A universal scaling relation in high-temperature superconductors

Modulations in Superconductors: Probes of Underlying Physics

The importance of modulations is elevated to an unprecedented level, due to the delicate conditions required to bring out exotic phenomena in quantum materials, such as topological materials, magnetic materials, and superconductors. Recently, state-of-the-art modulation techniques in material science, such as electric-double-layer transistor, piezoelectric-based strain apparatus, angle twisting, and nanofabrication, have been utilized in superconductors. They not only efficiently increase the tuning capability to the broader ranges but also extend the tuning dimensionality to unprecedented degrees of freedom, including quantum fluctuations of competing phases, electronic correlation, and phase coherence essential to global superconductivity. Here, for a comprehensive review, these techniques together with the established modulation methods, such as elemental substitution, annealing, and polarization-induced gating, are contextualized. Depending on the mechanism of each method, the modulations are categorized into stoichiometric manipulation, electrostatic gating, mechanical modulation, and geometrical design. Their recent advances are highlighted by applications in newly discovered superconductors, e.g., nickelates, Kagome metals, and magic-angle graphene. Overall, the review is to provide systematic modulations in emergent superconductors and serve as the coordinate for future investigations, which can stimulate researchers in superconductivity and other fields to perform various modulations toward a thorough understanding of quantum materials.

BaTiO3/NixZn1−xFe2O4 (x = 0, 0.5, 1) Composites Synthesized by Thermal Decomposition: Magnetic, Dielectric and Ferroelectric Properties

To investigate the influence of spinel structure and sintering temperature on the functional properties of BaTiO3/NixZn1−xFe2O4 (x = 0, 0.5, 1), NiFe2O4, ZnFe2O4, and Ni0.5Zn0.5Fe2O4 were in situ prepared by thermal decomposition onto BaTiO3 surface from acetylacetonate precursors. As-prepared powders were additionally sintered at 1150 °C and 1300 °C. X-ray powder diffraction (XRPD) and scanning electron microscopy (SEM) coupled with electron dispersive spectroscopy (EDS) were used for the detailed examination of phase composition and morphology. The magnetic, dielectric, and ferroelectric properties were investigated. The optimal phase composition in the BaTiO3/NiFe2O4 composite, sintered at 1150 °C, resulted in a wide frequency range stability. Additionally, particular phase composition indicates favorable properties such as low conductivity and ideal-like hysteresis loop behavior. The favorable properties of BaTiO3/NiFe2O4 make this particular composite an ideal material choice for further studies on applications of multi-ferroic devices.

Quantifying Nonadiabaticity in Major Families of Superconductors

The classical Bardeen−Cooper−Schrieffer and Eliashberg theories of the electron−phonon-mediated superconductivity are based on the Migdal theorem, which is an assumption that the energy of charge carriers, kBTF, significantly exceeds the phononic energy, ℏωD, of the crystalline lattice. This assumption, which is also known as adiabatic approximation, implies that the superconductor exhibits fast charge carriers and slow phonons. This picture is valid for pure metals and metallic alloys because these superconductors exhibit ℏωDkBTF<0.01. However, for n-type-doped semiconducting SrTiO3, this adiabatic approximation is not valid, because this material exhibits ℏωDkBTF≅50. There is a growing number of newly discovered superconductors which are also beyond the adiabatic approximation. Here, leaving aside pure theoretical aspects of nonadiabatic superconductors, we classified major classes of superconductors (including, elements, A-15 and Heusler alloys, Laves phases, intermetallics, noncentrosymmetric compounds, cuprates, pnictides, highly-compressed hydrides, and two-dimensional superconductors) by the strength of nonadiabaticity (which we defined by the ratio of the Debye temperature to the Fermi temperature, TθTF). We found that the majority of analyzed superconductors fall into the 0.025≤TθTF≤0.4 band. Based on the analysis, we proposed the classification scheme for the strength of nonadiabatic effects in superconductors and discussed how this classification is linked with other known empirical taxonomies in superconductivity.

Upper limit of the transition temperature of superconducting materials

Why are the transition temperatures (T c) of superconducting materials so different? The answer to this question is not only of great significance in revealing the mechanism of high-T c superconductivity but also can be used as a guide for the design of new superconductors. However, so far, it is still challenging to identify the governing factors affecting the T c. In this work, with the aid of machine learning and first-principles calculations, we found a close relevance between the upper limit of the T c and the energy-level distribution of valence electrons. It implies that some additional inter-orbital electron-electron interaction should be considered in the interpretation of high-T c superconductivity.

