The strain of CuO2lattice: the second variable for the phase diagram of cuprate perovskites

Nanoscale Phase Separation of Incommensurate and Quasi-Commensurate Spin Stripes in Low Temperature Spin Glass of La2−xSrxNiO4

While spin striped phases in La2−xSrxNiO4+y for 0.25 < x < 0.33 are the archetypal case of a 1D spin density wave (SDW) phase in doped antiferromagnetic strongly correlated perovskites, few information is available on the SDW spatial organization. In this context, we have measured the spatial variation of the wave vector of the SDW reflection profile by scanning micro X-ray diffractions with a coherent beam. We obtained evidence of a SDW order–disorder transition by lowering a high temperature phase (T > 50 K) to a low temperature phase (T < 50 K). We have identified quasi-commensurate spin stripe puddles in the ordered phase at 50 < T < 70 K, while the low temperature spin glassy phase presents a nanoscale phase separation of T = 30 K, with the coexistence of quasi-commensurate and incommensurate spin stripe puddles assigned to the interplay of quantum frustration and strong electronic correlations.

Nonadiabatic coupling of the dynamical structure to the superconductivity in YSr2Cu2.75Mo0.25O7.54 and Sr2CuO3.3

The Cu extended X-ray absorption fine structure of YSr₂Cu_2.75Mo_0.25O_7.54 (with superconducting critical temperature, T_c, = 84 K) and Sr₂CuO_3.3 (T_c = 95 K) through their superconducting transitions demonstrates that the common factor in superconductivity in cuprates, including those prepared by high-pressure oxygenation, is an internal quantum tunneling polaron in its dynamical structure. In addition, Sr₂CuO_3.3 is the first material to show a concomitant transformation in this structure involving atom displacements >1 Å that would be expected to modify its Fermi surface, which would complicate the transition beyond a purely electronic one consisting of the pairing of electrons of opposite momentum across fixed electronic states.

A crucial issue in cuprates is the extent and mechanism of the coupling of the lattice to the electrons and the superconductivity. Here we report Cu K edge extended X-ray absorption fine structure measurements elucidating the internal quantum tunneling polaron (iqtp) component of the dynamical structure in two heavily overdoped superconducting cuprate compounds, tetragonal YSr₂Cu_2.75Mo_0.25O_7.54 with superconducting critical temperature, T_c = 84 K and hole density p = 0.3 to 0.5 per planar Cu, and the tetragonal phase of Sr₂CuO_3.3 with T_c = 95 K and p = 0.6. In YSr₂Cu_2.75Mo_0.25O_7.54 changes in the Cu-apical O two-site distribution reflect a sequential renormalization of the double-well potential of this site beginning at T_c, with the energy difference between the two minima increasing by ∼6 meV between T_c and 52 K. Sr₂CuO_3.3 undergoes a radically larger transformation at T_c, >1-Å displacements of the apical O atoms. The principal feature of the dynamical structure underlying these transformations is the strongly anharmonic oscillation of the apical O atoms in a double-well potential that results in the observation of two distinct O sites whose Cu–O distances indicate different bonding modes and valence-charge distributions. The coupling of the superconductivity to the iqtp that originates in this nonadiabatic coupling between the electrons and lattice demonstrates an important role for the dynamical structure whereby pairing occurs even in a system where displacements of the atoms that are part of the transition are sufficiently large to alter the Fermi surface. The synchronization and dynamic coherence of the iqtps resulting from the strong interactions within a crystal would be expected to influence this process.

Structural Phase Diagram of LaO1−xFxBiSSe: Suppression of the Structural Phase Transition by Partial F Substitutions

