Nearly singular magnetic fluctuations in the normal state of a high-Tc cuprate superconductor

Quantum criticality at cryogenic melting of polar bubble lattices

Quantum fluctuations (QFs) caused by zero-point phonon vibrations (ZPPVs) are known to prevent the occurrence of polar phases in bulk incipient ferroelectrics down to 0 K. On the other hand, little is known about the effects of QFs on the recently discovered topological patterns in ferroelectric nanostructures. Here, by using an atomistic effective Hamiltonian within classical Monte Carlo (CMC) and path integral quantum Monte Carlo (PI-QMC), we unveil how QFs affect the topology of several dipolar phases in ultrathin Pb(Zr0.4Ti0.6)O3 (PZT) films. In particular, our PI-QMC simulations show that the ZPPVs do not suppress polar patterns but rather stabilize the labyrinth, bimeron and bubble phases within a wider range of bias field magnitudes. Moreover, we reveal that quantum fluctuations induce a quantum critical point (QCP) separating a hexagonal bubble lattice from a liquid-like state characterized by spontaneous motion, creation and annihilation of polar bubbles at cryogenic temperatures. Finally, we show that the discovered quantum melting is associated with anomalous physical response, as, e.g., demonstrated by a negative longitudinal piezoelectric coefficient.

Entropic Origin of Pseudogap Physics and a Mott-Slater Transition in Cuprates

We propose a new approach to understand the origin of the pseudogap in the cuprates, in terms of bosonic entropy. The near-simultaneous softening of a large number of different q-bosons yields an extended range of short-range order, wherein the growth of magnetic correlations with decreasing temperature T is anomalously slow. These entropic effects cause the spectral weight associated with the Van Hove singularity (VHS) to shift rapidly and nearly linearly toward half filling at higher T, consistent with a picture of the VHS driving the pseudogap transition at a temperature ~T*. As a byproduct, we develop an order-parameter classification scheme that predicts supertransitions between families of order parameters. As one example, we find that by tuning the hopping parameters, it is possible to drive the cuprates across a transition between Mott and Slater physics, where a spin-frustrated state emerges at the crossover.

Singularity of the London penetration depth at quantum critical points in superconductors

We present a general theory of the singularity in the London penetration depth at symmetry-breaking and topological quantum critical points within a superconducting phase. While the critical exponents and ratios of amplitudes on the two sides of the transition are universal, an overall sign depends upon the interplay between the critical theory and the underlying Fermi surface. We determine these features for critical points to spin density wave and nematic ordering, and for a topological transition between a superconductor with Z2 fractionalization and a conventional superconductor. We note implications for recent measurements of the London penetration depth in BaFe2(As(1-x)P(x))2 [K. Hashimoto et al., Science 336, 1554 (2012)].

Theory of a continuous stripe melting transition in a two-dimensional metal: a possible application to cuprate superconductors

We construct a theory of continuous stripe melting quantum phase transitions in two-dimensional metals and the associated Fermi surface reconstruction. Such phase transitions are strongly coupled but yet theoretically tractable in situations where the stripe ordering is destroyed by proliferating doubled dislocations of the charge stripe order. The resulting non-Landau quantum critical point has strong stripe fluctuations which we show decouple dynamically from the Fermi surface even though static stripe ordering reconstructs the Fermi surface. We discuss connections to various stripe phenomena in the cuprates. We point out several puzzling aspects of old experimental results [G. Aeppli et al., Science 278, 1432 (1997)] on singular stripe fluctuations in the cuprates, and provide a possible explanation within our theory. These results may thus have been the first observation of non-Landau quantum criticality in an experiment.