Anisotropic Scattering Caused by Apical Oxygen Vacancies in Thin Films of Overdoped High-Temperature Cuprate Superconductors

There is a hot debate on the anomalous behavior of superfluid density ρ_{s} in overdoped La_{2-x}Sr_{x}CuO_{4} films in recent years. The linear drop of ρ_{s} at low temperatures implies the superconductors are clean, but the linear scaling between ρ_{s} (in the zero temperature limit) and the transition temperature T_{c} is a hallmark of the dirty limit in the Bardeen-Cooper-Schrieffer (BCS) framework [I. Bozovic et al., Nature (London) 536, 309 (2016)NATUAS0028-083610.1038/nature19061]. This dichotomy motivated exotic theories beyond the standard BCS theory. We show, however, that such a dichotomy can be reconciled naturally by the role of increasing anisotropic scattering caused by the apical oxygen vacancies. Furthermore, the anisotropic scattering also explains the "missing" Drude weight upon doping in the optical conductivity, as reported in the THz experiment [F. Mahmood et al., Phys. Rev. Lett. 122, 027003 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.027003]. Therefore, the overdoped cuprates can actually be described consistently by the d-wave BCS theory with the unique anisotropic scattering.

High-T c Cuprates: a Story of Two Electronic Subsystems

A review of the phenomenology and microscopy of cuprate superconductors is presented, with particular attention to universal conductance features, which reveal the existence of two electronic subsystems. The overall electronic system consists of 1 + p charges, where p is the doping. At low dopings, exactly one hole is localized per planar copper-oxygen unit, while upon increasing doping and temperature, the hole is gradually delocalized and becomes itinerant. Remarkably, the itinerant holes exhibit identical Fermi liquid character across the cuprate phase diagram. This universality enables a simple count of carrier density and yields comprehensive understanding of the key features in the normal and superconducting state. A possible superconducting mechanism is presented, compatible with the key experimental facts. The base of this mechanism is the interaction of fast Fermi liquid carriers with localized holes. A change in the microscopic nature of chemical bonding in the copper oxide planes, from ionic to covalent, is invoked to explain the phase diagram of these fascinating compounds.

Pressure-Tuned Superconducting Dome in Chemically-Substituted κ-(BEDT-TTF)2Cu2(CN)3

The quantum spin liquid candidate κ-(BEDT-TTF)2Cu2(CN)3 has been established as the prime example of a genuine Mott insulator that can be tuned across the first-order insulator–metal transition either by chemical substitution or by physical pressure. Here, we explore the superconducting state that occurs at low temperatures, when both methods are combined, i.e., when κ-[(BEDT-TTF)1−x(BEDT-STF)x]2Cu2(CN)3 is pressurized. We discovered superconductivity for partial BEDT-STF substitution with x = 0.10–0.12 even at ambient pressure, i.e., a superconducting state is realized in the range between a metal and a Mott insulator without magnetic order. Furthermore, we observed the formation of a superconducting dome by pressurizing the substituted crystals; we assigned this novel behavior to disorder emanating from chemical tuning.

Approaching Two-Dimensional Superconductivity in Ultrathin DyBa_{2}Cu_{3}O_{7-δ}

The temperature dependence of the superfluid density ρ_{s}(T) has been measured for a series of ultrathin MBE-grown DyBa_{2}Cu_{3}O_{7-δ} superconducting (SC) films by submillimeter wave interferometry combined with time-domain terahertz spectroscopy and IR ellipsometry. We find that all films 10 u.c. and thicker show the same universal temperature dependence of ρ_{s}(T), which follows the critical behavior characteristic of single crystal YBa_{2}Cu_{3}O_{7-δ} as T approaches T_{c}. In 7 u.c. thick films, ρ_{s}(T) declines steeply upon approaching T_{c}, as expected for the Berezinskii-Kosterlitz-Thouless vortex unbinding transition. Our analysis provides evidence for a sharply defined 4 u.c. non-SC interfacial layer, leaving a quasi-2D SC layer on top. We propose that the SC state in this interfacial layer is suppressed by competing (possibly charge) order.