Recently, the anomalous two-fold-symmetric in-plane anisotropy of superconducting states has been observed in a layered superconductor system, LaO1−xFxBiSSe (x = 0.1 and 0.5), with a tetragonal (four-fold symmetric) in-plane structure. To understand the origin of the phenomena observed in LaO1−xFxBiSSe, clarification of the low-temperature structural phase diagram is needed. In this study, we have investigated the low-temperature crystal structure of LaO1−xFxBiSSe (x = 0, 0.01, 0.02, 0.03, and 0.5). From synchrotron X-ray diffraction experiments, a structural transition from tetragonal to monoclinic was observed for x = 0 and 0.01 at 340 and 240 K, respectively. For x = 0.03, a structural transition and broadening of the diffraction peak were not observed down to 100 K. These facts suggest that the structural transition could be suppressed by 3% F substitution in LaO1−xFxBiSSe. Furthermore, the crystal structure for x = 0.5 at 4 K was examined by low-temperature laboratory X-ray diffraction, which confirmed that the tetragonal structure is maintained at 4 K for x = 0.5. Our structural investigation suggests that the two-fold-symmetric in-plane anisotropy of superconducting states observed in LaO1−xFxBiSSe was not originated from structural symmetry lowering in its average structure. To evaluate the possibility of the local structural modification like nanoscale puddles in the average tetragonal structure, further experiments are desired.

Measuring the Electron–Phonon Interaction in Two-Dimensional Superconductors with He-Atom Scattering

Helium-atom scattering (HAS) spectroscopy from conducting surfaces has been shown to provide direct information on the electron–phonon interaction, more specifically the mass-enhancement factor λ from the temperature dependence of the Debye–Waller exponent, and the mode-selected electron–phonon coupling constants λQν from the inelastic HAS intensities from individual surface phonons. The recent applications of the method to superconducting ultra-thin films, quasi-1D high-index surfaces, and layered transition-metal and topological pnictogen chalcogenides are briefly reviewed.

A Lattice Litany for Transition Metal Oxides

In this tribute to K Alex Müller, I describe how his early insights have influenced future decades of research on perovskite ferroelectrics and more broadly transition metal oxides (TMOs) and related quantum materials. I use his influence on my own research journey to discuss impacts in three areas: structural phase transitions, precursor structure, and quantum paraelectricity. I emphasize materials functionality in ground, metastable, and excited states arising from competitions among lattice, charge, and spin degrees of freedom, which results in highly tunable landscapes and complex networks of multiscale configurations controlling macroscopic functions. I discuss competitions between short- and long-range forces as particularly important in TMOs (and related materials classes) because of their localized and directional metal orbitals and the polarizable oxygen ions. I emphasize crucial consequences of elasticity and metal–oxygen charge transfer.

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.

Probing Phase Separation and Local Lattice Distortions in Cuprates by Raman Spectroscopy

It is generally accepted that high temperature superconductors emerge when extra carriers are introduced in the parent state, which looks like a Mott insulator. Competition of the order parameters drives the system into a poorly defined pseudogap state before acquiring the normal Fermi liquid behavior with further doping. Within the low doping level, the system has the tendency for mesoscopic phase separation, which seems to be a general characteristic in all high Tc compounds, but also in the materials of colossal magnetoresistance or the relaxor ferroelectrics. In all these systems, metastable phases can be created by tuning physical variables, such as doping or pressure, and the competing order parameters can drive the compound to various states. Structural instabilities are expected at critical points and Raman spectroscopy is ideal for detecting them, since it is a very sensitive technique for detecting small lattice modifications and instabilities. In this article, phase separation and lattice distortions are examined on the most characteristic family of high temperature superconductors, the cuprates. The effect of doping or atomic substitutions on cuprates is examined concerning the induced phase separation and hydrostatic pressure for activating small local lattice distortions at the edge of lattice instability.

