Quadrupling the depairing current density in the iron-based superconductor SmFeAsO1-xHx

Iron-based 1111-type superconductors display high critical temperatures and relatively high critical current densities Jc. The typical approach to increasing Jc is to introduce defects to control dissipative vortex motion. However, when optimized, this approach is theoretically predicted to be limited to achieving a maximum Jc of only ∼30% of the depairing current density Jd, which depends on the coherence length and the penetration depth. Here we dramatically boost Jc in SmFeAsO1-xHx films using a thermodynamic approach aimed at increasing Jd and incorporating vortex pinning centres. Specifically, we reduce the penetration depth, coherence length and critical field anisotropy by increasing the carrier density through high electron doping using H substitution. Remarkably, the quadrupled Jd reaches 415 MA cm-2, a value comparable to cuprates. Finally, by introducing defects using proton irradiation, we obtain high Jc values in fields up to 25 T. We apply this method to other iron-based superconductors and achieve a similar enhancement of current densities.

Lifshitz transition enabling superconducting dome around a charge-order critical point

Superconductivity often emerges as a dome around a quantum critical point (QCP) where long-range order is suppressed to zero temperature, mostly in magnetically ordered materials. However, the emergence of superconductivity at charge-order QCPs remains shrouded in mystery, despite its relevance to high-temperature superconductors and other exotic phases of matter. Here, we present resistance measurements proving that a dome of superconductivity surrounds the putative charge-density-wave QCP in pristine samples of titanium diselenide tuned with hydrostatic pressure. In addition, our quantum oscillation measurements combined with electronic structure calculations show that superconductivity sets in precisely when large electron and hole pockets suddenly appear through an abrupt change of the Fermi surface topology, also known as a Lifshitz transition. Combined with the known repulsive interaction, this suggests that unconventional s± superconductivity is mediated by charge-density-wave fluctuations in titanium diselenide. These results highlight the importance of the electronic ground state and charge fluctuations in enabling unconventional superconductivity.

Quantum Interference between Quasi-2D Fermi Surface Sheets in UTe_{2}

UTe_{2} is a spin-triplet superconductor candidate for which high quality samples with long mean free paths have recently become available, enabling quantum oscillation measurements to probe its Fermi surface and effective carrier masses. It has recently been reported that UTe_{2} possesses a 3D Fermi surface component [Phys. Rev. Lett. 131, 036501 (2023)PRLTAO0031-900710.1103/PhysRevLett.131.036501]. The distinction between 2D and 3D Fermi surface sections in triplet superconductors can have important implications regarding the topological properties of the superconductivity. Here we report the observation of oscillatory components in the magnetoconductance of UTe_{2} at high magnetic fields. We find that these oscillations are well described by quantum interference between quasiparticles traversing semiclassical trajectories spanning magnetic breakdown networks. Our observations are consistent with a quasi-2D model of this material's Fermi surface based on prior dHvA-effect measurements. Our results strongly indicate that UTe_{2}-which exhibits a multitude of complex physical phenomena-possesses a remarkably simple Fermi surface consisting exclusively of two quasi-2D cylindrical sections.

Large Fermi surface in pristine kagome metal CsV3Sb5 and enhanced quasiparticle effective masses

The kagome metal CsV[Formula: see text]Sb[Formula: see text] is an ideal platform to study the interplay between topology and electron correlation. To understand the fermiology of CsV[Formula: see text]Sb[Formula: see text], intensive quantum oscillation (QO) studies at ambient pressure have been conducted. However, due to the Fermi surface reconstruction by the complicated charge density wave (CDW) order, the QO spectrum is exceedingly complex, hindering a complete understanding of the fermiology. Here, we directly map the Fermi surface of the pristine CsV[Formula: see text]Sb[Formula: see text] by measuring Shubnikov-de Haas QOs up to 29 T under pressure, where the CDW order is completely suppressed. The QO spectrum of the pristine CsV[Formula: see text]Sb[Formula: see text] is significantly simpler than the one in the CDW phase, and the detected oscillation frequencies agree well with our density functional theory calculations. In particular, a frequency as large as 8,200 T is detected. Pressure-dependent QO studies further reveal a weak but noticeable enhancement of the quasiparticle effective masses on approaching the critical pressure where the CDW order disappears, hinting at the presence of quantum fluctuations. Our high-pressure QO results reveal the large, unreconstructed Fermi surface of CsV[Formula: see text]Sb[Formula: see text], paving the way to understanding the parent state of this intriguing metal in which the electrons can be organized into different ordered states.

Electronic structure and correlations in planar trilayer nickelate Pr4Ni3O8

The discovery of superconductivity in planar nickelates raises the question of how the electronic structure and correlations of Ni¹⁺ compounds compare to those of the Cu²⁺ cuprate superconductors. Here, we present an angle-resolved photoemission spectroscopy (ARPES) study of the trilayer nickelate Pr₄Ni₃O₈, revealing a Fermi surface resembling that of the hole-doped cuprates but with critical differences. Specifically, the main portions of the Fermi surface are extremely similar to that of the bilayer cuprates, with an additional piece that can accommodate additional hole doping. We find that the electronic correlations are about twice as strong in the nickelates and are almost k-independent, indicating that they originate from a local effect, likely the Mott interaction, whereas cuprate interactions are somewhat less local. Nevertheless, the nickelates still demonstrate the strange-metal behavior in the electron scattering rates. Understanding the similarities and differences between these two families of strongly correlated superconductors is an important challenge.