Translational-Invariant Bipolarons and Superconductivity

A translation-invariant (TI) bipolaron theory of superconductivity based, like Bardeen–Cooper–Schrieffer theory, on Fröhlich Hamiltonian is presented. Here the role of Cooper pairs belongs to TI bipolarons which are pairs of spatially delocalized electrons whose correlation length of a coupled state is small. The presence of Fermi surface leads to the stabilization of such states in its vicinity and a possibility of their Bose–Einstein condensation (BEC). The theory provides a natural explanation of the existence of a pseudogap phase preceding the superconductivity and enables one to estimate the temperature of a transition T * from a normal state to a pseudogap one. It is shown that the temperature of BEC of TI bipolarons determines the temperature of a superconducting transition T c which depends not on the bipolaron effective mass but on the ordinary mass of a band electron. This removes restrictions on the upper limit of T c for a strong electron-phonon interaction. A natural explanation is provided for the angular dependence of the superconducting gap which is determined by the angular dependence of the phonon spectrum. It is demonstrated that a lot of experiments on thermodynamic and transport characteristics, Josephson tunneling and angle-resolved photoemission spectroscopy (ARPES) of high-temperature superconductors does not contradict the concept of a TI bipolaron mechanism of superconductivity in these materials. Possible ways of enhancing T c and producing new room-temperature superconductors are discussed on the basis of the theory suggested.

Photoenhanced metastable c-axis electrodynamics in stripe-ordered cuprate La1.885Ba0.115CuO4

The emergence of superconductivity in high-temperature cuprates arises out of a rich landscape of competing order. For example, stripe order can hoard the electrons needed to form Cooper pairs and establish superconductivity. Intriguingly, the complex interactions of such intertwined orders can be manipulated with light, where nonequilibrium dynamics alter the primacy of one order over another. Following photoexcitation of La_2−xBa_xCuO₄ (x = 0.115) with near-infrared pulses, we observe a long-lived state that exhibits enhanced superconducting correlations well above the equilibrium superconducting transition temperature. Our analysis reveals that this metastable phase arises from a collapse of stripe order, providing an important demonstration of light-directed control in quantum materials.

Quantum materials are amenable to nonequilibrium manipulation with light, enabling modification and control of macroscopic properties. Light-based augmentation of superconductivity is particularly intriguing. Copper-oxide superconductors exhibit complex interplay between spin order, charge order, and superconductivity, offering the prospect of enhanced coherence by altering the balance between competing orders. We utilize terahertz time-domain spectroscopy to monitor the c-axis Josephson plasma resonance (JPR) in La_2−xBa_xCuO₄ (x = 0.115) as a direct probe of superconductivity dynamics following excitation with near-infrared pulses. Starting from the superconducting state, c-axis polarized excitation with a fluence of 100 μJ/cm² results in an increase of the far-infrared spectral weight by more than an order of magnitude as evidenced by a blueshift of the JPR, interpreted as resulting from nonthermal collapse of the charge order. The photoinduced signal persists well beyond our measurement window of 300 ps and exhibits signatures of spatial inhomogeneity. The electrodynamic response of this metastable state is consistent with enhanced superconducting fluctuations. Our results reveal that La_2−xBa_xCuO₄ is highly sensitive to nonequilibrium excitation over a wide fluence range, providing an unambiguous example of photoinduced modification of order-parameter competition.

Phase transition in the cuprates from a magnetic-field-free stiffness meter viewpoint

A method to measure the superconducting (SC) stiffness tensor [Formula: see text], without subjecting the sample to external magnetic field, is applied to La_1.875Sr_0.125CuO₄. The method is based on the London equation [Formula: see text], where J is the current density and A is the vector potential which is applied in the SC state. Using rotor free A and measuring J via the magnetic moment of superconducting rings, [Formula: see text] at T → T_c is extracted. The technique is sensitive to very small stiffnesses (penetration depths on the order of a few millimeters). The method is applied to two different rings: one with the current running only in the CuO₂ planes, and another where the current must cross planes. We find different transition temperatures for the two rings, namely, there is a temperature range with two-dimensional stiffness. Additional low energy muon spin rotation measurements on the same sample determine the stiffness anisotropy at T < T_c.

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.