Toward a theory for low-frequency spin dynamics in plane copper oxide superconductors: crossover from localized spins to weak coupling charge carriers with doping

We explore for all wavevectors through the Brillouin zone the dynamic spin susceptibility χ(total)(+,-)(ω, q) that takes into account the interplay of localized and itinerant charge carriers. The imaginary part, Imχ(total)(+,-)(ω, q), has peaks at the antiferromagnetic wavevector Q = (π, π) and a diffusive-like, extremely narrow and sharp peak (symmetric ring of maxima |q| = q(0)) at very small wavevectors Q(0) is proportional to w/J ≈ 10(-6) with the nuclear magnetic/quadrupole resonance frequency ω and the superexchange coupling constant J. We demonstrate the capability of Imχ(total)(+,-)(ω, q) for plane copper (63)(1/T(1)) and oxygen (17)(1/T(1)) nuclear spin-lattice relaxation rate calculations from carrier free right up to optimally doped La(2 - x)Sr(x)CuO(4) and obtain the basic features of temperature and doping behavior for (63)(1/T(1)) in agreement with experimental observations.

Quantum oscillations in the high-Tc cuprates

We review recent progress in the study of quantum oscillations as a tool for uniquely probing low-energy electronic excitations in high-T(c) cuprate superconductors. Quantum oscillations in the underdoped cuprates reveal that a close correspondence with Landau Fermi-liquid behaviour persists in the accessed regions of the phase diagram, where small pockets are observed. Quantum oscillation results are viewed in the context of momentum-resolved probes such as photoemission, and evidence examined from complementary experiments for potential explanations for the transformation from a large Fermi surface into small sections. Indications from quantum oscillation measurements of a low-energy Fermi surface instability at low dopings under the superconducting dome at the metal-insulator transition are reviewed, and potential implications for enhanced superconducting temperatures are discussed.

Finite doping signatures of the Mott transition in the two-dimensional Hubbard model

Experiments on layered materials call for a study of the influence of short-range spin correlations on the Mott transition. To this end, we solve the cellular dynamical mean-field equations for the Hubbard model on a plaquette with continuous-time quantum Monte Carlo calculations. The normal-state phase diagram as a function of temperature T, interaction strength U, and filling n reveals that upon increasing n towards the insulator, there is a surface of first-order transition between two metals at nonzero doping. For T above the critical end line there is a maximum in scattering rate.

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.

Elucidation of the origins of transport behaviour and quantum oscillations in high temperature superconducting cuprates

A detailed exposition is given of recent transport and 'quantum oscillation' results from high temperature superconducting (HTSC) systems covering the full carrier range from overdoped to underdoped material. This now very extensive and high quality data set is here interpreted within the framework developed by the author of local pairs and boson-fermion resonance, arising in the context of negative- U behaviour within an inhomogeneous electronic environment. The strong inhomogeneity comes with the mixed-valence condition of these materials, which when underdoped lie in close proximity to the Mott-Anderson transition. The observed intense scattering is presented as resulting from pair formation and from electron-boson collisions in the resonant crossover circumstance. The high level of scattering carries the systems to incoherence in the pseudogapped state, p<p(c)(= 0.183). In a high magnetic field the striped partition of the inhomogeneous charge distribution becomes much strengthened and regularized. Magnetization and resistance oscillations, of period dictated by the favoured positioning of the fluxon array within the real space environment of the diagonal 2D charge striping array, are demonstrated to be responsible for the recently reported behaviour hitherto widely attributed to the quantum oscillation response of a much more standard Fermi liquid condition. A detailed analysis embracing all the experimental data serves to reveal that in the given conditions of very high field, low temperature, 2D-striped, underdoped, d-wave superconducting, HTSC material the flux quantum becomes doubled to h/e.

Magnetic-field-induced soft-mode quantum phase transition in the high-temperature superconductor La1.855Sr0.145CuO4: an inelastic neutron-scattering study

Inelastic neutron-scattering experiments on the high-temperature superconductor La1.855Sr0.145CuO4 reveal a magnetic excitation gap Delta that decreases continuously upon application of a magnetic field perpendicular to the CuO2 planes. The gap vanishes at the critical field required to induce long-range incommensurate antiferromagnetic order, providing compelling evidence for a field-induced soft-mode driven quantum phase transition.

