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Multilayered cuprates possess not only the highest superconducting temperature transition but also offer a unique platform to study disorder-free CuO$_2$ planes and the interplay between competing orders with superconductivity. Here, we study the underdoped trilayer cuprate HgBa$_2$Ca$_2$Cu$_3$O$_{8+ \delta}$ and we report the first quantum oscillation and Hall effect measurements in magnetic field up to 88 T. A careful analysis of the complex spectra of quantum oscillations strongly supports the coexistence of an antiferromagnetic order in the inner plane and a charge order in the outer planes. The presence of an ordered antiferromagnetic metallic state that extends deep in the superconducting phase is a key ingredient that supports magnetically mediated pairing interaction in cuprates., Comment: 6+5 pages, 4+6 figures

Despite immense efforts, the cuprate Fermi surface (FS) has been unambiguously determined in only two distinct, low-temperature regions of the phase diagram: a large hole-like FS at high doping, and a small electron-like pocket associated with charge-density-wave driven FS reconstruction at moderate doping. Moreover, there exists incomplete understanding of the reconstructed state, which is stabilized by high magnetic fields, and its connection with the normal state that consists of arc-like remnants of the large underlying FS. Part of the problem is that compound-specific idiosyncrasies, such as disorder effects and low structural symmetry, can obscure the fundamental properties of the quintessential CuO$_2$ planes. Here we present planar magnetotransport measurements for moderately-doped HgBa$_2$CuO$_{4+{\delta}}$ that enable a quantitative understanding of the phase transition between the normal and reconstructed states and of the charge transport in the latter, and that demonstrate that the quasiparticle scattering rate in both states is due to Umklapp scattering. Building on prior insights, we furthermore arrive at a comprehensive understanding of the evolution of the planar transport properties throughout the entire cuprate phase diagram.

High-$T_{\rm{c}}$ cuprate superconductors host spin, charge and lattice instabilities. In particular, in the antiferromagnetic glass phase, over a large doping range, lanthanum based cuprates display a glass-like spin freezing with antiferromagnetic correlations. Previously, sound velocity anomalies in La$_{2-x}$Sr$_{x}$CuO$_4$ (LSCO) for hole doping $p\geq 0.145$ were reported and interpreted as arising from a coupling of the lattice to the magnetic glass [Frachet, Vinograd et al., Nat. Phys. 16, 1064-1068 (2020)]. Here we report both sound velocity and attenuation in LSCO $p=0.12$, i.e. at a doping level for which the spin freezing temperature is the highest. Using high magnetic fields and comparing with nuclear magnetic resonance (NMR) measurements, we confirm that the anomalies in the low temperature ultrasound properties of LSCO are produced by a coupling between the lattice and the spin glass. Moreover, we show that both sound velocity and attenuation can be simultaneously accounted for by a simple phenomenological model originally developed for canonical spin glasses. Our results point towards a strong competition between superconductivity and spin freezing, tuned by the magnetic field. A comparison of different acoustic modes suggests that the slow spin fluctuations have a nematic character., Comment: 12 pages, 8 figures

Solid 4He may acquire superfluid characteristics due to the frustration of the solid phase at grain boundaries. Here, we show that an analogous effect occurs in systems with competition among charge-density-waves (CDWs) and superconductivity in the presence of disorder, as cuprate or dichalcogenide superconductors. The CDWs breaks apart in domains with topologically protected filamentary superconductivity (FSC) at the interfaces. Transport experiments carried out in underdoped cuprates with the magnetic field acting as a control parameter are shown to be in excellent agreement with the theoretical expectation. At high temperature and low fields we find a transition from CDWs to fluctuating superconductivity, weakly affected by disorder, while at high field and low temperature the protected filamentary superconducting phase appears in close analogy with "glassy" supersolid phenomena in 4He.

The perfectly linear temperature dependence of the electrical resistivity observed as $T \rightarrow$ 0 in a variety of metals close to a quantum critical point is a major puzzle of condensed matter physics . Here we show that $T$-linear resistivity as $T \rightarrow$ 0 is a generic property of cuprates, associated with a universal scattering rate. We measured the low-temperature resistivity of the bi-layer cuprate Bi2212 and found that it exhibits a $T$-linear dependence with the same slope as in the single-layer cuprates Bi2201, Nd-LSCO and LSCO, despite their very different Fermi surfaces and structural, superconducting and magnetic properties. We then show that the $T$-linear coefficient (per CuO$_2$ plane), $A_1$, is given by the universal relation $A_1 T_F = h / 2e^2$, where $e$ is the electron charge, $h$ is the Planck constant and $T_F$ is the Fermi temperature. This relation, obtained by assuming that the scattering rate 1 / $\tau$ of charge carriers reaches the Planckian limit whereby $\hbar / \tau = k_B T$, works not only for hole-doped cuprates but also for electron-doped cuprates despite the different nature of their quantum critical point and strength of their electron correlations., Comment: main + SI