Stranger than metals

In traditional metals, the temperature ( T ) dependence of electrical resistivity vanishes at low or high T , albeit for different reasons. Here, we review a class of materials, known as “strange” metals, that can violate both of these principles. In strange metals, the change in slope of the resistivity as the mean free path drops below the lattice constant, or as T → 0, can be imperceptible, suggesting continuity between the charge carriers at low and high T . We focus on transport and spectroscopic data on candidate strange metals in an effort to isolate and identify a unifying physical principle. Special attention is paid to quantum criticality, Planckian dissipation, Mottness, and whether a new gauge principle is needed to account for the nonlocal transport seen in these materials.

Magic Gap Ratio for Optimally Robust Fermionic Condensation and Its Implications for High-T_{c} Superconductivity

Bardeen-Schrieffer-Cooper (BCS) and Bose-Einstein condensation (BEC) occur at opposite limits of a continuum of pairing interaction strength between fermions. A crossover between these limits is readily observed in a cold atomic Fermi gas. Whether it occurs in other systems such as the high temperature superconducting cuprates has remained an open question. We uncover here unambiguous evidence for a BCS-BEC crossover in the cuprates by identifying a universal magic gap ratio 2Δ/k_{B}T_{c}≈6.5 (where Δ is the pairing gap and T_{c} is the transition temperature) at which paired fermion condensates become optimally robust. At this gap ratio, corresponding to the unitary point in a cold atomic Fermi gas, the measured condensate fraction N_{0} and the height of the jump δγ(T_{c}) in the coefficient γ of the fermionic specific heat at T_{c} are strongly peaked. In the cuprates, δγ(T_{c}) is peaked at this gap ratio when Δ corresponds to the antinodal spectroscopic gap, thus reinforcing its interpretation as the pairing gap. We find the peak in δγ(T_{c}) also to coincide with a normal state maximum in γ, which is indicative of a pairing fluctuation pseudogap above T_{c}.

Pure nematic quantum critical point accompanied by a superconducting dome

SignificanceThe notion of the quantum critical point (QCP) is at the core of modern condensed matter physics. Near a QCP of the symmetry-breaking order, associated quantum-mechanical fluctuations are intensified, which can lead to unconventional superconductivity. Indeed, dome-shaped superconducting phases are often observed near the magnetic QCPs, which supports the spin fluctuation-driven superconductivity. However, the fundamental question remains as to whether a nonmagnetic QCP of electronic nematic order characterized by spontaneous rotational symmetry breaking can promote superconductivity in real materials. Here, we provide an experimental demonstration that a pure nematic QCP exists near the center of a superconducting dome in nonmagnetic FeSe[Formula: see text] Te_x. This result evidences that nematic fluctuations enhanced around the nematic QCP can boost superconductivity.

Comparison of temperature and doping dependence of elastoresistivity near a putative nematic quantum critical point

Strong electronic nematic fluctuations have been discovered near optimal doping for several families of Fe-based superconductors, motivating the search for a possible link between these fluctuations, nematic quantum criticality, and high temperature superconductivity. Here we probe a key prediction of quantum criticality, namely power-law dependence of the associated nematic susceptibility as a function of composition and temperature approaching the compositionally tuned putative quantum critical point. To probe the ‘bare’ quantum critical point requires suppression of the superconducting state, which we achieve by using large magnetic fields, up to 45 T, while performing elastoresistivity measurements to follow the nematic susceptibility. We performed these measurements for the prototypical electron-doped pnictide, Ba(Fe_1−xCo_x)₂As₂, over a dense comb of dopings. We find that close to the putative quantum critical point, the elastoresistivity appears to obey power-law behavior as a function of composition over almost a decade of variation in composition. Paradoxically, however, we also find that the temperature dependence for compositions close to the critical value cannot be described by a single power law.

Evidence for quantum criticality in Fe-based superconductors is still being accumulated. Here, the authors observe power-law behavior of the elastoresistivity as a function of composition in Ba(Fe_1−xCo_x)₂As₂ near a putative nematic quantum critical point, consistent with expectations for quantum criticality, while the temperature dependence near the critical doping deviates from a power law.

Vanishing nematic order beyond the pseudogap phase in overdoped cuprate superconductors

During the last decade, translational and rotational symmetry-breaking phases-density wave order and electronic nematicity-have been established as generic and distinct features of many correlated electron systems, including pnictide and cuprate superconductors. However, in cuprates, the relationship between these electronic symmetry-breaking phases and the enigmatic pseudogap phase remains unclear. Here, we employ resonant X-ray scattering in a cuprate high-temperature superconductor [Formula: see text] (Nd-LSCO) to navigate the cuprate phase diagram, probing the relationship between electronic nematicity of the Cu 3d orbitals, charge order, and the pseudogap phase as a function of doping. We find evidence for a considerable decrease in electronic nematicity beyond the pseudogap phase, either by raising the temperature through the pseudogap onset temperature T* or increasing doping through the pseudogap critical point, p*. These results establish a clear link between electronic nematicity, the pseudogap, and its associated quantum criticality in overdoped cuprates. Our findings anticipate that electronic nematicity may play a larger role in understanding the cuprate phase diagram than previously recognized, possibly having a crucial role in the phenomenology of the pseudogap phase.

