Signature of optimal doping in Hall-effect measurements on a high-temperature superconductor

Spin Echo, Fidelity, and the Quantum Critical Fan in TmVO_{4}

Using spin-echo nuclear magnetic resonance in the model transverse field Ising system TmVO_{4}, we show that low frequency quantum fluctuations at the quantum critical point have a very different effect on ^{51}V nuclear spins than classical low-frequency noise or fluctuations that arise at a finite temperature critical point. Spin echoes filter out the low-frequency classical noise but not the quantum fluctuations. This allows us to directly visualize the quantum critical fan and demonstrate the persistence of quantum fluctuations at the critical coupling strength in TmVO_{4} to high temperatures in an experiment that remains transparent to finite temperature classical phase transitions. These results show that while dynamical decoupling schemes can be quite effective in eliminating classical noise in a qubit, a quantum critical environment may lead to rapid entanglement and decoherence.

Superconductivity in an extreme strange metal

Some of the highest-transition-temperature superconductors across various materials classes exhibit linear-in-temperature 'strange metal' or 'Planckian' electrical resistivities in their normal state. It is thus believed by many that this behavior holds the key to unlock the secrets of high-temperature superconductivity. However, these materials typically display complex phase diagrams governed by various competing energy scales, making an unambiguous identification of the physics at play difficult. Here we use electrical resistivity measurements into the micro-Kelvin regime to discover superconductivity condensing out of an extreme strange metal state-with linear resistivity over 3.5 orders of magnitude in temperature. We propose that the Cooper pairing is mediated by the modes associated with a recently evidenced dynamical charge localization-delocalization transition, a mechanism that may well be pertinent also in other strange metal superconductors.

Magnetic field reveals vanishing Hall response in the normal state of stripe-ordered cuprates

The origin of the weak insulating behavior of the resistivity, i.e. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\rho }_{xx}\propto {\mathrm{ln}}\,(1/T)$$\end{document}ρxx∝ln(1/T), revealed when magnetic fields (H) suppress superconductivity in underdoped cuprates has been a longtime mystery. Surprisingly, the high-field behavior of the resistivity observed recently in charge- and spin-stripe-ordered La-214 cuprates suggests a metallic, as opposed to insulating, high-field normal state. Here we report the vanishing of the Hall coefficient in this field-revealed normal state for all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T\ <\ (2-6){T}_{{\rm{c}}}^{0}$$\end{document}T<(2−6)Tc0, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${T}_{{\rm{c}}}^{0}$$\end{document}Tc0 is the zero-field superconducting transition temperature. Our measurements demonstrate that this is a robust fundamental property of the normal state of cuprates with intertwined orders, exhibited in the previously unexplored regime of T and H. The behavior of the high-field Hall coefficient is fundamentally different from that in other cuprates such as YBa₂Cu₃O_6+x and YBa₂Cu₄O₈, and may imply an approximate particle-hole symmetry that is unique to stripe-ordered cuprates. Our results highlight the important role of the competing orders in determining the normal state of cuprates.

The Hall effect has been used as a probe of the normal state of cuprates, when superconductivity is supressed by a magnetic field. Here, the authors report the vanishing of the Hall coefficient at high magnetic field in cuprates with stripe order and interpret it as a signature of the stripe-ordered phase.

Anomalies in the pseudogap phase of the cuprates: competing ground states and the role of umklapp scattering

Over the past two decades, advances in computational algorithms have revealed a curious property of the two-dimensional Hubbard model (and related theories) with hole doping: the presence of close-in-energy competing ground states that display very different physical properties. On the one hand, there is a complicated state exhibiting intertwined spin, charge, and pair density wave orders. We call this 'type A'. On the other hand, there is a uniform d-wave superconducting state that we denote as 'type B'. We advocate, with the support of both microscopic theoretical calculations and experimental data, dividing the high-temperature cuprate superconductors into two corresponding families, whose properties reflect either the type A or type B ground states at low temperatures. We review the anomalous properties of the pseudogap phase that led us to this picture, and present a modern perspective on the role that umklapp scattering plays in these phenomena in the type B materials. This reflects a consistent framework that has emerged over the last decade, in which Mott correlations at weak coupling drive the formation of the pseudogap. We discuss this development, recent theory and experiments, and open issues.