Thermal and electrical signatures of a hydrodynamic electron fluid in tungsten diphosphide

In stark contrast to ordinary metals, in materials in which electrons strongly interact with each other or with phonons, electron transport is thought to resemble the flow of viscous fluids. Despite their differences, it is predicted that transport in both conventional and correlated materials is fundamentally limited by the uncertainty principle applied to energy dissipation. Here we report the observation of experimental signatures of hydrodynamic electron flow in the Weyl semimetal tungsten diphosphide. Using thermal and magneto-electric transport experiments, we find indications of the transition from a conventional metallic state at higher temperatures to a hydrodynamic electron fluid below 20 K. The hydrodynamic regime is characterized by a viscosity-induced dependence of the electrical resistivity on the sample width and by a strong violation of the Wiedemann–Franz law. Following the uncertainty principle, both electrical and thermal transport are bound by the quantum indeterminacy, independent of the underlying transport regime.

Advances in the fabrication of low-disorder metallic materials have made it possible to reach the hydrodynamic regime of electronic transport. Here the authors investigate a hydrodynamic electron fluid in tungsten diphosphide and find that both electrical and thermal transport are limited by the quantum indeterminacy.

Single-Gap Superconductivity and Dome of Superfluid Density in Nb-Doped SrTiO_{3}

SrTiO_{3} exhibits a superconducting dome upon doping with Nb, with a maximum critical temperature T_{c}≈0.4  K. Using microwave stripline resonators at frequencies from 2 to 23 GHz and temperatures down to 0.02 K, we probe the low-energy optical response of superconducting SrTiO_{3} with a charge carrier concentration from 0.3 to 2.2×10^{20}  cm^{-3}, covering the majority of the superconducting dome. We find single-gap electrodynamics even though several electronic bands are superconducting. This is explained by a single energy gap 2Δ due to gap homogenization over the Fermi surface consistent with the low level of defect scattering in Nb-doped SrTiO_{3}. Furthermore, we determine T_{c}, 2Δ, and the superfluid density as a function of charge carrier concentration, and all three quantities exhibit the characteristic dome shape.

A peak in the critical current for quantum critical superconductors

Generally, studies of the critical current I_c are necessary if superconductors are to be of practical use, because I_c sets the current limit below which there is a zero-resistance state. Here, we report a peak in the pressure dependence of the zero-field I_c, I_c(0), at a hidden quantum critical point (QCP), where a continuous antiferromagnetic transition temperature is suppressed by pressure toward 0 K in CeRhIn₅ and 4.4% Sn-doped CeRhIn₅. The I_c(0)s of these Ce-based compounds under pressure exhibit a universal temperature dependence, underlining that the peak in zero-field I_c(P) is determined predominantly by critical fluctuations associated with the hidden QCP. The dc conductivity σ_dc is a minimum at the QCP, showing anti-correlation with I_c(0). These discoveries demonstrate that a quantum critical point hidden inside the superconducting phase in strongly correlated materials can be exposed by the zero-field I_c, therefore providing a direct link between a QCP and unconventional superconductivity.

Review of pseudogaps in strongly interacting Fermi gases

A central challenge in modern condensed matter physics is developing the tools for understanding nontrivial yet unordered states of matter. One important idea to emerge in this context is that of a 'pseudogap': the fact that under appropriate circumstances the normal state displays a suppression of the single particle spectral density near the Fermi level, reminiscent of the gaps seen in ordered states of matter. While these concepts arose in a solid state context, they are now being explored in cold gases. This article reviews the current experimental and theoretical understanding of the normal state of strongly interacting Fermi gases, with particular focus on the phenomonology which is traditionally associated with the pseudogap.

Universal linear-temperature resistivity: possible quantum diffusion transport in strongly correlated superconductors

The strongly correlated electron fluids in high temperature cuprate superconductors demonstrate an anomalous linear temperature (T) dependent resistivity behavior, which persists to a wide temperature range without exhibiting saturation. As cooling down, those electron fluids lose the resistivity and condense into the superfluid. However, the origin of the linear-T resistivity behavior and its relationship to the strongly correlated superconductivity remain a mystery. Here we report a universal relation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d{\boldsymbol{\rho }}/{\boldsymbol{dT}}=({{\boldsymbol{\mu }}}_{{\bf{0}}}{{\boldsymbol{k}}}_{{\boldsymbol{B}}}/{\boldsymbol{\hslash }})\,{{\boldsymbol{\lambda }}}_{{\boldsymbol{L}}}^{{\bf{2}}}$$\end{document}dρ/dT=(μ0kB/ℏ)λL2, which bridges the slope of the linear-T-dependent resistivity (dρ/dT) to the London penetration depth λ_L at zero temperature among cuprate superconductor Bi₂Sr₂CaCu₂O_8+δ and heavy fermion superconductors CeCoIn₅, where μ₀ is vacuum permeability, k_B is the Boltzmann constant and ħ is the reduced Planck constant. We extend this scaling relation to different systems and found that it holds for other cuprate, pnictide and heavy fermion superconductors as well, regardless of the significant differences in the strength of electronic correlations, transport directions, and doping levels. Our analysis suggests that the scaling relation in strongly correlated superconductors could be described as a hydrodynamic diffusive transport, with the diffusion coefficient (D) approaching the quantum limit D ~ ħ/m*, where m* is the quasi-particle effective mass.