Ising t-J model close to half filling: a Monte Carlo study

Within the recently proposed doped-carrier representation of the projected lattice electron operators we derive a full Ising version of the t-J model. This model possesses the global discrete Z(2) symmetry as a maximal spin symmetry of the Hamiltonian at any values of the coupling constants, t and J. In contrast, in the spin anisotropic limit of the t-J model, usually referred to as the t-J(z) model, the global SU(2) invariance is fully restored at J(z) = 0, so that only the spin-spin interaction has in this model the true Ising form. We discuss a relationship between these two models and the standard isotropic t-J model. We show that the low-energy quasiparticles in all three models share qualitatively similar properties at low doping and small values of J/t. The main advantage of the proposed Ising t-J model over the t-J(z) one is that the former allows for the unbiased Monte Carlo calculations on large clusters of up to 10(3) sites. Within this model we discuss in detail the destruction of the antiferromagnetic (AF) order by doping as well as the interplay between the AF order and hole mobility. We also discuss the effect of the exchange interaction and that of the next-nearest-neighbour hoppings on the destruction of the AF order at finite doping. We show that the short-range AF order is observed in a wide range of temperatures and dopings, much beyond the boundaries of the AF phase. We explicitly demonstrate that the local no-double-occupancy constraint plays the dominant role in destroying the magnetic order at finite doping. Finally, a role of inhomogeneities is discussed.

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.

Quantum phase transition in the itinerant antiferromagnet (V0.9Ti0.1)2O3

Quantum-critical behavior of the itinerant electron antiferromagnet (V0.9Ti0.1)2O3 has been studied by single-crystal neutron scattering. By directly observing antiferromagnetic spin fluctuations in the paramagnetic phase, we have shown that the characteristic energy depends on temperature as c1 +c2T3/2, where c1 and c2 are constants. This T3/2 dependence demonstrates that the present strongly correlated d-electron antiferromagnet clearly shows the criticality of the spin-density-wave quantum phase transition in three space dimensions.

Magnetic-field-induced spin excitations and renormalized spin gap of the underdoped La1.895Sr0.105CuO4 superconductor

High-resolution neutron inelastic scattering experiments in applied magnetic fields have been performed on La1.895Sr0.105CuO4 (LSCO). In zero field, the temperature dependence of the low-energy peak intensity at the incommensurate momentum transfer QIC=(0.5,0.5+/-delta,0),(0.5+/-delta,0.5,0) exhibits an anomaly at the superconducting Tc which broadens and shifts to lower temperature upon the application of a magnetic field along the c axis. A field-induced enhancement of the spectral weight is observed, but only at finite energy transfers and in an intermediate temperature range. These observations establish the opening of a strongly downward renormalized spin gap in the underdoped regime of LSCO. This behavior contrasts with the observed doping dependence of most electronic energy features.

Phenomenological model of protected behavior in the pseudogap state of underdoped cuprate superconductors

By extending previous work on the scaling of low frequency magnetic properties of the 2-1-4 cuprates to the 1-2-3 materials, we arrive at a consistent phenomenological description of protected behavior in the pseudogap state of the magnetically underdoped cuprates. Between zero hole doping and a doping level of approximately 0.22, it reflects the presence of a mixture of an insulating spin liquid that produces the measured magnetic scaling behavior and a Fermi liquid that becomes superconducting for doping levels x>0.06. Our analysis suggests the existence of two quantum critical points, at doping levels x approximately 0.05 and x approximately 0.22, and that d-wave superconductivity in the pseudogap region arises from quasiparticle-spin liquid interaction, i.e., magnetic interactions between quasiparticles in the Fermi liquid induced by their coupling to the spin liquid excitations.