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.

Superconducting Properties of 3D Low-Density TI-Bipolaron Gas in Magnetic Field

Consideration is given to thermodynamical properties of a three-dimensional Bose-condensate of translation-invariant bipolarons (TI-bipolarons) in magnetic field. The critical temperature of transition, critical magnetic fields, energy, heat capacity and the transition heat of TI-bipolaron gas are calculated. Such values as maximum magnetic field, London penetration depth and their temperature dependencies are calculated. The results obtained are used to explain experiments on high-temperature superconductors.

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.

Response of the Lattice across the Filling-Controlled Mott Metal-Insulator Transition of a Rare Earth Titanate

The lattice response of a prototype Mott insulator, SmTiO_{3}, to hole doping is investigated with atomic-scale spatial resolution. SmTiO_{3} films are doped with Sr on the Sm site with concentrations that span the insulating and metallic sides of the filling-controlled Mott metal-insulator transition (MIT). The GdFeO_{3}-type distortions are investigated using an atomic resolution scanning transmission electron microscopy technique that can resolve small lattice distortions with picometer precision. We show that these distortions are gradually and uniformly reduced as the Sr concentration is increased without any phase separation. Significant distortions persist into the metallic state. The results present a new picture of the physics of this prototype filling-controlled MIT, which is discussed.

Indications of an electronic phase transition in two-dimensional superconducting YBa2Cu3O(7-x) thin films induced by electrostatic doping

We successfully tuned an underdoped ultrathin YBa2Cu3O(7-x) film into the overdoped regime by means of electrostatic doping using an ionic liquid as a dielectric material. This process proved to be reversible. Transport measurements showed a series of anomalous features compared to chemically doped bulk samples and a different two-step doping mechanism for electrostatic doping was revealed. The normal resistance increased with carrier concentration on the overdoped side and the high temperature (180 K) Hall number peaked at a doping level of p∼0.15. These anomalous behaviors suggest that there is an electronic phase transition in the Fermi surface around the optimal doping level.

From underdoped to overdoped cuprates: two quantum phase transitions

Several experimental and theoretical studies indicate the existence of a critical point separating the underdoped and overdoped regions of the high-T(c) cuprates' phase diagram. There are at least two distinct proposals on the critical concentration and its physical origin. The first one is associated with the pseudogap formation for p < p, with p≈0.2. The other relies on the Hall effect measurements and suggests that the critical point and the quantum phase transition (QPT) take place at optimal doping, p(opt)≈0.16. Here we have performed a precise density of states calculation and found that there are two QPTs and the corresponding critical concentrations associated with the change of the Fermi surface topology upon doping.

Lattice distortion and magnetic quantum phase transition in CeFeAs(1-x)P(x)O

We use neutron diffraction to study the structural and magnetic phase diagram of CeFeAs(1-x)P(x)O. We find that replacing the larger arsenic with smaller phosphorus in CeFeAs(1-x)P(x)O simultaneously suppresses the AFM order and orthorhombic distortion near x=0.4, thus suggesting the presence of a magnetic quantum critical point. Our detailed structural analysis reveals that the pnictogen height is an important controlling parameter for their electronic and magnetic properties, and may play an important role in electron pairing and superconductivity of these materials.

Fermi surface reconstruction in high-T(c) superconductors

The recent observation of quantum oscillations in underdoped high-T(c) superconductors, combined with their negative Hall coefficient at low temperature, reveals that the Fermi surface of hole-doped cuprates includes a small electron pocket. This strongly suggests that the large hole Fermi surface characteristic of the overdoped regime undergoes a reconstruction caused by the onset of some order which breaks translational symmetry. Here we consider the possibility that this order is 'stripe' order, a form of combined charge/spin modulation observed most clearly in materials like Eu-doped and Nd-doped LSCO (La(2-x)Sr(x)CuO(4)). In these materials, the onset of stripe order coincides with major changes in transport properties, providing strong evidence that stripe order is indeed the cause of Fermi surface reconstruction. We identify the critical doping where this reconstruction occurs and show that the temperature dependence of transport coefficients at that doping is typical of metals at a quantum critical point. We discuss how the pseudogap phase may be a fluctuating precursor of the stripe-ordered phase.