Perspective on the phase diagram of cuprate high-temperature superconductors

Universal scaling laws can guide the understanding of new phenomena, and for cuprate high-temperature superconductivity the influential Uemura relation showed, early on, that the maximum critical temperature of superconductivity correlates with the density of the superfluid measured at low temperatures. Here we show that the charge content of the bonding orbitals of copper and oxygen in the ubiquitous CuO2 plane, measured with nuclear magnetic resonance, reproduces this scaling. The charge transfer of the nominal copper hole to planar oxygen sets the maximum critical temperature. A three-dimensional phase diagram in terms of the charge content at copper as well as oxygen is introduced, which has the different cuprate families sorted with respect to their maximum critical temperature. We suggest that the critical temperature could be raised substantially if one were able to synthesize materials that lead to an increased planar oxygen hole content at the expense of that of planar copper.

Superconducting fluctuations in organic molecular metals enhanced by Mott criticality

Unconventional superconductivity typically occurs in materials in which a small change of a parameter such as bandwidth or doping leads to antiferromagnetic or Mott insulating phases. As such competing phases are approached, the properties of the superconductor often become increasingly exotic. For example, in organic superconductors and underdoped high-T_c cuprate superconductors a fluctuating superconducting state persists to temperatures significantly above T_c. By studying alloys of quasi-two-dimensional organic molecular metals in the κ-(BEDT-TTF)₂X family, we reveal how the Nernst effect, a sensitive probe of superconducting phase fluctuations, evolves in the regime of extreme Mott criticality. We find strong evidence that, as the phase diagram is traversed through superconductivity towards the Mott state, the temperature scale for superconducting fluctuations increases dramatically, eventually approaching the temperature at which quasiparticles become identifiable at all.

Interlayer penetration depth in the pseudogap phase of cuprate superconductors

The opening of a pseudogap in the electronic structure of the underdoped high Tc cuprates has a profound effect on superconducting properties. Here we consider the c-axis penetration depth. A phenomenological model of the pseudogap due to Yang, Rice, and Zhang (YRZ) is used. It is based on the idea of a resonating valence bond spin liquid. A simplifying limit, the arc model, is also considered as it provides useful analytic formulas. The zero temperature value of the superfluid density n(s)(T = 0) is greatly reduced with increasing values of the pseudogap (Δpg). This value reflects the reconstruction of the Fermi surface from the large contour of Fermi liquid theory to ever smaller Luttinger pockets as Δpg becomes larger. Also, as temperature is increased the ratio n(s)(T)/n(s)(0) as a function of the reduced temperature t = T/T(c) decreases more rapidly than in the corresponding Fermi liquid (Δpg = 0) as states which have both superconducting and pseudogap become more significantly sampled.

Do organic and other exotic superconductors fail universal scaling relations?

Universal scaling relations are of tremendous importance in science, as they reveal fundamental laws of nature. Several such scaling relations have recently been proposed for superconductors; however, they are not really universal in the sense that some important families of superconductors appear to fail the scaling relations, or obey the scaling with different scaling pre-factors. In particular, a large group of materials called organic (or molecular) superconductors are a notable example. Here, we show that such apparent violations are largely due to the fact that the required experimental parameters were collected on different samples, with different experimental techniques. When experimental data is taken on the same sample, using a single experimental technique, organic superconductors, as well as all other studied superconductors, do in fact follow universal scaling relations.