Quantum critical point of an itinerant antiferromagnet in a heavy fermion

A quantum critical point of the heavy fermion Ce(Ru(1-x)Rh(x))2Si2, (x = 0,0.03) has been studied by single-crystalline neutron scattering. By accurately measuring the dynamical susceptibility at the antiferromagnetic wave vector k3 = 0.35c*, we have shown that the inverse energy width gamma(k3), i.e., the inverse correlation time, depends on temperature as gamma(k3) = c1 + c2T((3/2)+/-0.1), where c1 and c2 are x dependent constants, in a low temperature range. This critical exponent 3/2 +/- 0.1 proves that the quantum critical point is controlled by that of the itinerant antiferromagnet.

Quantum criticality and universal scaling of a quantum antiferromagnet

Quantum effects dominate the behaviour of many diverse materials. Of particular current interest are those systems in the vicinity of a quantum critical point (QCP). Their physical properties are predicted to reflect those of the nearby QCP with universal features independent of the microscopic details. The prototypical QCP is the Luttinger liquid (LL), which is of relevance to many quasi-one-dimensional materials. The magnetic material KCuF3 realizes an array of weakly coupled spin chains (or LLs) and thus lies close to but not exactly at the LL quantum critical point. By using inelastic neutron scattering we have collected a complete data set of the magnetic correlations of KCuF3 as a function of momentum, energy and temperature. The LL description is found to be valid over an extensive range of these parameters, and departures from this behaviour at high and low energies and temperatures are identified and explained.

Dispersive excitations in the high-temperature superconductor La2-xSrxCuO4

High-resolution neutron scattering experiments on optimally doped La2-xSrxCuO4 (x=0.16) reveal that the magnetic excitations are dispersive. The dispersion is the same as in YBa2Cu3O6.85, and is quantitatively related to that observed with charge sensitive probes. The associated velocity in La2-xSrxCuO4 is only weakly dependent on doping with a value close to the spin-wave velocity of the insulating (x=0) parent compound. In contrast with the insulator, the excitations broaden rapidly with increasing energy, forming a continuum at higher energy and bear a remarkable resemblance to multiparticle excitations observed in 1D S=1/2 antiferromagnets. The magnetic correlations are 2D, and so rule out the simplest scenarios where the copper oxide planes are subdivided into weakly interacting 1D magnets.

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.

Dichotomy between nodal and antinodal quasiparticles in underdoped (La2-xSrx)CuO4 superconductors

High resolution angle-resolved photoemission measurements on an underdoped (La(2-x)Srx)CuO4 system show that, at energies below 70 meV, the quasiparticle peak is well defined around the (pi/2,pi/2) nodal region and disappears rather abruptly when the momentum is changed from the nodal point to the (pi,0) antinodal point along the underlying "Fermi surface." It indicates that there is an extra low energy scattering mechanism acting upon the antinodal quasiparticles. We propose that this mechanism is the scattering of quasiparticles across the nearly parallel segments of the Fermi surface near the antinodes.

Scaling of the magnetic response in doped antiferromagnets

A theory of the anomalous omega/T scaling of the dynamic magnetic response in cuprates at low doping is presented. It is based on the memory function representation of the dynamical spin susceptibility in a doped antiferromagnet where the damping of the collective mode is constant and large, whereas the equal-time spin correlations saturate at low T. Exact diagonalization results within the t-J model are shown to support assumptions. Consequences, for both the scaling function and the normalization amplitude, are well in agreement with neutron scattering results.

Novel dynamic ccaling regime in hole-doped La2CuO4

Only 3% hole doping by Li is sufficient to suppress the long-range three-dimensional (3D) antiferromagnetic order in La2CuO4. The spin dynamics of such a 2D spin liquid state at T<<J was investigated with measurements of the dynamic magnetic structure factor S(omega,q), using cold neutron spectroscopy, for single crystalline La2Cu0.94Li0.06O4. S(omega,q) peaks sharply at (pi,pi) and crosses over around 50 K from omega/T scaling to a novel low temperature regime characterized by a constant-energy scale. The possible connection to a crossover from the quantum critical to the quantum disordered regime of the 2D antiferromagnetic spin liquid is discussed.