Dzyaloshinskii–Moriya Coupling in 3d Insulators

We present an overview of the microscopic theory of the Dzyaloshinskii–Moriya (DM) coupling in strongly correlated 3d compounds. Most attention in the paper centers around the derivation of the Dzyaloshinskii vector, its value, orientation, and sense (sign) under different types of the (super)exchange interaction and crystal field. We consider both the Moriya mechanism of the antisymmetric interaction and novel contributions, in particular, that of spin–orbital coupling on the intermediate ligand ions. We have predicted a novel magnetic phenomenon, weak ferrimagnetism in mixed weak ferromagnets with competing signs of Dzyaloshinskii vectors. We revisit a problem of the DM coupling for a single bond in cuprates specifying the local spin–orbital contributions to the Dzyaloshinskii vector focusing on the oxygen term. We predict a novel puzzling effect of the on-site staggered spin polarization to be a result of the on-site spin–orbital coupling and the cation-ligand spin density transfer. The intermediate ligand nuclear magnetic resonance (NMR) measurements are shown to be an effective tool to inspect the effects of the DM coupling in an external magnetic field. We predict the effect of a strong oxygen-weak antiferromagnetism in edge-shared CuO 2 chains due to uncompensated oxygen Dzyaloshinskii vectors. We revisit the effects of symmetric spin anisotropy directly induced by the DM coupling. A critical analysis will be given of different approaches to exchange-relativistic coupling based on the cluster and the DFT (density functional theory) based calculations. Theoretical results are applied to different classes of 3d compounds from conventional weak ferromagnets ( α -Fe 2 O 3 , FeBO 3 , FeF 3 , RFeO 3 , RCrO 3 , ...) to unconventional systems such as weak ferrimagnets (e.g., RFe 1 - x Cr x O 3 ), helimagnets (e.g., CsCuCl 3 ), and parent cuprates (La 2 CuO 4 , ...).

Direct Visualization of Spatial Inhomogeneity of Spin Stripes Order in La1.72Sr0.28NiO4

In several strongly correlated electron systems, the short range ordering of defects, charge and local lattice distortions are found to show complex inhomogeneous spatial distributions. There is growing evidence that such inhomogeneity plays a fundamental role in unique functionality of quantum complex materials. La1.72Sr0.28NiO4 is a prototypical strongly correlated perovskite showing spin stripes order. In this work we present the spatial distribution of the spin order inhomogeneity by applying micro X-ray diffraction to La1.72Sr0.28NiO4, mapping the spin-density-wave order below the 120 K onset temperature. We find that the spin-density-wave order shows the formation of nanoscale puddles with large spatial fluctuations. The nano-puddle density changes on the microscopic scale forming a multiscale phase separation extending from nanoscale to micron scale with scale-free distribution. Indeed spin-density-wave striped puddles are disconnected by spatial regions with negligible spin-density-wave order. The present work highlights the complex spatial nanoscale phase separation of spin stripes in nickelate perovskites and opens new perspectives of local spin order control by strain.

Tc and Other Cuprate Properties in Relation to Planar Charges as Measured by NMR

Nuclear magnetic resonance (NMR) in cuprate research is a prominent bulk local probe of magnetic properties. NMR also, as was shown over the last years, actually provides a quantitative measure of local charges in the CuO 2 plane. This has led to fundamental insights, e.g., that the maximum T c is determined by the sharing of the parent planar hole between Cu and O. Using bonding orbital hole contents on planar Cu and O measured by NMR, instead of the total doping x, the thus defined two-dimensional cuprate phase diagram reveals significant differences between the various cuprate materials. Even more importantly, the reflected differences in material chemistry appear to set a number of electronic properties as we discuss here, for undoped, underdoped and optimally doped cuprates. These relations should advise attempts at a theoretical understanding of cuprate physics as well as inspire material chemists towards new high- T c materials. Probing planar charges, NMR is also sensitive to charge variations or ordering phenomena in the CuO 2 plane. Thereby, local charge order on planar O in optimally doped YBCO could recently be proven. Charge density variations seen by NMR in both planar bonding orbitals with amplitudes between 1% to 5% appear to be omnipresent in the doped CuO 2 plane, i.e., not limited to underdoped cuprates and low temperatures.

Is There Any Hidden Symmetry in the Stripe Structure of Perovskite High-Temperature Superconductors?

Local and fast structural probes using synchrotron radiation have shown nanoscale striped puddles and nanoscale phase separation in doped perovskites. It is known that the striped phases in doped perovskites are due to competing interactions involving charge, spin, and lattice degrees of freedom. In this work, we show that two different stripes can be represented as a superposition of a pair of stripes, U(θ _n) or D(θ _n), characterized by perovskite tilts where one of the pair is rotated in relation to the other partner by an angle Δθ _n = π/2. The spatial distribution of the U and D stripes is reduced to all possible maps in the well-known mathematical four-color theorem. Both the periodic striped puddles and random structures can be represented by using planar graphs with a chromatic number χ ≤ 4. To observe the colors in mapping experiments, it is necessary to recover variously oriented tilting effects from the replica. It is established that there is an interplay between the annihilation/creation of new stripes and ordering/disordering tilts in relation to the θ _n angle in the CuO₂ plane, where the characteristic shape of the stripes coincides with the tilting-ordered regions.