Similarity of scattering rates in metals showing T-linear resistivity

Many exotic compounds, such as cuprate superconductors and heavy fermion materials, exhibit a linear in temperature (T) resistivity, the origin of which is not well understood. We found that the resistivity of the quantum critical metal Sr(3)Ru(2)O(7) is also T-linear at the critical magnetic field of 7.9 T. Using the precise existing data for the Fermi surface topography and quasiparticle velocities of Sr(3)Ru(2)O(7), we show that in the region of the T-linear resistivity, the scattering rate per kelvin is well approximated by the ratio of the Boltzmann constant to the Planck constant divided by 2π. Extending the analysis to a number of other materials reveals similar results in the T-linear region, in spite of large differences in the microscopic origins of the scattering.

New insights into the phase diagram of the copper oxide superconductors from electronic Raman scattering

The mechanism of unconventional superconductivity is still unknown despite over 25 years passing since the discovery of high-T(c) cuprate superconductors by Bednorz and Muller (1986 Z. Phys. B 64 189). Here, we explore the cuprate phase diagram by electronic Raman spectroscopy and shed light on the superconducting state in hole-doped curates, namely, how superconductivity and the critical temperature T(c) are affected by the pseudogap.

ns-Tc correlations in granular superconductors

Following a short discussion of the granular model for an inhomogeneous superconductor, we review the Uemura and Homes correlations and show how both follow in two limits of a simple granular superconductor model. Definite expressions are given for the almost universal coefficients appearing in these relationships in terms of known constants.

Correlation between the superconducting transition temperature and anisotropic quasiparticle scattering in Tl2Ba2CuO6+delta

Angle-dependent magnetoresistance measurements are used to determine the isotropic and anisotropic components of the transport scattering rate in overdoped Tl2Ba2CuO6+delta for a range of Tc values between 15 and 35 K. The size of the anisotropic scattering term is found to scale linearly with Tc, establishing a link between the superconducting and normal state physics. A comparison with results from angle resolved photoemission spectroscopy indicates that the transport and quasiparticle lifetimes are distinct.

Competing ferromagnetism in high-temperature copper oxide superconductors

The extreme variability of observables across the phase diagram of the cuprate high-temperature superconductors has remained a profound mystery, with no convincing explanation for the superconducting dome. Although much attention has been paid to the underdoped regime of the hole-doped cuprates because of its proximity to a complex Mott insulating phase, little attention has been paid to the overdoped regime. Experiments are beginning to reveal that the phenomenology of the overdoped regime is just as puzzling. For example, the electrons appear to form a Landau Fermi liquid, but this interpretation is problematic; any trace of Mott phenomena, as signified by incommensurate antiferromagnetic fluctuations, is absent, and the uniform spin susceptibility shows a ferromagnetic upturn. Here, we show and justify that many of these puzzles can be resolved if we assume that competing ferromagnetic fluctuations are simultaneously present with superconductivity, and the termination of the superconducting dome in the overdoped regime marks a quantum critical point beyond which there should be a genuine ferromagnetic phase at zero temperature. We propose experiments and make predictions to test our theory and suggest that an effort must be mounted to elucidate the nature of the overdoped regime, if the problem of high-temperature superconductivity is to be solved. Our approach places competing order as the root of the complexity of the cuprate phase diagram.

Electric-field-effect modulation of the transition temperature, mobile carrier density, and in-plane penetration depth of NdBa2Cu3O7-delta thin films

We explore the relationship between the critical temperature T(c), the mobile areal carrier density n(2D), and the zero-temperature magnetic in-plane penetration depth lambda(ab)(0) in very thin underdoped NdBa(2)Cu(3)O(7-delta) films near the superconductor to insulator transition using the electric-field-effect technique. Having established consistency with a Kosterlitz-Thouless transition, we observe that T(KT) depends linearly on n(2D), the signature of a quantum superconductor to insulator transition in two dimensions with znu(over)=1, where z is the dynamic and nu is the critical exponent of the in-plane correlation length.

Electrostatic modulation of the superfluid density in an ultrathin film

By capacitively charging an underdoped ultrathin La2-xSrxCuO4 film with an electric field applied across a gate insulator with a high dielectric constant, relative changes of the areal superfluid density ns of unprecedented strength were observed in measurements of the film kinetic inductance. Although ns appears to be substantially reduced by disorder, the data provide, for the first time on the same sample, direct compelling evidence for the Uemura relation Tc proportional to ns(T=0) in the underdoped regime of copper-oxide superconductors.