Quantum phase transition in a common metal

The classical theory of solids, based on the quantum mechanics of single electrons moving in periodic potentials, provides an excellent description of substances ranging from semiconducting silicon to superconducting aluminium. Over the last fifteen years, it has become increasingly clear that there are substances for which the conventional approach fails. Among these are certain rare earth compounds and transition metal oxides, including high-temperature superconductors. A common feature of these materials is complexity, in the sense that they have relatively large unit cells containing heterogeneous mixtures of atoms. Although many explanations have been put forward for their anomalous properties, it is still possible that the classical theory might suffice. Here we show that a very common chromium alloy has some of the same peculiarities as the more exotic materials, including a quantum critical point, a strongly temperature-dependent Hall resistance and evidence for a 'pseudogap'. This implies that complexity is not a prerequisite for unconventional behaviour. Moreover, it should simplify the general task of explaining anomalous properties because chromium is a relatively simple system in which to work out in quantitative detail the consequences of the conventional theory of solids.

Magnetoresistance of untwinned YBa(2)Cu(3)O(y) single crystals in a wide range of doping: anomalous hole-doping dependence of the coherence length

Magnetoresistance (MR) in the a-axis resistivity of untwinned YBa(2)Cu(3)O(y) single crystals is measured for a wide range of doping ( y = 6.45-7.0). The y dependence of the in-plane coherence length xi(ab) estimated from the fluctuation magnetoconductance indicates that the superconductivity is anomalously weakened in the 60-K phase; this observation, together with the Hall coefficient and the a-axis thermopower data which suggest the hole doping to be 12% for y approximately equal to 6.65, gives evidence that the origin of the 60-K plateau is the 1/8 anomaly. At high temperatures, the normal-state MR data show signatures of the Zeeman effect on the pseudogap in underdoped samples.

Freezing of a stripe liquid

The existence of a stripe-liquid phase in a layered nickelate, La(1.725)Sr(0.275)NiO(4), is demonstrated through neutron scattering measurements. We show that incommensurate magnetic fluctuations evolve continuously through the charge-ordering temperature, although an abrupt decrease in the effective damping energy is observed on cooling through the transition. The energy and momentum dependence of the magnetic scattering are parametrized with a damped-harmonic-oscillator model describing overdamped spin waves in the antiferromagnetic domains defined instantaneously by charge stripes.

Antiferromagnetic order induced by an applied magnetic field in a high-temperature superconductor

One view of the high-transition-temperature (high-Tc) copper oxide superconductors is that they are conventional superconductors where the pairing occurs between weakly interacting quasiparticles (corresponding to the electrons in ordinary metals), although the theory has to be pushed to its limit. An alternative view is that the electrons organize into collective textures (for example, charge and spin stripes) which cannot be 'mapped' onto the electrons in ordinary metals. Understanding the properties of the material would then need quantum field theories of objects such as textures and strings, rather than point-like electrons. In an external magnetic field, magnetic flux penetrates type II superconductors via vortices, each carrying one flux quantum. The vortices form lattices of resistive material embedded in the non-resistive superconductor, and can reveal the nature of the ground state-for example, a conventional metal or an ordered, striped phase-which would have appeared had superconductivity not intervened, and which provides the best starting point for a pairing theory. Here we report that for one high-Tc superconductor, the applied field that imposes the vortex lattice also induces 'striped' antiferromagnetic order. Ordinary quasiparticle models can account for neither the strength of the order nor the nearly field-independent antiferromagnetic transition temperature observed in our measurements.

Thermodynamics of the interplay between magnetism and high-temperature superconductivity

Copper-oxide-based high-temperature superconductors have complex phase diagrams with multiple ordered phases. It even appears that the highest superconducting transition temperatures for certain cuprates are found in samples that display simultaneous onset of magnetism and superconductivity. We show here how the thermodynamics of fluid mixtures-a touchstone for chemistry as well as hard and soft condensed matter physics-accounts for this startling observation, as well as many other properties of the cuprates in the vicinity of the instability toward "striped" magnetism.

