Determination of the local lattice distortions in the CuO2 plane of La1.85Sr0.15CuO4

Unconventional short-range structural fluctuations in cuprate superconductors

The interplay between structural and electronic degrees of freedom in complex materials is the subject of extensive debate in physics and materials science. Particularly interesting questions pertain to the nature and extent of pre-transitional short-range order in diverse systems ranging from shape-memory alloys to unconventional superconductors, and how this microstructure affects macroscopic properties. Here we use neutron and X-ray diffuse scattering to uncover universal structural fluctuations in La2-xSrxCuO4 and Tl2Ba2CuO6+δ, two cuprate superconductors with distinct point disorder effects and with optimal superconducting transition temperatures that differ by more than a factor of two. The fluctuations are present in wide doping and temperature ranges, including compositions that maintain high average structural symmetry, and they exhibit unusual, yet simple scaling behaviour. The scaling regime is robust and universal, similar to the well-known critical fluctuations close to second-order phase transitions, but with a distinctly different physical origin. We relate this behaviour to pre-transitional phenomena in a broad class of systems with structural and magnetic transitions, and propose an explanation based on rare structural fluctuations caused by intrinsic nanoscale inhomogeneity. We also uncover parallels with superconducting fluctuations, which indicates that the underlying inhomogeneity plays an important role in cuprate physics.

Exploring the 4d1analogue of cuprates: theoretical studies on bulk NbF4and NbF4monolayer stabilized on MgO (001) plane

The recent research in infinite-layer nickelates has inspired new effort in finding the cuprate analogs. Here we propose that NbF₄, which contains niobium-centered fluorine octahedra, is a promising 4d¹analogue of cuprates. Using the density functional theory, we first show that bulk NbF₄is in close proximity tod¹configuration, with Nb4dxyorbital nearly half-filled. A single band with dominating4dxycharacter crosses the Fermi level, forming a square-like Fermi surface. The intralayer G-type antiferromagnetic (AFM) order is energetically favored and the Coulomb interaction drives the system into an AFM insulator. Next we demonstrate that the NbF₄layer can be stabilized on MgO substrate with main electronic and magnetic features retained, offering an alternative route to realize the NbF₄-related high-T_csuperconductors. Furthermore, we derive effective single orbital models for both systems and investigate the electron correlation effects via functional renormalization group. We find that the G-type AFM dominates near half-filling butdx2-y2-wave superconductivity (SC) prevails upon suitable hole/electron doping. Based on the striking similarities between NbF₄and cuprates, we suggest that NbF₄-related compounds may be exotic candidates for searching new high-T_csuperconductors.

Hidden Local Symmetry Breaking in a Kagome-Lattice Magnetic Weyl Semimetal

Exploring the relationship between intriguing physical properties and structural complexity is a central topic in studying modern functional materials. Co₃Sn₂S₂, a newly discovered kagome-lattice magnetic Weyl semimetal, has triggered intense interest owing to the intimate coupling between topological semimetallic states and peculiar magnetic properties. However, the origins of the magnetic phase separation and spin glass state below T_C in this ordered compound are two unresolved yet important puzzles in understanding its magnetism. Here, we report the discovery of local symmetry breaking surprisingly co-emerges with the onset of ferromagnetic order in Co₃Sn₂S₂, by a combined use of neutron total scattering and half-polarized neutron diffraction. An anisotropic distortion of the cobalt kagome lattice at the atomic/nano level is also found, with distinct distortion directions among the two Co1 and four Co2 atoms. The mismatch of local and average symmetries occurs below T_C, indicating that Co₃Sn₂S₂ evolves to an intrinsically lattice disordered system when the ferromagnetic order is established. The local symmetry breaking with intrinsic lattice disorder provides new understanding of the puzzling magnetic properties. Our density functional theory (DFT) calculation indicates that the local symmetry breaking is expected to reorient local ferromagnetic moments, unveiling the existence of the ferromagnetic instability associated with the lattice instability. Furthermore, DFT calculation unveils that the local symmetry breaking could affect the Weyl property by breaking the mirror plane. Our findings highlight the fundamentally important role that the local symmetry breaking plays in advancing our understanding on the magnetic and topological properties in Co₃Sn₂S₂, which may draw attention to explore the overlooked local symmetry breaking in Co₃Sn₂S₂, its derivatives and more broadly in other topological Dirac/Weyl semimetals and kagome-lattice magnets.

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.

The Strange-Metal Behavior of Cuprates

Recent resonant X-ray scattering experiments on cuprates allowed to identify a new kind of collective excitations, known as charge density fluctuations, which have finite characteristic wave vector, short correlation length and small characteristic energy. It was then shown that these fluctuations provide a microscopic scattering mechanism that accounts for the anomalous transport properties of cuprates in the so-called strange-metal phase and are a source of anomalies in the specific heat. In this work, we retrace the main steps that led us to attributing a central role to charge density fluctuations in the strange-metal phase of cuprates, discuss the state of the art on the issue and provide an in-depth analysis of the contribution of charge density fluctuations to the specific heat.

Superconductivity and the Jahn–Teller Polaron

In this article, we review the essential properties of high-temperature superconducting cuprates, which are unconventional isotope effects, heterogeneity, and lattice responses. Since their discovery was based on ideas stemming from Jahn–Teller polarons, their special role, together with the Jahn–Teller effect itself, is discussed in greater detail. We conclude that the underlying physics of cuprates cannot stem from purely electronic mechanisms, but that the intricate interaction between lattice and charge is at its origin.