We present a detailed synchrotron x-ray scattering study of the charge-density-wave (CDW) order in simple tetragonal HgBa$_2$CuO$_{4+\delta}$ (Hg1201). Resonant soft x-ray scattering measurements reveal that short-range order appears at a temperature that is distinctly lower than the pseudogap temperature and in excellent agreement with a prior transient reflectivity result. Despite considerable structural differences between Hg1201 and YBa$_2$Cu$_3$O$_{6+\delta}$, the CDW correlations exhibit similar doping dependencies, and we demonstrate a universal relationship between the CDW wave vector and the size of the reconstructed Fermi pocket observed in quantum oscillation experiments. The CDW correlations in Hg1201 vanish already below optimal doping, once the correlation length is comparable to the CDW modulation period, and they appear to be limited by the disorder potential from unit cells hosting two interstitial oxygen atoms. A complementary hard x-ray diffraction measurement, performed on an underdoped Hg1201 sample in magnetic fields along the crystallographic $c$ axis of up to 16 T, provides information about the form factor of the CDW order. As expected from the single-CuO$_2$-layer structure of Hg1201, the CDW correlations vanish at half-integer values of $L$ and appear to be peaked at integer $L$. We conclude that the atomic displacements associated with the short-range CDW order are mainly planar, within the CuO$_2$ layers.

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)

The exciton dynamics in monolayer black phosphorus is investigated over a very wide range of photoexcited exciton densities using time resolved photoluminescence. At low excitation densities, the exciton dynamics is successfully described in terms of a double exponential decay. With increasing exciton population, a fast, non-exponential component develops as exciton-exciton annihilation takes over as the dominant recombination mechanism under high excitation conditions. Our results identify an upper limit for the injection density, after which exciton-exciton annihilation reduces the quantum yield, which will significantly impact the performance of light emitting devices based on single layer black phosphorus., Comment: 6 pages, 5 figures

We present two methods to determine whether the interactions in a Tomonaga-Luttinger liquid (TLL) state of a spin-$1/2$ Heisenberg antiferromagnetic ladder are attractive or repulsive. The first method combines two bulk measurements, of magnetization and specific heat, to deduce the TLL parameter that distinguishes between the attraction and repulsion. The second one is based on a local-probe, NMR measurements of the spin-lattice relaxation. For the strong-leg spin ladder compound $\mathrm{(C_7H_{10}N)_2CuBr_4}$ we find that the isothermal magnetic field dependence of the relaxation rate, $T_1^{-1}(H)$, displays a concave curve between the two critical fields that bound the TLL regime. This is in sharp contrast to the convex curve previously reported for a strong-rung ladder $\mathrm{(C_5H_{12}N)_2CuBr_4}$. Within the TLL description, we show that the concavity directly reflects the attractive interactions, while the convexity reflects the repulsive ones., Comment: 6 pages, 2 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 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.

The microscopic nature of an insulating state in the vicinity of a superconducting state, in the presence of disorder, is a hotly debated question. While the simplest scenario proposes that Coulomb interactions destroy the Cooper pairs at the transition, leading to localization of single electrons, an alternate possibility supported by experimental observations suggests that Cooper pairs instead directly localize. The question of the homogeneity, granularity, or possibly glassiness of the material on the verge of this transition is intimately related to this fundamental issue. Here, by combining macroscopic and nano-scale studies of superconducting ultrathin NbN films, we reveal nanoscopic electronic inhomogeneities that emerge when the film thickness is reduced. In addition, while thicker films display a purely two-dimensional behaviour in the superconducting fluctuations, we demonstrate a zero-dimensional regime for the thinner samples precisely on the scale of the inhomogeneities. Such behavior is somehow intermediate between the Fermi and Bose insulator paradigms and calls for further investigation to understand the way Cooper pairs continuously evolve from a bound state of fermionic objects into localized bosonic entities., Comment: 29 pages 9 figures

