Dynamical charge density fluctuations pervading the phase diagram of a Cu-based high-T c superconductor.

Charge density modulations have been observed in all families of high-critical temperature (T c) superconducting cuprates. Although they are consistently found in the underdoped region of the phase diagram and at relatively low temperatures, it is still unclear to what extent they influence the unusual properties of these systems. Using resonant x-ray scattering, we carefully determined the temperature dependence of charge density modulations in YBa2Cu3O7-δ and Nd1+ x Ba2- x Cu3O7-δ for several doping levels. We isolated short-range dynamical charge density fluctuations in addition to the previously known quasi-critical charge density waves. They persist up to well above the pseudogap temperature T*, are characterized by energies of a few milli-electron volts, and pervade a large area of the phase diagram.

Gap suppression at a Lifshitz transition in a multi-condensate superconductor.

In multi-orbital materials, superconductivity can exhibit several coupled condensates. In this context, quantum confinement in two-dimensional superconducting oxide interfaces offers new degrees of freedom to engineer the band structure and selectively control the occupancy of 3d orbitals by electrostatic doping. Here, we use resonant microwave transport to extract the superfluid stiffness of the (110)-oriented LaAlO3/SrTiO3 interface in the entire phase diagram. We provide evidence of a transition from single-condensate to two-condensate superconductivity driven by continuous and reversible electrostatic doping, which we relate to the Lifshitz transition between 3d bands based on numerical simulations of the quantum well. We find that the superconducting gap is suppressed while the second band is populated, challenging Bardeen-Cooper-Schrieffer theory. We ascribe this behaviour to the existence of superconducting order parameters with opposite signs in the two condensates due to repulsive coupling. Our findings offer an innovative perspective on the possibility to tune and control multiple-orbital physics in superconducting interfaces.

Re-entrant charge order in overdoped (Bi,Pb)2.12Sr1.88CuO6+δ outside the pseudogap regime.

In the underdoped regime, the cuprate high-temperature superconductors exhibit a host of unusual collective phenomena, including unconventional spin and charge density modulations, Fermi surface reconstructions, and a pseudogap in various physical observables. Conversely, overdoped cuprates are generally regarded as conventional Fermi liquids possessing no collective electronic order. In partial contradiction to this widely held picture, we report resonant X-ray scattering measurements revealing incommensurate charge order reflections for overdoped (Bi,Pb)2.12Sr1.88CuO6+δ (Bi2201), with correlation lengths of 40-60 lattice units, that persist up to temperatures of at least 250 K. The value of the charge order wavevector decreases with doping, in line with the extrapolation of the trend previously observed in underdoped Bi2201. In overdoped materials, however, charge order coexists with a single, unreconstructed Fermi surface without nesting or pseudogap features. The discovery of re-entrant charge order in Bi2201 thus calls for investigations in other cuprate families and for a reconsideration of theories that posit an essential relationship between these phenomena.

Competition between electron pairing and phase coherence in superconducting interfaces.

In LaAlO3/SrTiO3 heterostructures, a gate tunable superconducting electron gas is confined in a quantum well at the interface between two insulating oxides. Remarkably, the gas coexists with both magnetism and strong Rashba spin-orbit coupling. However, both the origin of superconductivity and the nature of the transition to the normal state over the whole doping range remain elusive. Here we use resonant microwave transport to extract the superfluid stiffness and the superconducting gap energy of the LaAlO3/SrTiO3 interface as a function of carrier density. We show that the superconducting phase diagram of this system is controlled by the competition between electron pairing and phase coherence. The analysis of the superfluid density reveals that only a very small fraction of the electrons condenses into the superconducting state. We propose that this corresponds to the weak filling of high-energy dxz/dyz bands in the quantum well, more apt to host superconductivity.

Phase Separation from Electron Confinement at Oxide Interfaces.

Oxide heterostructures are of great interest for both fundamental and applicative reasons. In particular, the two-dimensional electron gas at the LaAlO_{3}/SrTiO_{3} or LaTiO_{3}/SrTiO_{3} interfaces displays many different properties and functionalities. However, there are clear experimental indications that the interface electronic state is strongly inhomogeneous and therefore it is crucial to investigate possible intrinsic mechanisms underlying this inhomogeneity. Here, the electrostatic potential confining the electron gas at the interface is calculated self-consistently, finding that such confinement may induce phase separation, to avoid a thermodynamically unstable state with a negative compressibility. This provides a robust mechanism for the inhomogeneous character of these interfaces.

Glue function of optimally and overdoped cuprates from inversion of the Raman spectra.

We address the issue of identifying the mediators of effective interactions in cuprates superconductors. Specifically, we use inversion theory to analyze Raman spectra of optimally and over-doped La2-x Sr x CuO4 samples. This allows us to extract the so-called glue function without making any a priori assumption based on any specific model. We use instead two different techniques, namely the singular value decomposition and a multi-rectangle decomposition. With both techniques we find consistent results showing that: (i) two distinct excitations are responsible for the glue function, which have completely different doping dependence. One excitation becomes weak above optimal doping, where on the contrary the other keeps (or even slightly increases) its strength; (ii) there is a marked temperature dependence on the weight and spectral distribution of these excitations, which therefore must have a somewhat critical character. It is quite natural to identify and characterize these two distinct excitations as damped antiferromagnetic spin waves and damped charge density waves, respectively. This sets the stage for a scenario in which superconductivity is concomitant and competing with a charge ordering instability.