Specific Heat of a Quantum Critical Metal

We investigate the specific heat c, near an Ising nematic quantum critical point (QCP), using sign problem-free quantum Monte Carlo simulations. Cooling towards the QCP, we find a broad regime of temperature where c/T is close to the value expected from the noninteracting band structure, even for a moderately large coupling strength. At lower temperature, we observe a rapid rise of c/T, followed by a drop to zero as the system becomes superconducting. The spin susceptibility begins to drop at roughly the same temperature where the enhancement of c/T onsets, most likely due to the opening of a gap associated with superconducting fluctuations. These findings suggest that superconductivity and non-Fermi liquid behavior (manifested in an enhancement of the effective mass) onset at comparable energy scales. We support these conclusions with an analytical perturbative calculation.

Controlling unconventional superconductivity in artificially engineeredf-electron Kondo superlattices

Unconventional superconductivity and magnetism are intertwined on a microscopic level in a wide class of materials, including high-T_ccuprates, iron pnictides, and heavy-fermion compounds. Interactions between superconducting electrons and bosonic fluctuations at the interface between adjacent layers in heterostructures provide a new approach to this most fundamental and hotly debated subject. We have been able to use a recent state-of-the-art molecular-beam-epitaxy technique to fabricate superlattices consisting of different heavy-fermion compounds with atomic thickness. These Kondo superlattices provide a unique opportunity to study the mutual interaction between unconventional superconductivity and magnetic order through the atomic interface. Here, we design and fabricate hybrid Kondo superlattices consisting of alternating layers of superconducting CeCoIn₅withd-wave pairing symmetry and nonmagnetic metal YbCoIn₅or antiferromagnetic heavy fermion metals such as CeRhIn₅and CeIn₃. In these Kondo superlattices, superconducting heavy electrons are confined within the two-dimensional CeCoIn₅block layers and interact with neighboring nonmagnetic or magnetic layers through the interface. Superconductivity is strongly influenced by local inversion symmetry breaking at the interface in CeCoIn₅/YbCoIn₅superlattices. The superconducting and antiferromagnetic states coexist in spatially separated layers in CeCoIn₅/CeRhIn₅and CeCoIn₅/CeIn₃superlattices, but their mutual coupling via the interface significantly modifies the superconducting and magnetic properties. The fabrication of a wide variety of hybrid superlattices paves a new way to study the relationship between unconventional superconductivity and magnetism in strongly correlated materials.

Room-temperature-superconducting Tc driven by electron correlation

Room-temperature-superconducting Tc measured by high pressure in hydrides can be theoretically explained by a Brinkman-Rice (BR)-Bardeen-Cooper-Schrieffer (BCS) Tc combining both the generalized BCS Tc and the diverging effective mass, m*/m = 1/(1 - (U/Uc)2), with the on-site Coulomb interaction U in the BR picture. A transition from U in a correlated metal of the normal state to Uc in the superconducting state can lead to superconductivity, which can be caused by volume contraction induced by high pressure or low temperature.

Revival of Charge Density Waves and Charge Density Fluctuations in Cuprate High-Temperature Superconductors

I present here a short memory of my scientific contacts with K.A. Müller starting from the Interlaken Conference (1988), Erice (1992 and 1993), and Cottbus (1994) on the initial studies on phase separation (PS) and charge inhomogeneity in cuprates carried out against the view of the majority of the scientific community at that time. Going over the years and passing through the charge density wave (CDW) instability of the correlated Fermi liquid (FL) and to the consequences of charge density fluctuations (CDFs), I end with a presentation of my current research activity on CDWs and the related two-dimensional charge density fluctuations (2D-CDFs). A scenario follows of the physics of cuprates, which includes the solution of the decades-long problem of the strange metal (SM) state.

Charge ordering in superconducting copper oxides

Charge order has recently been identified as a leading competitor of high-temperature superconductivity in moderately doped cuprates. We provide a survey of universal and materials-specific aspects of this phenomenon, with emphasis on results obtained by scattering methods. In particular, we discuss the structure, periodicity, and stability range of the charge-ordered state, its response to various external perturbations, the influence of disorder, the coexistence and competition with superconductivity, as well as collective charge dynamics. In the context of this journal issue which honors Roger Cowley's legacy, we also discuss the connection of charge ordering with lattice vibrations and the central-peak phenomenon. We end the review with an outlook on research opportunities offered by new synthesis methods and experimental platforms, including cuprate thin films and superlattices.

Extent of Fermi-surface reconstruction in the high-temperature superconductor HgBa2CuO4+δ

High magnetic fields have revealed a surprisingly small Fermi surface in underdoped cuprates, possibly resulting from Fermi-surface reconstruction due to an order parameter that breaks translational symmetry of the crystal lattice. A crucial issue concerns the doping extent of such a state and its relationship to the principal pseudogap and superconducting phases. We employ pulsed magnetic-field measurements on the cuprate [Formula: see text]Cu[Formula: see text] to identify signatures of Fermi-surface reconstruction from a sign change of the Hall effect and a peak in the temperature-dependent planar resistivity. We trace the termination of Fermi-surface reconstruction to two hole concentrations where the superconducting upper critical fields are found to be enhanced. One of these points is associated with the pseudogap endpoint near optimal doping. These results connect the Fermi-surface reconstruction to both superconductivity and the pseudogap phenomena.