Quantum phase transition in the magnetic-field-induced normal state of optimum-doped high-Tc cuprate superconductors at low temperatures

A 60 T magnetic field suppresses the superconducting transition temperature T_{c} in La_{2-p}Sr_{p}CuO_{4} to reveal a Hall number anomaly, which develops only at temperatures below zero-field T_{c} and peaks at the exact location of p that maximizes T_{c}. The anomaly bears a striking resemblance to observations in Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta}, suggesting a normal-state phenomenology common to the cuprates that underlies the high-temperature superconducting phase. The peak is ascribed to a Fermi surface reconstruction at a quantum phase transition near optimum doping that is coincident with the collapse of the pseudogap state.

Electron pockets in the Fermi surface of hole-doped high-Tc superconductors

High-temperature superconductivity in copper oxides occurs when the materials are chemically tuned to have a carrier concentration intermediate between their metallic state at high doping and their insulating state at zero doping. The underlying evolution of the electron system in the absence of superconductivity is still unclear, and a question of central importance is whether it involves any intermediate phase with broken symmetry. The Fermi surface of the electronic states in the underdoped 'YBCO' materials YBa2Cu3O(y) and YBa2Cu4O8 was recently shown to include small pockets, in contrast with the large cylinder that characterizes the overdoped regime, pointing to a topological change in the Fermi surface. Here we report the observation of a negative Hall resistance in the magnetic-field-induced normal state of YBa2Cu3O(y) and YBa2Cu4O8, which reveals that these pockets are electron-like rather than hole-like. We propose that these electron pockets most probably arise from a reconstruction of the Fermi surface caused by the onset of a density-wave phase, as is thought to occur in the electron-doped copper oxides near the onset of antiferromagnetic order. Comparison with materials of the La2CuO4 family that exhibit spin/charge density-wave order suggests that a Fermi surface reconstruction also occurs in those materials, pointing to a generic property of high-transition-temperature (T(c)) superconductors.

High-field Hall resistivity and magnetoresistance of electron-doped Pr2-xCexCuO4-delta

We report resistivity and Hall effect measurements in electron-doped Pr2-xCexCuO4-delta films in magnetic field up to 58 T. In contrast to hole-doped cuprates, we find a surprising nonlinear magnetic field dependence of Hall resistivity at high field in the optimally doped and overdoped films. We also observe a crossover from quadratic to linear field dependence of the positive magnetoresistance in the overdoped films. A spin density wave induced Fermi surface reconstruction model can be used to qualitatively explain both the Hall effect and magnetoresistance.

An Intrinsic Bond-Centered Electronic Glass with Unidirectional Domains in Underdoped Cuprates

Removing electrons from the CuO2 plane of cuprates alters the electronic correlations sufficiently to produce high-temperature superconductivity. Associated with these changes are spectral-weight transfers from the high-energy states of the insulator to low energies. In theory, these should be detectable as an imbalance between the tunneling rate for electron injection and extraction-a tunneling asymmetry. We introduce atomic-resolution tunneling-asymmetry imaging, finding virtually identical phenomena in two lightly hole-doped cuprates: Ca(1.88)Na(0.12)CuO(2)Cl2 and Bi2Sr2Dy(0.2)Ca(0.8)Cu2O(8+delta). Intense spatial variations in tunneling asymmetry occur primarily at the planar oxygen sites; their spatial arrangement forms a Cu-O-Cu bond-centered electronic pattern without long-range order but with 4a(0)-wide unidirectional electronic domains dispersed throughout (a(0): the Cu-O-Cu distance). The emerging picture is then of a partial hole localization within an intrinsic electronic glass evolving, at higher hole densities, into complete delocalization and highest-temperature superconductivity.

Interplay of externally doped and thermally activated holes in La(2-x)Sr(x)CuO4 and their impact on the pseudogap crossover

We presented the recent Hall effect data for a number of carriers in La(2-x)Sr(x)CuO4 as the sum of two components: the temperature independent term n0(x), which is due to external doping, and the thermally activated contribution. Their balance determines the crossover temperature T*(x) from the marginal Fermi liquid to pseudogap regime. The activation energy Delta(x) for thermally excited carriers equals the energy between the Fermi surface "arc" and the band bottom, as seen in angle-resolved photoemission spectroscopy experiments. Other implications for the (T, x)-phase diagram of cuprates are also discussed.