Our knowledge of the ground state of underdoped hole-doped cuprates has evolved considerably over the last few years. There is now compelling evidence that inside the pseudogap phase, charge order breaks translational symmetry leading to a reconstructed Fermi surface made of small pockets. Quantum oscillations, [Doiron-Leyraud N, et al. (2007) Nature 447:564-568], optical conductivity [Mirzaei SI, et al. (2013) Proc Natl Acad Sci USA 110:5774-5778] and the validity of Wiedemann-Franz law [Grissonnache G, et al. (2016) Phys. Rev. B 93:064513] point to a Fermi liquid regime at low temperature in the underdoped regime. However, the observation of a quadratic temperature dependence in the electrical resistivity at low temperatures, the hallmark of a Fermi liquid regime, is still missing. Here, we report magnetoresistance measurements in the magnetic-field-induced normal state of underdoped YBa_2Cu_4O_8 which are consistent with a T^2 resistivity extending down to 1.5 K. The magnitude of the T^2 coefficient, however, is much smaller than expected for a single pocket of the mass and size observed in quantum oscillations, implying that the reconstructed Fermi surface must consist of at least one additional pocket., Comment: Main + SI : published version

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

Two critical points have been revealed in the normal-state phase diagram of the electron-doped cuprate superconductor Nd$_{2-x}$Ce$_x$CuO$_4$ by exploring the Fermi surface properties of high quality single crystals by high-field magnetotransport. First, the quantitative analysis of the Shubnikov-de Haas effect shows that the weak superlattice potential responsible for the Fermi surface reconstruction in the overdoped regime extrapolates to zero at the doping level $x_c = 0.175$ corresponding to the onset of superconductivity. Second, the high-field Hall coefficient exhibits a sharp drop right below optimal doping $x_{\mathrm{opt}} = 0.145$ where the superconducting transition temperature is maximum. This drop is most likely caused by the onset of long-range antiferromagnetic ordering. Thus, the superconducting dome appears to be pinned by two critical points to the normal state phase diagram., Comment: 9 pages; 7 figures; 1 table

The upper critical field Hc2 is a fundamental measure of the pairing strength, yet there is no agreement on its magnitude and doping dependence in cuprate superconductors. We have used thermal conductivity as a direct probe of Hc2 in the cuprates YBa2Cu3Oy and YBa2Cu4O8 to show that there is no vortex liquid at T = 0, allowing us to use high-field resistivity measurements to map out the doping dependence of Hc2 across the phase diagram. Hc2(p) exhibits two peaks, each located at a critical point where the Fermi surface undergoes a transformation. The condensation energy obtained directly from Hc2, and previous Hc1 data, undergoes a 20-fold collapse below the higher critical point. These data provide quantitative information on the impact of competing phases in suppressing superconductivity in cuprates., Comment: to appear in Nature Communications; Supplementary Information file available upon request

Charge density-wave order has been observed in cuprate superconductors whose crystal structure breaks the square symmetry of the CuO2 planes, such as orthorhombic YBa2Cu3Oy (YBCO), but not so far in cuprates that preserve that symmetry, such as tetragonal HgBa2CuO4+d (Hg1201). We have measured the Hall (R_H), Seebeck (S), and Nernst coefficients of underdoped Hg1201 in magnetic fields large enough to suppress superconductivity. The high-field R_H(T) and S(T) are found to drop with decreasing temperature and become negative, as also observed in YBCO at comparable doping. In YBCO, the negative R_H and S are signatures of a small electron pocket caused by Fermi-surface reconstruction, attributed to charge density-wave modulations observed in the same range of doping and temperature. We deduce that a similar Fermi-surface reconstruction takes place in Hg1201, evidence that density-wave order exists in this material. A striking similarity is also found in the normal-state Nernst coefficient, further supporting this interpretation. Given the model nature of Hg1201, Fermi-surface reconstruction appears to be common to all hole-doped cuprates, suggesting that density-wave order is a fundamental property of these materials.