Interplay between density and superconducting quantum critical fluctuations.

We consider the case of a density-driven metal-superconductor transition in the proximity of an electronic phase separation. In particular, we investigate the interplay between superconducting fluctuations and density fluctuations, which become quantum critical when the electronic phase separation vanishes at zero temperature into a quantum critical point. In this situation, the critical dynamical density fluctuations strongly affect the dynamics of the Cooper-pair fluctuations, which acquire a more singular character with a z = 3 dynamical critical index. This gives rise to a scenario that possibly rules the disappearance of superconductivity when the electron density is reduced by electrostatic gating at the LaAlO3/SrTiO3 interface.

Field-effect control of superconductivity and Rashba spin-orbit coupling in top-gated LaAlO3/SrTiO3 devices.

The recent development in the fabrication of artificial oxide heterostructures opens new avenues in the field of quantum materials by enabling the manipulation of the charge, spin and orbital degrees of freedom. In this context, the discovery of two-dimensional electron gases (2-DEGs) at LaAlO3/SrTiO3 interfaces, which exhibit both superconductivity and strong Rashba spin-orbit coupling (SOC), represents a major breakthrough. Here, we report on the realisation of a field-effect LaAlO3/SrTiO3 device, whose physical properties, including superconductivity and SOC, can be tuned over a wide range by a top-gate voltage. We derive a phase diagram, which emphasises a field-effect-induced superconductor-to-insulator quantum phase transition. Magneto-transport measurements show that the Rashba coupling constant increases linearly with the interfacial electric field. Our results pave the way for the realisation of mesoscopic devices, where these two properties can be manipulated on a local scale by means of top-gates.

Electronic polymers and soft-matter-like broken symmetries in underdoped cuprates.

Empirical evidence in heavy fermion, pnictide and other systems suggests that unconventional superconductivity appears associated to some form of real-space electronic order. For the cuprates, despite several proposals, the emergence of order in the phase diagram between the commensurate antiferromagnetic state and the superconducting state is not well understood. Here we show that in this regime doped holes assemble in 'electronic polymers'. Within a Monte Carlo study, we find that in clean systems by lowering the temperature the polymer melt condenses first in a smectic state and then in a Wigner crystal both with the addition of inversion symmetry breaking. Disorder blurs the positional order leaving a robust inversion symmetry breaking and a nematic order, accompanied by vector chiral spin order and with the persistence of a thermodynamic transition. Such electronic phases, whose properties are reminiscent of soft-matter physics, produce charge and spin responses in good accord with experiments.

Miniaturization in voltammetry: ultratrace element analysis and speciation with twenty-fold sample size reduction.

Voltammetric techniques have emerged as powerful methods for the determination and speciation of trace and ultratrace elements without any preconcentration in several research fields. Nevertheless, large sample volumes are typically required (10 mL), which strongly limits their application and/or the precision of the results. In this work, we report a 20-fold reduction in sample size for trace and ultratrace elemental determination and speciation by conventional voltammetric instrumentation, introducing the lowest amount of sample (0.5 mL) in which ultratrace detection has been performed up to now. This goal was achieved by a careful design of a new sample holder. Reliable, validated results were obtained for the determination of trace/ultratrace elements in rainwater (Cd, Co, Cu, Ni, Pb) and seawater (Cu). Moreover, copper speciation in seawater samples was consistently determined by competitive ligand equilibration-cathodic stripping voltammetry (CLE-CSV). The proposed apparatus showed several advantages: (1) 20-fold reduction in sample volume (the sample size is lowered from 120 to 6 mL for the CLE-CSV procedure); (2) decrease in analysis time due to the reduction in purging time up to 2.5 fold; (3) 20-fold drop in reagent consumption. Moreover, the analytical performances were not affected: similar detection capabilities, precision and accuracy were obtained. Application to sample of limited availability (e.g. porewaters, snow, rainwater, open ocean water, biological samples) and to the description of high resolution temporal trends may be easily foreseen.

Multiple quantum criticality in a two-dimensional superconductor.

The diverse phenomena associated with the two-dimensional electron gas (2DEG) that occurs at oxide interfaces include, among others, exceptional carrier mobilities, magnetism and superconductivity. Although these have mostly been the focus of interest for potential future applications, they also offer an opportunity for studying more fundamental quantum many-body effects. Here, we examine the magnetic-field-driven quantum phase transition that occurs in electrostatically gated superconducting LaTiO3/SrTiO3 interfaces. Through a finite-size scaling analysis, we show that it belongs to the (2+1)D XY model universality class. The system can be described as a disordered array of superconducting puddles coupled by a 2DEG and, depending on its conductance, the observed critical behaviour is single (corresponding to the long-range phase coherence in the whole array) or double (one related to local phase coherence, the other one to the array). A phase diagram illustrating the dependence of the critical field on the 2DEG conductance is constructed, and shown to agree with theoretical proposals. Moreover, by retrieving the coherence-length critical exponent ν, we show that the quantum critical behaviour can be clean or dirty according to the Harris criterion, depending on whether the phase-coherence length is smaller or larger than the size of the puddles.