Physics of the resonating valence bond (pseudogap) state of the doped mott insulator: spin-charge locking

The properties of the pseudogap phase above T(C) of the high-T(C) cuprate superconductors are described by showing that the Anderson-Nambu SU(2) spinors of a resonating valence bond spin gap "lock" to those of the electron charge system because of the resulting improvement of kinetic energy. This enormously extends the range of the vortex liquid state in these materials. A heuristic description of the nonlocal electrodynamics of this pseudogap-vortex liquid state is proposed.

Charge-transfer excitations in the model superconductor HgBa(2)CuO(4+delta)

We report a Cu -edge resonant inelastic x-ray scattering (RIXS) study of charge-transfer excitations in the 2-8 eV range in the structurally simple compound HgBa(2)CuO(4+delta) at optimal doping (T(c)=96.5 K). The spectra exhibit a significant dependence on the incident photon energy which we carefully utilize to resolve a multiplet of weakly dispersive (<0.5 eV) electron-hole excitations, including a mode at 2 eV. The observation of this 2 eV excitation suggests the existence of a remnant charge-transfer gap deep in the superconducting phase. Quite generally, our results, which include additional data for the Mott insulator La(2)CuO(4), demonstrate the importance of exploring the incident photon-energy dependence of the RIXS cross section.

Correlation between superfluid density and T(C) of underdoped YBa2Cu3O6+x near the superconductor-insulator transition

We report measurements of the ab-plane superfluid density n(s) (magnetic penetration depth lambda) of heavily underdoped films of YBa2Cu3O6+x, with T(C)'s from 6 to 50 K. We find the characteristic length for vortex unbinding transition equal to the film thickness, suggesting strongly coupled CuO2 layers. At the lowest dopings, T(C) is as much as 5 times larger than the upper limit set by the 2D Kosterlitz-Thouless-Berezinskii transition temperature calculated for individual CuO2 bilayers. Our main finding is that T(C) is not proportional to n(s)(0); instead, we find T(C) proportional to ns(1/2.3+/-0.4). This conflicts with a popular point of view that quasi-2D thermal phase fluctuations determine the transition temperature.

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.

Complexity in Strongly Correlated Electronic Systems

A wide variety of experimental results and theoretical investigations in recent years have convincingly demonstrated that several transition metal oxides and other materials have dominant states that are not spatially homogeneous. This occurs in cases in which several physical interactions-spin, charge, lattice, and/or orbital-are simultaneously active. This phenomenon causes interesting effects, such as colossal magnetoresistance, and it also appears crucial to understand the high-temperature superconductors. The spontaneous emergence of electronic nanometer-scale structures in transition metal oxides, and the existence of many competing states, are properties often associated with complex matter where nonlinearities dominate, such as soft materials and biological systems. This electronic complexity could have potential consequences for applications of correlated electronic materials, because not only charge (semiconducting electronic), or charge and spin (spintronics) are of relevance, but in addition the lattice and orbital degrees of freedom are active, leading to giant responses to small perturbations. Moreover, several metallic and insulating phases compete, increasing the potential for novel behavior.

Superconductivity: small steps towards the “grand unification”

The existence of various families of super conducting materials and their T(C) values are qualitatively rationalized within a simple model. Novel families of superconducting materials, particularly those based on fluoride and hydride anions, are predicted. [Figure: see text]. We predict that existing families of moderate- and high-T(C) superconductors should hopefully be enriched by novel compounds containing hardly polarizable anions (such as F(-)). Covalent chlorides and hydrides also merit careful exploration.

Bridging the Gap between mesoscopic and macroscopic models: the case of multicellular tumor spheroids

Multicellular tumor spheroids are valuable experimental tools in cancer research. By introducing an intermediate model, we have been able to successfully relate mesoscopic and macroscopic descriptions of spheroid growth. Since these descriptions stem from completely different roots (cell dynamics, and energy conservation and scaling arguments, respectively), their consistency validates both approaches and allows us to establish a direct correspondence between parameters characterizing processes occurring at different scales. Our approach may find applications as an example of bridging the gap between models at different scale levels in other contexts.

Universal scaling relations in molecular superconductors

Scaling relations between the superconducting transition temperature T(c), the superfluid stiffness rho(s), and the normal state conductivity sigma(0)(T(c)) are identified within the class of molecular superconductors. These new scaling properties hold as T(c) varies over 2 orders of magnitude for materials with differing dimensionality and contrasting molecular structure and are dramatically different from the equivalent scaling properties observed for cuprate superconductors. These scaling relations place strong constraints on theories for molecular superconductivity.