The electrical resistivity rho_c of the underdoped cuprate superconductor YBCO was measured perpendicular to the CuO_2 planes on ultra-high quality single crystals in magnetic fields large enough to suppress superconductivity. The incoherent insulating-like behavior of rho_c at high temperature, characteristic of all underdoped cuprates, is found to cross over to a coherent regime of metallic behavior at low temperature. This crossover coincides with the emergence of the small electron pocket detected in the Fermi surface of YBCO via quantum oscillations, the Hall and Seebeck coefficients and with the detection of a unidirectional modulation of the charge density as seen by high-field NMR measurements. The low coherence temperature is quantitatively consistent with the small hopping integral t_perp inferred from the splitting of the quantum oscillation frequencies. We conclude that the Fermi-surface reconstruction in YBCO at dopings from p = 0.08 to at least p = 0.15, attributed to stripe order, produces a metallic state with 3D coherence deep in the underdoped regime., Comment: 7 pages, 7 figures

The Hall coefficient R_H of the cuprate superconductor YBa2Cu3Oy was measured in magnetic fields up to 60 T for a hole concentration p from 0.078 to 0.152, in the underdoped regime. In fields large enough to suppress superconductivity, R_H(T) is seen to go from positive at high temperature to negative at low temperature, for p > 0.08. This change of sign is attributed to the emergence of an electron pocket in the Fermi surface at low temperature. At p < 0.08, the normal-state R_H(T) remains positive at all temperatures, increasing monotonically as T \to 0. We attribute the change of behaviour across p = 0.08 to a Lifshitz transition, namely a change in Fermi-surface topology occurring at a critical concentration p_L = 0.08, where the electron pocket vanishes. The loss of the high-mobility electron pocket across p_L coincides with a ten-fold drop in the conductivity at low temperature, revealed in measurements of the electrical resistivity $\rho$ at high fields, showing that the so-called metal-insulator crossover of cuprates is in fact driven by a Lifshitz transition. It also coincides with a jump in the in-plane anisotropy of $\rho$, showing that without its electron pocket the Fermi surface must have strong two-fold in-plane anisotropy. These findings are consistent with a Fermi-surface reconstruction caused by a unidirectional spin-density wave or stripe order., Comment: 16 pages, 13 figures, see associated Viewpoint: M. Vojta, Physics 4, 12 (2011)

We report transport measurements using pulsed magnetic fields to suppress the superconducting fluctuations (SCF) conductivity in a series of YBa_2Cu_3O_(6+x) samples. These experiments allow us altogether to measure the temperature T'c at which SCF disappear, and the pseudogap temperature T*. While the latter are consistent with previous determinations of T*, we find that T'c is slightly larger than similar data taken by Nernst measurements. A careful investigation near optimal doping shows that T* becomes smaller than T'c, which is an unambiguous evidence that the pseudogap cannot be assigned to preformed pairs. Studies of the incidence of disorder on both T'c and T* allow us to propose a phase diagram including disorder which explains most observations done in other cuprate families, and to discuss the available knowledge on the pseudogap line in the phase diagram., Comment: New version with minor corrections

A study of the antiferromagnet CeRh$_2$Si$_2$ by torque, magnetostriction, and transport in pulsed magnetic fields up to 50 Tesla and by thermal expansion in static fields up to 13 Tesla is presented. The magnetic field-temperature phase diagram of CeRh$_2$Si$_2$, where the magnetic field is applied along the easy axis $\mathbf{c}$, is deduced from these measurements. The second-order phase transition temperature $T_{N}$ and the first-order phase transition temperature $T_{1,2}$ (=~36 K and 26 K at zero-field, respectively) decrease with increasing field. The field-induced antiferromagnetic-to-paramagnetic borderline $H_c$, which equals 26 T at 1.5 K, goes from first-order at low temperature to second-order at high temperature. The magnetic field-temperature phase diagram is found to be composed of (at least) three different antiferromagnetic phases. These are separated by the first-order lines $H_{1,2}$, corresponding to $T_{1,2}$ at H=0, and $H_{2,3}$, which equals 25.5 T at 1.5 K. A maximum of the $T^2$-coefficient $A$ of the resistivity is observed at the onset of the high-field polarized regime, which is interpreted as the signature of an enhanced effective mass at the field-induced quantum instability. The magnetic field dependence of the $A$ coefficient in CeRh$_2$Si$_2$ is compared with its pressure dependence, and also with the field dependence of $A$ in the prototypal heavy-fermion system CeRu$_2$Si$_2$., Comment: 10 pages, 11 figures

From analysis of the in-plane resistivity $\rho_{ab}(T)$ of La$_{2-x}$Sr$_x$CuO$_4$, we show that normal state transport in overdoped cuprates can be delineated into two regimes in which the electrical resistivity varies approximately linearly with temperature. In the low temperature limit, the $T$-linear resistivity extends over a very wide doping range, in marked contrast to expectations from conventional quantum critical scenarios. The coefficient of this $T$-linear resistivity scales with the superconducting transition temperature $T_c$, implying that the interaction causing this anomalous scattering is also associated with the superconducting pairing mechanism. At high temperatures, the coefficient of the $T$-linear resistivity is essentially doping independent beyond a critical doping $p_{\rm crit}$ = 0.19 at which the ratio of the two coefficients is maximal. Taking our cue from earlier thermodynamic and photoemission measurements, we conclude that the opening of the normal state pseudogap at $p_{\rm crit}$ is driven by the loss of coherence of anti-nodal quasiparticles at low temperatures., Comment: 18 pages, 4 figures, to appear in Special Theme Issue of Phil. Trans. Roy. Soc. A