Pauli-limit upper critical field of high-temperature superconductor La1.84Sr0.16CuO4

The upper critical field of a cuprate high-temperature superconductor, La_1.84Sr_0.16CuO₄, was investigated by high-frequency self-resonant contactless electrical conductivity measurements in magnetic fields up to 102 T. An irreversible transition was observed at 85 T (T = 4.2 K), defined as the upper critical field. The temperature-dependent upper critical field was argued on the basis of the Werthamer-Helfand-Hohenberg theory. The Pauli-limiting pair-breaking process with a small contribution of the spin-orbit coupling explained the first-order phase transition exhibiting a hysteresis observed at low temperatures.

Possible quantum critical behavior revealed by the critical current density of hole doped high-Tc cuprates in comparison to heavy fermion superconductors

The superconducting critical current density, Jc, in hole doped cuprates show strong dependence on the doped hole content, p, within the copper oxide plane(s). The doping dependent Jc mainly exhibits the variation of the intrinsic depairing critical current density as p is varied. Jc(p) tends to peak at p ~ 0.185 in copper oxide superconductors. This particular value of the hole content, often termed as the critical hole concentration, has several features putative to a quantum critical point (QCP). Very recently, the pressure dependences of the superconducting transition temperature (Tc) and the critical current (Ic) in pure CeRhIn5 and Sn doped CeRhIn5 heavy fermion compounds have been reported (Nature Communications (2018) 9:44, https://doi.org/10.1038/s41467-018-02899-5 ). The critical pressure demarcates an antiferromagnetic quantum critical point where both Tc and Ic are maximized. We have compared and contrasted this behavior with those found for Y1-xCaxBa2Cu3O7-δ in this brief communication. The resemblance of the systematic behavior of the critical current with pressure and hole content between heavy fermion systems and hole doped cuprates is significant. This adds to the circumstantial evidence that quantum critical physics probably plays a notable role behind the unconventional normal and superconducting state properties of copper oxide superconductors.

Sequential localization of a complex electron fluid

Complex and correlated quantum systems with promise for new functionality often involve entwined electronic degrees of freedom. In such materials, highly unusual properties emerge and could be the result of electron localization. Here, a cubic heavy fermion metal governed by spins and orbitals is chosen as a model system for this physics. Its properties are found to originate from surprisingly simple low-energy behavior, with 2 distinct localization transitions driven by a single degree of freedom at a time. This result is unexpected, but we are able to understand it by advancing the notion of sequential destruction of an SU(4) spin-orbital-coupled Kondo entanglement. Our results implicate electron localization as a unified framework for strongly correlated materials and suggest ways to exploit multiple degrees of freedom for quantum engineering.

Disorder raises the critical temperature of a cuprate superconductor

With the discovery of charge-density waves (CDWs) in most members of the cuprate high-temperature superconductors, the interplay between superconductivity and CDWs has become a key point in the debate on the origin of high-temperature superconductivity. Some experiments in cuprates point toward a CDW state competing with superconductivity, but others raise the possibility of a CDW-superconductivity intertwined order or more elusive pair-density waves (PDWs). Here, we have used proton irradiation to induce disorder in crystals of [Formula: see text] and observed a striking 50% increase of [Formula: see text], accompanied by a suppression of the CDWs. This is in sharp contrast with the behavior expected of a d-wave superconductor, for which both magnetic and nonmagnetic defects should suppress [Formula: see text] Our results thus make an unambiguous case for the strong detrimental effect of the CDW on bulk superconductivity in [Formula: see text] Using tunnel diode oscillator (TDO) measurements, we find indications for potential dynamic layer decoupling in a PDW phase. Our results establish irradiation-induced disorder as a particularly relevant tuning parameter for the many families of superconductors with coexisting density waves, which we demonstrate on superconductors such as the dichalcogenides and [Formula: see text].

Correlation between scale-invariant normal-state resistivity and superconductivity in an electron-doped cuprate

An understanding of the normal state in the high-temperature superconducting cuprates is crucial to the ultimate understanding of the long-standing problem of the origin of the superconductivity itself. This so-called "strange metal" state is thought to be associated with a quantum critical point (QCP) hidden beneath the superconductivity. In electron-doped cuprates-in contrast to hole-doped cuprates-it is possible to access the normal state at very low temperatures and low magnetic fields to study this putative QCP and to probe the T ➔ 0 K state of these materials. We report measurements of the low-temperature normal-state magnetoresistance (MR) of the n-type cuprate system La_2-x Ce _x CuO₄ and find that it is characterized by a linear-in-field behavior, which follows a scaling relation with applied field and temperature, for doping (x) above the putative QCP (x = 0.14). The magnitude of the unconventional linear MR decreases as T _c decreases and goes to zero at the end of the superconducting dome (x ~ 0.175) above which a conventional quadratic MR is found. These results show that there is a strong correlation between the quantum critical excitations of the strange metal state and the high-T _c superconductivity.

Anomalous quantum criticality in the electron-doped cuprates

In the physics of condensed matter, quantum critical phenomena and unconventional superconductivity are two major themes. In electron-doped cuprates, the low critical field (H_C2) allows one to study the putative quantum critical point (QCP) at low temperature and to understand its connection to the long-standing problem of the origin of the high-T_C superconductivity. Here we present measurements of the low-temperature normal-state thermopower (S) of the electron-doped cuprate superconductor La_2-x Ce _x CuO₄ (LCCO) from x = 0.11-0.19. We observe quantum critical [Formula: see text] versus [Formula: see text] behavior over an unexpectedly wide doping range x = 0.15-0.17 above the QCP (x = 0.14), with a slope that scales monotonically with the superconducting transition temperature (T_C with H = 0). The presence of quantum criticality over a wide doping range provides a window on the criticality. The thermopower behavior also suggests that the critical fluctuations are linked with T_C Above the superconductivity dome, at x = 0.19, a conventional Fermi-liquid [Formula: see text] behavior is found for [Formula: see text] 40 K.