Multiple Electronic Components and Lifshitz Transitions by Oxygen Wires Formation in Layered Cuprates and Nickelates

There is growing compelling experimental evidence that a quantum complex matter scenario made of multiple electronic components and competing quantum phases is needed to grab the key physics of high critical temperature ( T c ) superconductivity in layered cuprates. While it is known that defect self-organization controls T c , the mechanism remains an open issue. Here we focus on the theoretical prediction of the multiband electronic structure and the formation of broken Fermi surfaces generated by the self-organization of oxygen interstitials O i atomic wires in the spacer layers in HgBa 2 CuO 4 ± δ , La 2 CuO 4 ± δ and La 2 NiO 4 ± δ , by means of self-consistent Linear Muffin-Tin Orbital (LMTO) calculations. The electronic structure of a first phase of ordered O i atomic wires and of a second glassy phase made of disordered O i impurities have been studied through supercell calculations. We show the common features of the influence of O i wires in the electronic structure in three types of materials. The ordering of O i into wires leads to a separation of the electronic states between the O i ensemble and the rest of the bulk. The wire formation first produces quantum confined localized states near the wire, which coexist with, Second, delocalized states in the Fermi surface (FS) of doped cuprates. A new scenario emerges for high T c superconductivity, where Kitaev wires with Majorana bound states are proximity-coupled to a 2D d-wave superconductor.

Exchange Interactions and Curie Temperature of Ce-Substituted SmCo5

A partial substitution such as Ce in SmCo 5 could be a brilliant way to improve the magnetic performance, because it will introduce strain in the structure and breaks the lattice symmetry in a way that enhances the contribution of the Co atoms to magnetocrystalline anisotropy. However, Ce substitutions, which are benefit to improve the magnetocrystalline anisotropy, are detrimental to enhance the Curie temperature ( T C ). With the requirements of wide operating temperature range of magnetic devices, it is important to quantitatively explore the relationship between the T C and ferromagnetic exchange energy. In this paper we show, based on mean-field approximation, artificial tensile strain in SmCo 5 induced by substitution leads to enhanced effective ferromagnetic exchange energy and T C , even though Ce atom itself reduces T C .

Contrasting Phenomenology of NMR Shifts in Cuprate Superconductors

Nuclear magnetic resonance (NMR) shifts, if stripped of their uncertainties, must hold key information about the electronic fluid in the cuprates. The early shift interpretation that favored a single-fluid scenario will be reviewed, as well as recent experiments that reported its failure. Thereafter, based on literature shift data for planar Cu, a contrasting shift phenomenology for cuprate superconductors is developed, which is very different from the early view while being in agreement with all published data. For example, it will be shown that the hyperfine scenario used up to now is inadequate as a large isotropic shift component is discovered. Furthermore, the changes of the temperature dependences of the shifts above and below the superconducting transitions temperature proceed according to a few rules that were not discussed before. It appears that there can be substantial spin shift at the lowest temperature if the magnetic field is perpendicular to the CuO 2 plane, which points to a localization of spin in the 3 d ( x 2 − y 2 ) orbital. A simple model is presented based on the most fundamental findings. The analysis must have new consequences for theory of the cuprates.

Nanoscale heterogeneity in thermoelectrics: the occurrence of phase separation in Fe-doped Ca3Co4O9

The thermoelectricity of Fe doped Ca₃Co₄O₉ is tuned by nanoscale structural heterogeneity, as unveiled by X-ray absorption spectroscopy and density functional theory.