Breakdown of one-parameter scaling in quantum critical scenarios for high-temperature copper-oxide superconductors

We show that if the excitations which become gapless at a quantum critical point also carry the electrical current, then a resistivity linear in temperature, as is observed in the copper-oxide high-temperature superconductors, obtains only if the dynamical exponent z satisfies the unphysical constraint, z < 0. At fault here is the universal scaling hypothesis that, at a continuous phase transition, the only relevant length scale is the correlation length. Consequently, either the electrical current in the normal state of the cuprates is carried by degrees of freedom which do not undergo a quantum phase transition, or quantum critical scenarios must forgo this basic scaling hypothesis and demand that more than a single-correlation length scale is necessary to model transport in the cuprates.

Quantum critical 5f electrons avoid singularities in U(Ru,Rh)2Si2

We present specific heat measurements of 4% Rh-doped URu2Si2 at magnetic fields around the proposed metamagnetic transition field H(m) approximately 34 T, revealing striking similarities to the isotructural Ce analog CeRu2Si2 for H>H(m). This suggests that strongly renormalized hybridized-band models apply equally well to both systems. The vanishing bandwidths as H-->H(m) are consistent with a quantum-critical point close to H(m). The existence of a phase transition into an ordered phase in the vicinity of H(m) for 4% Rh-doped URu2Si2, but not for CeRu2Si2, is consistent with a stronger superexchange in the case of the U 5f system. Irreversible processes at the transition indicate a strong coupling of the 5f orbitals to the lattice, most suggestive of electric quadrupolar order.

Mapping sites of positive selection and amino acid diversification in the HIV genome: an alternative approach to vaccine design?

A safe and effective HIV-1 vaccine is urgently needed to control the worldwide AIDS epidemic. Traditional methods of vaccine development have been frustratingly slow, and it is becoming increasingly apparent that radical new approaches may be required. Computational and mathematical approaches, combined with evolutionary reasoning, may provide new insights for the design of an efficacious AIDS vaccine. Here, we used codon-based substitution models and maximum-likelihood (ML) methods to identify positively selected sites that are likely to be involved in the immune control of HIV-1. Analysis of subtypes B and C revealed widespread adaptive evolution. Positively selected amino acids were detected in all nine HIV-1 proteins, including Env. Of particular interest was the high level of positive selection within the C-terminal regions of the immediate-early regulatory proteins, Tat and Rev. Many of the amino acid replacements were associated with the emergence of novel (or alternative) myristylation and casein kinase II (CKII) phosphorylation sites. The impact of these changes on the conformation and antigenicity of Tat and Rev remains to be established. In rhesus macaques, a single CTL-associated amino substitution in Tat has been linked to escape from acute SIV infection. Understanding the relationship between host-driven positive selection and antigenic variation may lead to the development of novel vaccine strategies that preempt the escape process.

Hall-effect evolution across a heavy-fermion quantum critical point

A quantum critical point (QCP) develops in a material at absolute zero when a new form of order smoothly emerges in its ground state. QCPs are of great current interest because of their singular ability to influence the finite temperature properties of materials. Recently, heavy-fermion metals have played a key role in the study of antiferromagnetic QCPs. To accommodate the heavy electrons, the Fermi surface of the heavy-fermion paramagnet is larger than that of an antiferromagnet. An important unsolved question is whether the Fermi surface transformation at the QCP develops gradually, as expected if the magnetism is of spin-density-wave (SDW) type, or suddenly, as expected if the heavy electrons are abruptly localized by magnetism. Here we report measurements of the low-temperature Hall coefficient (R(H))--a measure of the Fermi surface volume--in the heavy-fermion metal YbRh2Si2 upon field-tuning it from an antiferromagnetic to a paramagnetic state. R(H) undergoes an increasingly rapid change near the QCP as the temperature is lowered, extrapolating to a sudden jump in the zero temperature limit. We interpret these results in terms of a collapse of the large Fermi surface and of the heavy-fermion state itself precisely at the QCP.