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.

Electrical resistivity across a nematic quantum critical point

Correlated electron systems are highly susceptible to various forms of electronic order. By tuning the transition temperature towards absolute zero, striking deviations from conventional metallic (Fermi-liquid) behaviour can be realized. Evidence for electronic nematicity, a correlated electronic state with broken rotational symmetry, has been reported in a host of metallic systems^1-5 that exhibit this so-called quantum critical behaviour. In all cases, however, the nematicity is found to be intertwined with other forms of order, such as antiferromagnetism^5-7 or charge-density-wave order⁸, that might themselves be responsible for the observed behaviour. The iron chalcogenide FeSe_1-xS_x is unique in this respect because its nematic order appears to exist in isolation^9-11, although until now, the impact of nematicity on the electronic ground state has been obscured by superconductivity. Here we use high magnetic fields to destroy the superconducting state in FeSe_1-xS_x and follow the evolution of the electrical resistivity across the nematic quantum critical point. Classic signatures of quantum criticality are revealed: an enhancement in the coefficient of the T² resistivity (due to electron-electron scattering) on approaching the critical point and, at the critical point itself, a strictly T-linear resistivity that extends over a decade in temperature T. In addition to revealing the phenomenon of nematic quantum criticality, the observation of T-linear resistivity at a nematic critical point also raises the question of whether strong nematic fluctuations play a part in the transport properties of other 'strange metals', in which T-linear resistivity is observed over an extended regime in their respective phase diagrams.

Reconstructing the quantum critical fan of strongly correlated systems using quantum correlations

Albeit occurring at zero temperature, quantum critical phenomena have a huge impact on the finite-temperature phase diagram of strongly correlated systems, giving experimental access to their observation. Indeed, the existence of a gapless, zero-temperature quantum critical point induces the existence of an extended region in parameter space-the quantum critical fan (QCF)-characterized by power-law temperature dependences of all observables. Identifying experimentally the QCF and its crossovers to other regimes (renormalized classical, quantum disordered) remains nonetheless challenging. Focusing on paradigmatic models of quantum phase transitions, here we show that quantum correlations-captured by the quantum variance of the order parameter-exhibit the temperature scaling associated with the QCF over a parameter region much broader than that revealed by ordinary correlations. The link existing between the quantum variance and the dynamical susceptibility paves the way to an experimental reconstruction of the QCF using spectroscopic techniques.

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.

Electron Mass Enhancement near a Nematic Quantum Critical Point in NaFe_{1-x}Co_{x}As

A magnetic order can be completely suppressed at zero temperature (T), by doping carriers or applying pressure, at a quantum critical point, around which physical properties change drastically. However, the situation is unclear for an electronic nematic order that breaks rotation symmetry. Here, we report nuclear magnetic resonance studies on NaFe_{1-x}Co_{x}As where magnetic and nematic transitions are well separated. The nuclear magnetic resonance spectrum is sensitive to inhomogeneous magnetic fields in the vortex state, which is related to London penetration depth λ_{L} that measures the electron mass m^{*}. We discovered two peaks in the doping dependence of λ_{L}^{2}(T∼0), one at x_{M}=0.027 where the spin-lattice relaxation rate shows quantum critical behavior, and another at x_{c}=0.032 around which the nematic transition temperature extrapolates to zero and the electrical resistivity shows a T-linear variation. Our results indicate that a nematic quantum critical point lies beneath the superconducting dome at x_{c} where m^{*} is enhanced. The impact of the nematic fluctuations on superconductivity is discussed.

Scale-invariant magnetoresistance in a cuprate superconductor

The anomalous metallic state in the high-temperature superconducting cuprates is masked by superconductivity near a quantum critical point. Applying high magnetic fields to suppress superconductivity has enabled detailed studies of the normal state, yet the direct effect of strong magnetic fields on the metallic state is poorly understood. We report the high-field magnetoresistance of thin-film La_2-x Sr _x CuO₄ cuprate in the vicinity of the critical doping, 0.161 ≤ p ≤ 0.190. We find that the metallic state exposed by suppressing superconductivity is characterized by magnetoresistance that is linear in magnetic fields up to 80 tesla. The magnitude of the linear-in-field resistivity mirrors the magnitude and doping evolution of the well-known linear-in-temperature resistivity that has been associated with quantum criticality in high-temperature superconductors.

Evolution of the Kondo lattice and non-Fermi liquid excitations in a heavy-fermion metal

Strong electron correlations can give rise to extraordinary properties of metals with renormalized Landau quasiparticles. Near a quantum critical point, these quasiparticles can be destroyed and non-Fermi liquid behavior ensues. YbRh2Si2 is a prototypical correlated metal exhibiting the formation of quasiparticle and Kondo lattice coherence, as well as quasiparticle destruction at a field-induced quantum critical point. Here we show how, upon lowering the temperature, Kondo lattice coherence develops at zero field and finally gives way to non-Fermi liquid electronic excitations. By measuring the single-particle excitations through scanning tunneling spectroscopy, we find the Kondo lattice peak displays a non-trivial temperature dependence with a strong increase around 3.3 K. At 0.3 K and with applied magnetic field, the width of this peak is minimized in the quantum critical regime. Our results demonstrate that the lattice Kondo correlations have to be sufficiently developed before quantum criticality can set in.