Evidence for carrier localization in the pseudogap state of cuprate superconductors from coherent quench experiments

A 'pseudogap' was introduced by Mott to describe a state of matter that has a minimum in the density of states at the Fermi level, deep enough for states to become localized. It can arise either from Coulomb repulsion between electrons, and/or incipient charge or spin order. Here we employ ultrafast spectroscopy to study dynamical properties of the normal to pseudogap state transition in the prototype high-temperature superconductor Bi2Sr2CaCu2O8+δ. We perform a systematic temperature and doping dependence study of the pseudogap photodestruction and recovery in coherent quench experiments, revealing marked absence of critical behaviour of the elementary excitations, which implies an absence of collective electronic ordering beyond a few coherence lengths on short timescales. The data imply ultrafast carrier localization into a textured polaronic state arising from a competing Coulomb interaction and lattice strain, enhanced by a Fermi surface instability.

Pseudogap in cuprates in the loop-current ordered state

Scanning tunneling microscopy (STM) has revealed that the magnitude of the pseudo-gap in under-doped cuprates varies spatially and is correlated with disorder. The loop-current order, characterized by the anapole vector Ω, discovered in under-doped cuprates occurs in the same region of the temperature and doping as the pseudo gap observed in STM and ARPES experiments. Since translational symmetry remains unchanged in the pure limit, no gap occurs at the chemical potential. On the other hand for disorder coupling linearly to the different possible orientations of Ω, there can only be a finite temperature dependent static correlation length for the loop-current state at any temperature. This leads to formation of domains of the ordered state with different orientation and magnitude of Ω in each. For the characteristic size of the domains much larger than the Fermi-vectors [Formula: see text], the boundary of the domains leads to forward scattering of the Fermions. Such forward scattering is shown to push states near the chemical potential to energies both above and below it leading to a pseudo-gap with an angular dependence which is maximum in the [Formula: see text] directions because the single-particle energies are degenerate in these directions for all domains. The magnitude of the average gap systematically increases with the square of the average loop order parameter measured by polarized neutron scattering. This result is tested. A unique result of the gap due to forward scattering is the lack of a bump in the density of states at the 'edge' of the pseudo-gap so that the depletion of states near the chemical potential is recovered only in integration up to the edge of the band. This is also in agreement with a variety of experiments. Some predictions for further experiments are provided. Due to the finite correlation length, low frequency excitations are expected at long wavelength at all temperatures in the 'ordered' phase. Such fluctuations motionally average over the shifts in frequencies of local probes such as NMR and muon resonance expected for a truly static order.

Optimum inhomogeneity of local lattice distortions in La2CuO(4+y)

Electronic functionalities in materials from silicon to transition metal oxides are, to a large extent, controlled by defects and their relative arrangement. Outstanding examples are the oxides of copper, where defect order is correlated with their high superconducting transition temperatures. The oxygen defect order can be highly inhomogeneous, even in optimal superconducting samples, which raises the question of the nature of the sample regions where the order does not exist but which nonetheless form the "glue" binding the ordered regions together. Here we use scanning X-ray microdiffraction (with a beam 300 nm in diameter) to show that for La(2)CuO(4+y), the glue regions contain incommensurate modulated local lattice distortions, whose spatial extent is most pronounced for the best superconducting samples. For an underdoped single crystal with mobile oxygen interstitials in the spacer La(2)O(2+y) layers intercalated between the CuO(2) layers, the incommensurate modulated local lattice distortions form droplets anticorrelated with the ordered oxygen interstitials, and whose spatial extent is most pronounced for the best superconducting samples. In this simplest of high temperature superconductors, there are therefore not one, but two networks of ordered defects which can be tuned to achieve optimal superconductivity. For a given stoichiometry, the highest transition temperature is obtained when both the ordered oxygen and lattice defects form fractal patterns, as opposed to appearing in isolated spots. We speculate that the relationship between material complexity and superconducting transition temperature T(c) is actually underpinned by a fundamental relation between T(c) and the distribution of ordered defect networks supported by the materials.