Scaling near the quantum-critical point in the SO(5) theory of the high-T(c) superconductivity

We study the quantum-critical point scenario within the unified theory of superconductivity and antiferromagnetism based on the SO(5) symmetry. Closed-form expression for the quantum-critical scaling function for the dynamic spin susceptibility is obtained from the lattice SO(5) quantum nonlinear sigma-model in three dimensions, revealing that in the quantum-critical region the frequency scale for spin excitations is simply set by the absolute temperature. Implications for the non-Fermi liquid behavior of the normal-state resistivity due to spin fluctuations in the quantum-critical region are also presented.

Spin orthogonality catastrophe in two-dimensional antiferromagnets and superconductors

We compute the spectral function of a spin S hole injected into a two-dimensional antiferromagnet or superconductor in the vicinity of a magnetic quantum critical point. We show that, near Van Hove singularities, the problem maps onto that of a static vacancy carrying excess spin S. The hole creation operator is characterized by a new boundary anomalous dimension and a vanishing quasiparticle residue at the critical point. We discuss possible relevance to photoemission spectra of cuprate superconductors near the antinodal points.

Spins in the vortices of a high-temperature superconductor

Neutron scattering is used to characterize the magnetism of the vortices for the optimally doped high-temperature superconductor La(2-x)Sr(x)CuO4 (x = 0.163) in an applied magnetic field. As temperature is reduced, low-frequency spin fluctuations first disappear with the loss of vortex mobility, but then reappear. We find that the vortex state can be regarded as an inhomogeneous mixture of a superconducting spin fluid and a material containing a nearly ordered antiferromagnet. These experiments show that as for many other properties of cuprate superconductors, the important underlying microscopic forces are magnetic.

Room-temperature electronic phase transitions in the continuous phase diagrams of perovskite manganites

Highly correlated electronic systems--such as transition-metal oxides that are doped Mott insulators--are complex systems which exhibit puzzling phenomena, including high-temperature superconductivity and colossal magnetoresistivity. Recent studies suggest that in such systems collective electronic phenomena are important, arising from long-range Coulomb interactions and magnetic effects. The qualitative behaviour of these systems is strongly dependent on charge filling (the level of doping) and the lattice constant. Here we report a time-efficient and systematic experimental approach for studying the phase diagrams of condensed-matter systems. It involves the continuous mapping of the physical properties of epitaxial thin films of perovskite manganites (a class of doped Mott insulator) as their composition is varied. We discover evidence that suggests the presence of phase boundaries of electronic origin at room temperature.

The spin excitation spectrum in superconducting YBa(2)Cu(3)O(6.85)

A comprehensive inelastic neutron scattering study of magnetic excitations in the near optimally doped high-temperature superconductor YBa(2)Cu(3)O(6.85) is presented. The spin correlations in the normal state are commensurate with the crystal lattice, and the intensity is peaked around the wave vector characterizing the antiferromagnetic state of the insulating precursor, YBa(2)Cu(3)O(6). Profound modifications of the spin excitation spectrum appear abruptly below the superconducting transition temperature T(c), where a commensurate resonant mode and a set of weaker incommensurate peaks develop. The data are consistent with models that are based on an underlying two-dimensional Fermi surface, predicting a continuous, downward dispersion relation connecting the resonant mode and the incommensurate excitations. The magnetic incommensurability in the YBa(2)Cu(3)O(6+)(x) system is thus not simply related to that of another high-temperature superconductor, La(2-)(x)Sr(x)CuO(4), where incommensurate peaks persist well above T(c). The temperature-dependent incommensurability is difficult to reconcile with interpretations based on charge stripe formation in YBa(2)Cu(3)O(6+x) near optimum doping.

Advances in the physics of high-temperature superconductivity

The high-temperature copper oxide superconductors are of fundamental and enduring interest. They not only manifest superconducting transition temperatures inconceivable 15 years ago, but also exhibit many other properties apparently incompatible with conventional metal physics. The materials expand our notions of what is possible, and compel us to develop new experimental techniques and theoretical concepts. This article provides a perspective on recent developments and their implications for our understanding of interacting electrons in metals.