Photoemission perspective on pseudogap, superconducting fluctuations, and charge order in cuprates: a review of recent progress

In the course of seeking the microscopic mechanism of superconductivity in cuprate high temperature superconductors, the pseudogap phase- the very abnormal 'normal' state on the hole-doped side- has proven to be as big of a quandary as superconductivity itself. Angle-resolved photoemission spectroscopy (ARPES) is a powerful tool for assessing the momentum-dependent phenomenology of the pseudogap, and recent technological developments have permitted a more detailed understanding. This report reviews recent progress in understanding the relationship between superconductivity and the pseudogap, the Fermi arc phenomena, and the relationship between charge order and pseudogap from the perspective of ARPES measurements.

Quantum oscillations in a biaxial pair density wave state

At higher temperatures, and in high magnetic fields at low temperatures, an extraordinary and unidentified electronic phase, dubbed the “pseudogap,” appears in lightly hole-doped cuprates. At high fields and low temperatures, the pseudogap phase supports quantum oscillations that have resisted quantitative theoretical explanation since their discovery, and it also exhibits an unidentified density wave state. Although the latter has typically been referred to as a “charge” density wave because of the observed charge density modulations, theory indicates that it could actually be an electron-pair density wave (PDW) state. Here we demonstrate theoretically that a biaxial PDW state with 8a periodicity may provide a compelling quantitative explanation for much of the observed quantum oscillation data.

There has been growing speculation that a pair density wave state is a key component of the phenomenology of the pseudogap phase in the cuprates. Recently, direct evidence for such a state has emerged from an analysis of scanning tunneling microscopy data in halos around the vortex cores. By extrapolation, these vortex halos would then overlap at a magnetic-field scale where quantum oscillations have been observed. Here, we show that a biaxial pair density wave state gives a unique description of the quantum oscillation data, bolstering the case that the pseudogap phase in the cuprates may be a pair density wave state.

Tuning the Pairing Interaction in a d-Wave Superconductor by Paramagnons Injected through Interfaces

Unconventional superconductivity and magnetism are intertwined on a microscopic level in a wide class of materials. A new approach to this most fundamental and hotly debated issue focuses on the role of interactions between superconducting electrons and bosonic fluctuations at the interface between adjacent layers in heterostructures. Here we fabricate hybrid superlattices consisting of alternating atomic layers of the heavy-fermion superconductor CeCoIn_{5} and antiferromagnetic (AFM) metal CeRhIn_{5}, in which the AFM order can be suppressed by applying pressure. We find that the superconducting and AFM states coexist in spatially separated layers, but their mutual coupling via the interface significantly modifies the superconducting properties. An analysis of upper critical fields reveals that, upon suppressing the AFM order by applied pressure, the force binding superconducting electron pairs acquires an extreme strong-coupling nature. This demonstrates that superconducting pairing can be tuned nontrivially by magnetic fluctuations (paramagnons) injected through the interface.

A tale of two metals: contrasting criticalities in the pnictides and hole-doped cuprates

The iron-based high temperature superconductors share a number of similarities with their copper-based counterparts, such as reduced dimensionality, proximity to states of competing order, and a critical role for 3d electron orbitals. Their respective temperature-doping phase diagrams also contain certain commonalities that have led to claims that the metallic and superconducting (SC) properties of both families are governed by their proximity to a quantum critical point (QCP) located inside the SC dome. In this review, we critically examine these claims and highlight significant differences in the bulk physical properties of both systems. While there is now a large body of evidence supporting the presence of a (magnetic) QCP in the iron pnictides, the situation in the cuprates is much less apparent, at least for the end point of the pseudogap phase. We argue that the opening of the normal state pseudogap in cuprates, so often tied to a putative QCP, arises from a momentum-dependent breakdown of quasiparticle coherence that sets in at much higher doping levels but which is driven by the proximity to the Mott insulating state at half filling. Finally, we present a new scenario for the cuprates in which this loss of quasiparticle integrity and its evolution with momentum, temperature and doping plays a key role in shaping the resultant phase diagram.

Charge Order and Superconductivity in Underdoped YBa_{2}Cu_{3}O_{7-δ} under Pressure

In underdoped cuprates, an incommensurate charge density wave (CDW) order is known to coexist with superconductivity. A dip in T_{c} at the hole doping level where the CDW is strongest (n_{p}≃0.12) suggests that CDW order may suppress superconductivity. We investigate the interplay of charge order with superconductivity in underdoped YBa_{2}Cu_{3}O_{7-δ} by measuring the temperature dependence of the Hall coefficient R_{H}(T) at high magnetic field and at high hydrostatic pressure. We find that, although pressure increases T_{c} by up to 10 K at 2.6 GPa, it has very little effect on R_{H}(T). This suggests that pressure, at these levels, only weakly affects the CDW and that the increase in T_{c} with pressure cannot be attributed to a suppression of the CDW. We argue, therefore, that the dip in T_{c} at n_{p}≃0.12 at ambient pressure is probably not caused by the CDW formation.