Intrinsic instability of electronic interfaces with strong Rashba coupling.

We consider a model for the two-dimensional electron gas formed at the interface of oxide heterostructures, which includes a Rashba spin-orbit coupling proportional to the electric field perpendicular to the interface. Based on the standard mechanism of polarity catastrophe, we assume that the electric field has a contribution proportional to the electron density. Under these simple and general assumptions, we show that a phase separation instability (signaled by a negative compressibility) occurs for realistic values of the spin-orbit coupling and of the electronic band-structure parameters. This provides an intrinsic mechanism for the inhomogeneous phases observed at the LaAlO(3)/SrTiO(3) or LaTiO(3)/SrTiO(3) interfaces.

Transient hydrodynamical behavior by dynamical nonequilibrium molecular dynamics: the formation of convective cells.

We present a method based on dynamical nonequilibrium molecular dynamics (D-NEMD) that allows one to produce rigorous ensemble averages for the transient regimes. We illustrate the method by describing the formation of convective cells within a two-dimensional fluid system of soft disks in which a gravity field and a thermal gradient are present. We analyze two different physical settings, with the thermal gradient orthogonal or parallel to the gravity field. In both settings, we follow the formation of the convective flows from the initial time, when the perturbation is turned on, to the steady state. In the first setting (orthogonal fields) we investigate several different cases, varying the initial stationary ensemble and the perturbing field. We find that the final steady-state convective cell is independent of the specific sequence of perturbation fields, which only affects the transient behavior. In all cases, we find that the convective roll is formed through a sequence of damped oscillations of the local fields (density, temperature, and velocity), superimposed to an overall relaxation toward the local steady-state values. Then, we show how D-NEMD can be applied to the Rayleigh-Bénard (RB) setting (parallel fields). In these conditions, the convective flow only establishes above a threshold, without a preferred verse of rotation. We analyze only the response to the ignition of the gravity field in a stationary system under the action of a vertical thermal gradient. Also in this case we characterize the transient response by following the evolution of the density, temperature, and velocity fields until the steady-state RB convective cell is formed. The observed transients are similar to those observed in the case of orthogonal fields. However, the final steady states are quite different. Finally, we briefly discuss the conditions for the general applicability of the D-NEMD method.

Charge-fluctuation contribution to the Raman response in superconducting cuprates.

We calculate the Raman response contribution due to soft collective modes, finding a strong dependence on the photon polarizations and on the characteristic wave vectors of the modes. We compare our results with recent Raman spectroscopy experiments in underdoped cuprates, La2-xSrxCuO4 and (Y1.97Ca0.3)Ba2CuO6.05, where anomalous low-energy peaks are observed, which soften upon lowering the temperature. We show that the specific dependence on doping and on photon polarizations of these peaks can naturally arise from charge collective excitations at finite wavelength.

Anomalous optical absorption in the normal state of overdoped cuprates near the charge-ordering instability.

We argue that the hump observed in the optical conductivity at or below a few hundreds of cm(-1), in overdoped cuprates such as the electron-doped Nd(2-x)Ce(x)CuO(4-y) at x > or approximately equal to 0.15 and the hole-doped Bi2Sr2CuO6 and La2-xSrxCuO4, cannot be accounted for within a single-fluid description. We propose instead an interpretation based on the direct excitation of charge collective modes, which become nearly critical in the proximity to a charge-ordering instability. Their critical character entails a peculiar temperature dependence and a pseudoscaling form of the optical spectra, which agree with the experimental data.

Vertex corrections near the stripe phase.

We calculate the vertex corrections within a model for fermion quasiparticles coupled with charge and spin fluctuations, which provide the relevant scattering mechanism near the stripe instability in high- T(c) cuprates. The logarithmic divergence of the vertex, which characterizes the spin-fermion model near the antiferromagnetic instability, is ruled out, due to the incommensuration of the charge and spin modulation within the stripe phase, as revealed by neutron scattering. This simplifies the skeleton structure of the problem. The vertex is negative in the relevant kinematical regime, effectively reducing the interaction strength. Our results apply to generic incommensurate instabilities of electronic origin.

Anomalous isotopic effect near the charge-ordering quantum criticality.

Within the Hubbard-Holstein model, we evaluate the crossover lines marking the opening of pseudogaps in the cuprates, which, in our scenario, are ruled by the proximity to a charge-ordering quantum criticality (stripe formation). We find that their isotopic dependence, due to critical fluctuations, implies a substantial positive shift of the pseudogap-formation temperature T(*). We infer that the isotopic shift of the superconducting T(c) is nearly absent in the optimally and overdoped regimes and is negative and increasing upon underdoping. The dynamical nature of the charge-ordering transition may explain the spread of the experimental values of T(*).