Using the de Haas-van Alphen effect we have measured the evolution of the Fermi surface of BaFe_2(As_{1-x}P_x)_2 as function of isoelectric substitution (As/P) for 0.41

Using an elastic neutron scattering technique under a pulsed magnetic field up to 30 T, we determined the magnetic structure in the half-magnetization plateau phase in the spinel CdCr$_2$O$_4$. The magnetic structure has a cubic $P4_3$32 symmetry, which is the same as that observed in HgCr$_2$O$_4$. This suggests that there is a universal field induced spin-lattice coupling mechanism at work in the Cr-based spinels., Comment: 4 pages, 4 figures

We use inelastic neutron scattering to measure the magnetic excitations in the underdoped superconductor La2-xSrxCuO4 (x=0.085, Tc=22 K) over energy and temperatures ranges 5 < E < 200 meV and 5 < T < 300 K respectively. At high temperature (T = 300 K), we observe strongly damped excitations with a characteristic energy scale of approximately 50 meV. As the temperature is lowered to T = 30 K, and we move into the pseudogap state, the magnetic excitations become highly structured in energy and momentum below about 60 meV. This change appears to be associated with the development of the pseudogap in the electronic excitations.

The de Haas-van Alphen effect was observed in the underdoped cuprate YBa$_2$Cu$_3$O$_{6.5}$ via a torque technique in pulsed magnetic fields up to 59 T. Above an irreversibility field of $\sim$30 T, the magnetization exhibits clear quantum oscillations with a single frequency of 540 T and a cyclotron mass of 1.76 times the free electron mass, in excellent agreement with previously observed Shubnikov-de Haas oscillations. The oscillations obey the standard Lifshitz-Kosevich formula of Fermi-liquid theory. This thermodynamic observation of quantum oscillations confirms the existence of a well-defined, close and coherent, Fermi surface in the pseudogap phase of cuprates., Comment: published version

We report the observation of Shubnikov-de Haas oscillations in the underdoped cuprate superconductor YBa$_2$Cu$_4$O$_8$ (Y124). For field aligned along the c-axis, the frequency of the oscillations is $660\pm 30$ T, which corresponds to $\sim 2.4$ % of the total area of the first Brillouin zone. The effective mass of the quasiparticles on this orbit is measured to be $2.7\pm0.3$ times the free electron mass. Both the frequency and mass are comparable to those recently observed for ortho-II YBa$_2$Cu$_3$O$_{6.5}$ (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., Comment: v2: Version of paper accepted for publication in Physical Review Letters. Only minor changes to the text and references

We report a detailed inelastic neutron scattering study of the collective magnetic excitations of overdoped superconducting La1.78Sr0.22CuO4 for the energy range 0-160 meV. Our measurements show that overdoping suppresses the strong response present for optimally doped La2-xSrxCuO4 which is peaked near 50 meV. The remaining response is peaked at incommensurate wavevectors for all energies investigated. We observe a strong high-frequency magnetic response for E >= 80 meV suggesting that significant antiferromagnetic exchange couplings persist well into the overdoped part of the cuprate phase diagram., Comment: 4 pages, 4 figures

The excitations responsible for producing high-temperature superconductivity in the cuprates have not been identified. Two promising candidates are collective spin excitations and phonons. A recent argument against spin excitations has been their inability to explain structures seen in electronic spectroscopies such as photoemission and tunnelling. Here we use inelastic neutron scattering to demonstrate that collective spin excitations in optimally doped La$_{2-x}$Sr$_{x}$CuO$_{4}$ are more structured than previously thought. The excitations have a two component structure with a low-frequency component strongest around 18 meV and a broader component strongest near 40-70 meV. The second component carries most of the spectral weight and its energy matches structure seen in photoemission and tunnelling spectra in the range 50-90 meV. Our results demonstrate that collective spin excitations can explain features of quasiparticle spectroscopies and are therefore likely to be the strongest coupled excitations., Comment: accepted for publication in Nature Physics, original submission