Emergence of Quantum Critical Behavior in Metallic Quantum-Well States of Strongly Correlated Oxides

Controlling quantum critical phenomena in strongly correlated electron systems, which emerge in the neighborhood of a quantum phase transition, is a major challenge in modern condensed matter physics. Quantum critical phenomena are generated from the delicate balance between long-range order and its quantum fluctuation. So far, the nature of quantum phase transitions has been investigated by changing a limited number of external parameters such as pressure and magnetic field. We propose a new approach for investigating quantum criticality by changing the strength of quantum fluctuation that is controlled by the dimensional crossover in metallic quantum well (QW) structures of strongly correlated oxides. With reducing layer thickness to the critical thickness of metal-insulator transition, crossover from a Fermi liquid to a non-Fermi liquid has clearly been observed in the metallic QW of SrVO₃ by in situ angle-resolved photoemission spectroscopy. Non-Fermi liquid behavior with the critical exponent α = 1 is found to emerge in the two-dimensional limit of the metallic QW states, indicating that a quantum critical point exists in the neighborhood of the thickness-dependent Mott transition. These results suggest that artificial QW structures provide a unique platform for investigating novel quantum phenomena in strongly correlated oxides in a controllable fashion.

Spin susceptibility of charge-ordered YBa2Cu3O y across the upper critical field

The value of the upper critical field H_c2, a fundamental characteristic of the superconducting state, has been subject to strong controversy in high-T_c copper oxides. Since the issue has been tackled almost exclusively by macroscopic techniques so far, there is a clear need for local-probe measurements. Here, we use ¹⁷O NMR to measure the spin susceptibility [Formula: see text] of the CuO₂ planes at low temperature in charge-ordered YBa₂Cu₃O _y We find that [Formula: see text] increases (most likely linearly) with magnetic field H and saturates above field values ranging from 20 T to 40 T. This result is consistent with the lowest H_c2 values claimed previously and with the interpretation that the charge density wave (CDW) reduces H_c2 in underdoped YBa₂Cu₃O _y Furthermore, the absence of marked deviation in [Formula: see text] at the onset of long-range CDW order indicates that this [Formula: see text] reduction and the Fermi-surface reconstruction are primarily rooted in the short-range CDW order already present in zero field, not in the field-induced long-range CDW order. Above [Formula: see text], the relatively low values of [Formula: see text] at [Formula: see text] K show that the pseudogap is a ground-state property, independent of the superconducting gap.

Crossover from Collective to Incoherent Spin Excitations in Superconducting Cuprates Probed by Detuned Resonant Inelastic X-Ray Scattering

Spin excitations in the overdoped high temperature superconductors Tl_{2}Ba_{2}CuO_{6+δ} and (Bi,Pb)_{2}(Sr,La)_{2}CuO_{6+δ} were investigated by resonant inelastic x-ray scattering (RIXS) as functions of doping and detuning of the incoming photon energy above the Cu-L_{3} absorption peak. The RIXS spectra at optimal doping are dominated by a paramagnon feature with peak energy independent of photon energy, similar to prior results on underdoped cuprates. Beyond optimal doping, the RIXS data indicate a sharp crossover to a regime with a strong contribution from incoherent particle-hole excitations whose maximum shows a fluorescencelike shift upon detuning. The spectra of both compound families are closely similar, and their salient features are reproduced by exact-diagonalization calculations of the single-band Hubbard model on a finite cluster. The results are discussed in the light of recent transport experiments indicating a quantum phase transition near optimal doping.

Robust spin correlations at high magnetic fields in the harmonic honeycomb iridates

The complex antiferromagnetic orders observed in the honeycomb iridates are a double-edged sword in the search for a quantum spin-liquid: both attesting that the magnetic interactions provide many of the necessary ingredients, while simultaneously impeding access. Focus has naturally been drawn to the unusual magnetic orders that hint at the underlying spin correlations. However, the study of any particular broken symmetry state generally provides little clue about the possibility of other nearby ground states. Here we use magnetic fields approaching 100 Tesla to reveal the extent of the spin correlations in γ-lithium iridate. We find that a small component of field along the magnetic easy-axis melts long-range order, revealing a bistable, strongly correlated spin state. Far from the usual destruction of antiferromagnetism via spin polarization, the high-field state possesses only a small fraction of the total iridium moment, without evidence for long-range order up to the highest attainable magnetic fields.The complex antiferromagnetic orders observed in the honeycomb iridates prevent access to a spin-liquid ground state. Here the authors apply extremely high magnetic fields to destroy the antiferromagnetic order in γ-lithium iridate and reveal a bistable, strongly correlated spin state.

Mottness at finite doping and charge-instabilities in cuprates

The influence of the Mott physics on the doping-temperature phase diagram of copper oxides represents a major issue that is subject of intense theoretical and experimental effort. Here, we investigate the ultrafast electron dynamics in prototypical single-layer Bi-based cuprates at the energy scale of the O-2p→Cu-3d charge-transfer (CT) process. We demonstrate a clear evolution of the CT excitations from incoherent and localized, as in a Mott insulator, to coherent and delocalized, as in a conventional metal. This reorganization of the high-energy degrees of freedom occurs at the critical doping p_cr ≈0.16 irrespective of the temperature, and it can be well described by dynamical mean field theory calculations. We argue that the onset of the low-temperature charge instabilities is the low-energy manifestation of the underlying Mottness that characterizes the p < p_cr region of the phase diagram. This discovery sets a new framework for theories of charge order and low-temperature phases in underdoped copper oxides.

Fermi liquid behavior of the in-plane resistivity in the pseudogap state of YBa2Cu4O8

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(7144):565-568], optical conductivity [Mirzaei SI, et al. (2013) Proc Natl Acad Sci USA 110(15):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 YBa₂Cu₄O₈ that are consistent with a T² resistivity extending down to 1.5 K. The magnitude of the T² 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.