Evolution and control of oxygen order in a cuprate superconductor

The disposition of defects in metal oxides is a key attribute exploited for applications from fuel cells and catalysts to superconducting devices and memristors. The most typical defects are mobile excess oxygens and oxygen vacancies, which can be manipulated by a variety of thermal protocols as well as optical and d.c. electric fields. Here we report the X-ray writing of high-quality superconducting regions, derived from defect ordering, in the superoxygenated layered cuprate, La₂CuO(4+y). Irradiation of a poor superconductor prepared by rapid thermal quenching results first in the growth of ordered regions, with an enhancement of superconductivity becoming visible only after a waiting time, as is characteristic of other systems such as ferroelectrics, where strain must be accommodated for order to become extended. However, in La₂CuO(4+y), we are able to resolve all aspects of the growth of (oxygen) intercalant order, including an extraordinary excursion from low to high and back to low anisotropy of the ordered regions. We can also clearly associate the onset of high-quality superconductivity with defect ordering in two dimensions. Additional experiments with small beams demonstrate a photoresist-free, single-step strategy for writing functional materials.

Scale-free structural organization of oxygen interstitials in La(2)CuO(4+y)

It is well known that the microstructures of the transition-metal oxides, including the high-transition-temperature (high-T(c)) copper oxide superconductors, are complex. This is particularly so when there are oxygen interstitials or vacancies, which influence the bulk properties. For example, the oxygen interstitials in the spacer layers separating the superconducting CuO(2) planes undergo ordering phenomena in Sr(2)O(1+y)CuO(2) (ref. 9), YBa(2)Cu(3)O(6+y) (ref. 10) and La(2)CuO(4+y) (refs 11-15) that induce enhancements in the transition temperatures with no changes in hole concentrations. It is also known that complex systems often have a scale-invariant structural organization, but hitherto none had been found in high-T(c) materials. Here we report that the ordering of oxygen interstitials in the La(2)O(2+y) spacer layers of La(2)CuO(4+y) high-T(c) superconductors is characterized by a fractal distribution up to a maximum limiting size of 400 mum. Intriguingly, these fractal distributions of dopants seem to enhance superconductivity at high temperature.

Local structural disorder in REFeAsO oxypnictides by RE L(3) edge XANES

The REFeAsO (RE = La, Pr, Nd and Sm) system has been studied by RE L(3) x-ray absorption near edge structure (XANES) spectroscopy to explore the contribution of the REO spacers between the electronically active FeAs slabs in these materials. The XANES spectra have been simulated by full multiple scattering calculations to describe the different experimental features and their evolution with the RE size. The near edge feature just above the L(3) white line is found to be sensitive to the ordering/disordering of oxygen atoms in the REO layers. In addition, shape resonance peaks due to As and O scattering change systematically, indicating local structural changes in the FeAs slabs and the REO spacers due to RE size. The results suggest that interlayer coupling and oxygen order/disorder in the REO spacers may have an important role in the superconductivity and itinerant magnetism of the oxypnictides.

RE L(3) x-ray absorption study of REO(1-x)F(x)FeAs (RE = La, Pr, Nd, Sm) oxypnictides

Rare earth L(3)-edge x-ray absorption near-edge structure (XANES) spectroscopy has been used to study REOFeAs (RE = La, Pr, Nd, Sm) oxypnictides. The Nd L(3) XANES due to the [Formula: see text] transition shows a substantial change in both white line (WL) spectral weight and the higher energy multiple scattering resonances with the partial substitution of O by F. A systematic change in the XANES features is seen due to varying lattice parameters with ionic radius of the rare earth. On the other hand, we hardly see any change across the structural phase transition. The results provide timely information on the local atomic correlations showing the importance of the local structural chemistry of the REO spacer layer and interlayer coupling in the competing superconductivity and itinerant striped magnetic phase of the oxypnictides.

A possible mechanism for evading temperature quantum decoherence in living matter by feshbach resonance

A new possible scenario for the origin of the molecular collective behaviour associated with the emergence of living matter is presented. We propose that the transition from a non-living to a living cell could be mapped to a quantum transition to a coherent entanglement of condensates, like in a multigap BCS superconductor. Here the decoherence-evading qualities at high temperature are based on the Feshbach resonance that has been recently proposed as the driving mechanism for high T_c superconductors. Finally we discuss how the proximity to a particular critical point is relevant to the emergence of coherence in the living cell.