Electronic phase diagram of high-Tc cuprate superconductors from a mapping of the in-plane resistivity curvature

We propose that resistivity curvature mapping (RCM) based on the in-plane resistivity data is a useful way to objectively draw electronic phase diagrams of high-Tc cuprates, where various crossovers are important. In particular, the pseudogap crossover line can be conveniently determined by RCM. We show experimental phase diagrams obtained by RCM for Bi2Sr2-zLazCuO6+delta, La2-xSrxCuO4, and YBa2Cu3Oy, and demonstrate the universal nature of the pseudogap crossover. Intriguingly, the electronic crossover near optimum doping depicted by RCM appears to occur rather abruptly, suggesting that the quantum-critical regime, if it exists, must be very narrow.

Robust dx2-y2 pairing symmetry in hole-doped cuprate superconductors

Although initially quite controversial, it is now widely accepted that the Cooper pairs in optimally doped cuprate superconductors have predominantly dx2-y2 wave function symmetry, and the controversy has now shifted to whether the pairing symmetry changes away from optimal doping. Here we present phase-sensitive tricrystal experiments on three cuprate systems: Y(0.7)Ca(0.3)Ba(2)Cu(3)O(7-delta) (Ca-doped Y-123), La2-xSrxCuO4 (La-214), and Bi(2)Sr(2)CaCu(2)O(8+delta) (Bi-2212), with doping levels covering the underdoped, optimal, and overdoped regions. Our work implies that predominantly d x2-y2 pairing symmetry is robust over a large variation in doping.

Quantum phase transitions in the cuprate superconductor Bi2Sr2-xLaxCuO6+delta

To elucidate a quantum phase transition (QPT) in Bi(2)Sr(2-x)La(x)CuO(6+delta), we measure charge and heat transport properties at very low temperatures and examine the following characteristics for a wide range of doping: normal-state resistivity anisotropy under 58 T, temperature dependence of the in-plane thermal conductivity kappa(ab), and the magnetic-field dependence of kappa(ab). It turns out that all of them show signatures of a QPT at the 1/8 hole doping. Together with the recent normal-state Hall measurements under 58 T that signified the existence of a QPT at optimum doping, the present results indicate that there are two QPTs in the superconducting doping regime of this material.

Enhancement of pairing correlation by t' in the two-dimensional extended t-J model

We investigate the effects of the next-nearest-neighbor (t') and the third-nearest-neighbor (t") hopping terms on superconductivity correlation in the 2D hole-doped extended t-J model based on the variational Monte Carlo, mean-field calculation and exact diagonalization method. Despite the diversity of the methods employed, the results all point to a consistent conclusion: While the d-wave superconductivity correlation is slightly suppressed by t' and t" in underdoped regions, it is greatly enhanced in the optimal and overdoped regions. The optimal Tc is a result of the balance of these two opposite trends.

Evidence for a quantum phase transition in Pr2-xCe(x)CuO4-delta from transport measurements

The doping and temperature dependences of the Hall coefficient, R(H), and ab-plane resistivity in the normal state down to 350 mK is reported for oriented films of the electron-doped high-T(c) superconductor Pr(2-x)Ce(x)CuO(4-delta). The doping dependences of beta (rho=rho(0)+ATbeta) and R(H) (at 350 mK) suggest a quantum phase transition at a critical doping near x=0.165.

An explanation for a universality of transition temperatures in families of copper oxide superconductors

A remarkable mystery of the copper oxide high-transition-temperature (T(c)) superconductors is the dependence of T(c) on the number of CuO2 layers, n, in the unit cell of a crystal. In a given family of these superconductors, T(c) rises with the number of layers, reaching a peak at n = 3, and then declines: the result is a bell-shaped curve. Despite the ubiquity of this phenomenon, it is still poorly understood and attention has instead been mainly focused on the properties of a single CuO2 plane. Here we show that the quantum tunnelling of Cooper pairs between the layers simply and naturally explains the experimental results, when combined with the recently quantified charge imbalance of the layers and the latest notion of a competing order nucleated by this charge imbalance that suppresses superconductivity. We calculate the bell-shaped curve and show that, if materials can be engineered so as to minimize the charge imbalance as n increases, T(c) can be raised further.