Fermi Surface Reconstruction and Drop in the Hall Number due to Spiral Antiferromagnetism in High-T_{c} Cuprates

We show that a Fermi surface reconstruction due to spiral antiferromagnetic order may explain the rapid change in the Hall number as recently observed near optimal doping in cuprate superconductors [Badoux et al., Nature (London) 531, 210 (2016)]. The single-particle spectral function in the spiral state exhibits hole pockets which look like Fermi arcs due to a strong momentum dependence of the spectral weight. Adding charge-density wave order further reduces the Fermi surface to a single electron pocket. We propose quantum oscillation measurements to distinguish between commensurate and spiral antiferromagnetic order. Similar results apply to certain metals in which topological order replaces antiferromagnetic order.

Electron Doping of the Parent Cuprate La_{2}CuO_{4} without Cation Substitution

In the cuprates, carrier doping of the Mott insulating parent state is necessary to realize superconductivity as well as a number of other exotic states involving charge or spin density waves. Cation substitution is the primary method for doping carriers into these compounds, and is the only known method for electron doping in these materials. Here, we report electron doping without cation substitution in epitaxially stabilized thin films of La_{2}CuO_{4} grown via molecular-beam epitaxy. We use angle-resolved photoemission spectroscopy to directly measure their electronic structure and conclusively determine that these compounds are electron doped with a carrier concentration of 0.09±0.02 e^{-}/Cu. We propose that intrinsic defects, most likely oxygen vacancies, are the sources of doped electrons in these materials. Our results suggest a new approach to electron doping in the cuprates, one which could lead to a more detailed experimental understanding of their properties.

Single reconstructed Fermi surface pocket in an underdoped single-layer cuprate superconductor

The observation of a reconstructed Fermi surface via quantum oscillations in hole-doped cuprates opened a path towards identifying broken symmetry states in the pseudogap regime. However, such an identification has remained inconclusive due to the multi-frequency quantum oscillation spectra and complications accounting for bilayer effects in most studies. We overcome these impediments with high-resolution measurements on the structurally simpler cuprate HgBa₂CuO_4+δ (Hg1201), which features one CuO₂ plane per primitive unit cell. We find only a single oscillatory component with no signatures of magnetic breakdown tunnelling to additional orbits. Therefore, the Fermi surface comprises a single quasi-two-dimensional pocket. Quantitative modelling of these results indicates that a biaxial charge density wave within each CuO₂ plane is responsible for the reconstruction and rules out criss-crossed charge stripes between layers as a viable alternative in Hg1201. Lastly, we determine that the characteristic gap between reconstructed pockets is a significant fraction of the pseudogap energy.

The identification of broken symmetry states in underdoped cuprate superconductors via quantum oscillation measurements remains inconclusive. Here, Chan et al. report the reconstructed Fermi surface of HgBa₂CuO_4+δ comprises only a single pocket indicating a biaxial charge-density-wave order within each CuO₂ plane.

Nematic quantum critical point without magnetism in FeSe1-xSx superconductors

In most unconventional superconductors, the importance of antiferromagnetic fluctuations is widely acknowledged. In addition, cuprate and iron-pnictide high-temperature superconductors often exhibit unidirectional (nematic) electronic correlations, including stripe and orbital orders, whose fluctuations may also play a key role for electron pairing. In these materials, however, such nematic correlations are intertwined with antiferromagnetic or charge orders, preventing the identification of the essential role of nematic fluctuations. This calls for new materials having only nematicity without competing or coexisting orders. Here we report systematic elastoresistance measurements in FeSe1-xSx superconductors, which, unlike other iron-based families, exhibit an electronic nematic order without accompanying antiferromagnetic order. We find that the nematic transition temperature decreases with sulfur content x; whereas, the nematic fluctuations are strongly enhanced. Near [Formula: see text], the nematic susceptibility diverges toward absolute zero, revealing a nematic quantum critical point. The obtained phase diagram for the nematic and superconducting states highlights FeSe1-xSx as a unique nonmagnetic system suitable for studying the impact of nematicity on superconductivity.

Inverse correlation between quasiparticle mass and T c in a cuprate high-T c superconductor

Close to a zero-temperature transition between ordered and disordered electronic phases, quantum fluctuations can lead to a strong enhancement of 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 copper-oxide materials (cuprates) may also be driven by the same mechanism. Close to optimal doping, where the superconducting transition temperature T c is maximal in 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 YBa2Cu3O7-δ 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 YBa2Cu4O8 under hydrostatic pressure. In contrast to the results for YBa2Cu3O7-δ, we find that in YBa2Cu4O8, 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.

Sequence of Quantum Phase Transitions in Bi2Sr2CaCu2O(8+δ) Cuprates Revealed by In Situ Electrical Doping of One and the Same Sample

Our recently discovered electrical doping technique allows a broad-range variation of carrier concentration without changing the chemical composition. We show that it is possible to induce superconductivity in a nondoped insulating sample and to tune it reversibly all the way to an overdoped metallic state. This way, we can investigate the whole doping diagram of one and the same sample. Our study reveals two distinct critical points. The one at the overdoped side is associated with the onset of the pseudogap and with the metal-to-insulator transition in the c-axis transport. The other at optimal doping is associated with the appearance of a "dressed" electron energy. Our study confirms the existence of multiple phase transitions under the superconducting dome in cuprates.