Quantum criticality: competing ground states in low dimensions

Small changes in an external parameter can often lead to dramatic qualitative changes in the lowest energy quantum mechanical ground state of a correlated electron system. In anisotropic crystals, such as the high-temperature superconductors where electron motion occurs primarily on a two-dimensional square lattice, the quantum critical point between two such lowest energy states has nontrivial emergent excitations that control the physics over a significant portion of the phase diagram. Nonzero temperature dynamic properties near quantum critical points are described, using simple theoretical models. Possible quantum phases and transitions in the two-dimensional electron gas on a square lattice are discussed.

Strongly enhanced magnetic excitations near the quantum critical point of Cr1-xVx and why strong exchange enhancement need not imply heavy fermion behavior

Inelastic neutron scattering reveals strong spin fluctuations with energies as high as 0.4 eV in the nearly antiferromagnetic metal Cr0. 95V0.05. The magnetic response is well described by a modified Millis-Monien-Pines function. From the low-energy response, we deduce a large exchange enhancement, more than an order of magnitude larger than the corresponding enhancement of the low-temperature electronic heat capacity gammaT. A scaling relationship between gamma and the inverse of the wave vector-averaged spin relaxation rate gammaave is demonstrated for a number of magnetically correlated metals.

Quantum-critical conductivity scaling for a metal-insulator transition

Temperature (T)- and frequency (omega)-dependent conductivity measurements are reported here in amorphous niobium-silicon alloys with compositions (x) near the zero-temperature metal-insulator transition. There is a one-to-one correspondence between the frequency- and temperature-dependent conductivity on both sides of the critical concentration, thus establishing the quantum-critical nature of the transition. The analysis of the conductivity leads to a universal scaling function and establishes the critical exponents. This scaling can be described by an x-, T-, and omega-dependent characteristic length, the form of which is derived by experiment.

One-Dimensional Electronic Structure and Suppression of d-Wave Node State in (La(1.28)Nd(0.6)Sr(0.12))CuO(4)

Angle-resolved photoemission spectroscopy was carried out on (La(1.28)Nd(0.6) Sr(0.12))CuO(4), a model system of the charge- and spin-ordered state, or stripe phase. The electronic structure contains characteristic features consistent with other cuprates, such as the flat band at low energy near the Brillouin zone face. However, the low-energy excitation near the expected d-wave node region is strongly suppressed. The frequency-integrated spectral weight is confined inside one-dimensional segments in the momentum space (defined by horizontal momenta &cjs3539;k(x)&cjs3539; = pi/4 and vertical momenta &cjs3539;k(y)&cjs3539; = pi/4), deviating strongly from the more rounded Fermi surface expected from band calculations. This departure from the two-dimensional Fermi surface persists to a very high energy scale. These results provide important information for establishing a theory to understand the charge and spin ordering in cuprates and their relation with high-temperature superconductivity.

Evidence for quantum critical behavior in the optimally doped cuprate Bi(2)Sr(2)CaCu(2)O(8+delta)

The photoemission line shapes of the optimally doped cuprate Bi(2)Sr(2)CaCu(2)O(8+delta) were studied in the direction of a node in the superconducting order parameter by means of very high resolution photoemission spectroscopy. The peak width or inverse lifetime of the excitation displays a linear temperature dependence, independent of binding energy, for small energies, and a linear energy dependence, independent of temperature, for large binding energies. This behavior is unaffected by the superconducting transition, which is an indication that the nodal states play no role in the superconductivity. Temperature-dependent scaling suggests that the system displays quantum critical behavior.

Stripe phases in high-temperature superconductors

Stripe phases are predicted and observed to occur in a class of strongly correlated materials describable as doped antiferromagnets, of which the copper-oxide superconductors are the most prominent representatives. The existence of stripe correlations necessitates the development of new principles for describing charge transport and especially superconductivity in these materials.