementary material

Nematicity has emerged as a key feature of cuprate superconductors, but its link to other fundamental properties such as superconductivity, charge order and the pseudogap remains unclear. Here we use measurements of transport anisotropy in YBa$_2$Cu$_3$O$_y$ to distinguish two types of nematicity. The first is associated with short-range charge-density-wave modulations in a doping region near $p = 0.12$. It is detected in the Nernst coefficient, but not in the resistivity. The second type prevails at lower doping, where there are spin modulations but no charge modulations. In this case, the onset of in-plane anisotropy - detected in both the Nernst coefficient and the resistivity - follows a line in the temperature-doping phase diagram that tracks the pseudogap energy. We discuss two possible scenarios for the latter nematicity., Comment: 8 pages and 7 figures. Main text and supplementary material now combined into single article

The recent detection of charge-density modulations in YBa2Cu3Oy and other cuprate superconductors raises new questions about the normal state of underdoped cuprates. In one class of theories, the modulations are intertwined with pairing in a dual state, expected to persist up to high magnetic fields as a vortex liquid. In support of such a state, specific heat and magnetisation data on YBa2Cu3Oy have been interpreted in terms of a vortex liquid persisting above the vortex-melting field Hvs at T = 0. Here we report high-field measurements of the electrical and thermal Hall conductivities in YBa2Cu3O6.54 that allow us to probe the Wiedemann-Franz law, a sensitive test of the presence of superconductivity in a metal. In the T = 0 limit, we find that the law is satisfied for fields immediately above Hvs. This rules out the existence of a vortex liquid and it places strict constraints on the nature of the normal state in underdoped cuprates., Comment: 8 pages, includes main text and supplementary information

Cuprate superconductors have a universal tendency to form charge density-wave (CDW) order which competes with superconductivity and is strongest at a doping $p \simeq 0.12$. Here we show that in the archetypal cuprate YBa$_{2}$Cu$_{3}$O$_{y}$ (YBCO) pressure suppresses charge order, but does not affect the pseudogap phase. This is based on transport measurements under pressure, which reveal that the onset of the pseudogap at $T^*$ is independent of pressure, while the negative Hall effect, a clear signature of CDW order in YBCO, is suppressed by pressure. We also find that pressure and magnetic field shift the superconducting transition temperature $T_{\rm c}$ of YBCO in the same way as a function of doping - but in opposite directions - and most effectively at $p \simeq 0.12$. This shows that the competition between superconductivity and CDW order can be tuned in two ways, either by suppressing superconductivity with field or suppressing CDW order by pressure. Based on existing high-pressure data and our own work, we observe that when CDW order is fully suppressed at high pressure, the so-called "1/8 anomaly" in the superconducting dome vanishes, revealing a smooth $T_{\rm c}$ dome which now peaks at $p \simeq 0.13$. We propose that this $T_{\rm c}$ dome is shaped by the competing effects of the pseudogap phase below its critical point $p^{\star} \sim 0.19$ and spin order at low doping., Comment: New Hall data added. 11 pages, 9 figures and 2 tables

The Fermi surface of a metal is the fundamental basis from which its properties can be understood. 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 the discovery of 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 demonstrates 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 caused 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., Comment: 23 pages, 5 figures

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 BaFe$_2$(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 in which 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 strongly violate the expectations from the conventional theory taking into account the observed mass enhancement near the QCP. These anomalous behaviours of the critical fields 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 realised in quantum critical superconductors., Comment: 9 pages

The metallic state of the underdoped high-Tc cuprates has remained an enigma: How may seemingly disconnected Fermi surface segments, observed in zero magnetic field as a result of the opening of a partial gap (the pseudogap), possess conventional quasiparticle properties? How do the small Fermi-surface pockets evidenced by the observation of quantum oscillations (QO) emerge as superconductivity is suppressed in high magnetic fields? Such QO, discovered in underdoped YBa2Cu3O6.5 (Y123) and YBa2Cu4O8 (Y124), signify the existence of a conventional Fermi surface (FS). However, due to the complexity of the crystal structures of Y123 and Y124 (CuO2 double-layers, CuO chains, low structural symmetry), it has remained unclear if the QO are specific to this particular family of cuprates. Numerous theoretical proposals have been put forward to explain the route toward QO, including materials-specific scenarios involving CuO chains and scenarios involving the quintessential CuO2 planes. Here we report the observation of QO in underdoped HgBa2CuO4+{\delta} (Hg1201), a model cuprate superconductor with individual CuO2 layers, high tetragonal symmetry, and no CuO chains. This observation proves that QO are a universal property of the underdoped CuO2 planes, and it opens the door to quantitative future studies of the metallic state and of the Fermi-surface reconstruction phenomenon in this structurally simplest cuprate., Comment: 17 pages, 5 figures

We report a combined study of the specific heat and de Haas-van Alphen effect in the iron-pnictide superconductor BaFe$_2$(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 (QCP) 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 QCP., Comment: 5 pages