Evolution of Charge-Lattice Dynamics across the Kuramoto Synchronization Phase Diagram of Quantum Tunneling Polarons in Cuprate Superconductors

Because of its sensitivity to the instantaneous structure factor, S(Q,t = 0), Extended X-ray Absorption Fine Structure (EXAFS) is a powerful tool for probing the dynamic structure of condensed matter systems in which the charge and lattice dynamics are coupled. When applied to hole-doped cuprate superconductors, EXAFS has revealed the presence of internal quantum tunneling polarons (IQTPs). An IQTP arises in EXAFS as a two-site distribution for certain Cu–O pairs, which is also duplicated in inelastic scattering but not observed in standard diffraction measurements. The Cu–Sr pair distribution has been found to be highly anharmonic and strongly correlated to both the IQTPs and to superconductivity, as, for example, in YSr2Cu2.75Mo0.25O7.54(Tc=84 K). In order to describe such nontrivial, anharmonic charge-lattice dynamics, we have proposed a model Hamiltonian for a prototype six-atom cluster, in which two Cu-apical-O IQTPs are charge-transfer bridged through Cu atoms by an O atom in the CuO2 plane and are anharmonically coupled via a Sr atom. By applying an exact diagonalization procedure to this cluster, we have verified that our model indeed produces an intricate interplay between charge and lattice dynamics. Then, by using the Kuramoto model for the synchronization of coupled quantum oscillators, we have found a first-order phase transition for the IQTPs into a synchronized, phase-locked phase. Most importantly, we have shown that this transition results specifically from the anharmonicity. Finally, we have provided a phase diagram showing the onset of the phase-locking of IQTPs as a function of the charge-lattice and anharmonic couplings in our model. We have found that the charge, initially confined to the apical oxygens, is partially pumped into the CuO2 plane in the synchronized phase, which suggests a possible connection between the synchronized dynamic structure and high-temperature superconductivity (HTSC) in doped cuprates.

Out-of-Plane Sulfur Distortions in the Bi4O4S3 Superconductor

The local atomic structure of the non-magnetic layered superconductor Bi4O4S3 was investigated using neutron diffraction and pair density function (PDF) analysis. Although on average, the crystal structure is well ordered, evidence for local, out–of–plane sulfur distortions is provided, which may act as a conduit for charge transfer from the SO4 blocks into the superconducting BiS2 planes. In contrast with LaO1−xFxBiS2, no sulfur distortions were detected in the planes, which indicates that charge density wave fluctuations are not supported in Bi4O4S3.

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.

Functional Nanoscale Phase Separation and Intertwined Order in Quantum Complex Materials

Nanoscale phase separation (NPS), characterized by particular types of correlated disorders, plays an important role in the functionality of high-temperature superconductors (HTS). Our results show that multiscale heterogeneity is an essential ingredient of quantum functionality in complex materials. Here, the interactions developing between different structural units cause dynamical spatiotemporal conformations with correlated disorder; thus, visualizing conformational landscapes is fundamental for understanding the physical properties of complex matter and requires advanced methodologies based on high-precision X-ray measurements. We discuss the connections between the dynamical correlated disorder at nanoscale and the functionality in oxygen-doped perovskite superconducting materials.

Plexcitons, electric field gradient and electron-phonon coupling in tip-enhanced Raman spectroscopy (TERS)

Tip-Enhanced Raman Spectroscopy (TERS) provides very high spatial resolution and detection sensitivity, so it has important applications in nano-scale molecular analysis. Plexciton is a polarization mode caused by a strongly coupled interaction between plasma excitons and excitons. It is a hot topic in plasma photonics research. We introduce the characteristics, production methods, observation methods and some applications of TERS. The electric field gradient (EFG) is an important factor affecting TERS resolution. The electron-phonon interaction is a fundamental inelastic interaction and plays an important role in current-carrying single-molecular junctions. This article summarizes the characteristics and applications of these three parts for readers to gain a preliminary understanding.

On the Kinetic Energy Driven Superconductivity in the Two-Dimensional Hubbard Model

We investigate the role of kinetic energy for the stability of superconducting state in the two-dimensional Hubbard model on the basis of an optimization variational Monte Carlo method. The wave function is optimized by multiplying by correlation operators of site off-diagonal type. This wave function is written in an exponential-type form given as ψλ=exp(−λK)ψG for the Gutzwiller wave function ψG and a kinetic operator K. The kinetic correlation operator exp(−λK) plays an important role in the emergence of superconductivity in large-U region of the two-dimensional Hubbard model, where U is the on-site Coulomb repulsive interaction. We show that the superconducting condensation energy mainly originates from the kinetic energy in the strongly correlated region. This may indicate a possibility of high-temperature superconductivity due to the kinetic energy effect in correlated electron systems.

From SrTiO3 to Cuprates and Back to SrTiO3: A Way Along Alex Müller’s Scientific Career

K.A. Müller took a long route in science leaving many traces and imprints, which have been and are still today initiations for further research activities. We “walk” along this outstanding path but are certainly not able to provide a complete picture of it, since the way was not always straight, often marked by unintended detours, which had novel impact on the international research society.

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.

Monolayer NbF4: a 4d1-analogue of cuprates

The electronic structure and possible electronic orders in monolayer NbF₄ are investigated by density functional theory and functional renormalization group. Because of the niobium-centered octahedra, the energy band near the Fermi level is found to derive from the 4d_xy orbital, well separated from the other bands. Local Coulomb interaction drives the undoped system into an antiferromagnetic insulator. Upon suitable electron/hole doping, the system is found to develop [Formula: see text] -wave superconductivity with sizable transition temperature. Therefore, the monolayer NbF₄ may be an exciting 4d¹ analogue of cuprates, providing a new two-dimensional platform for high-T_c superconductivity.

Revival of Charge Density Waves and Charge Density Fluctuations in Cuprate High-Temperature Superconductors

I present here a short memory of my scientific contacts with K.A. Müller starting from the Interlaken Conference (1988), Erice (1992 and 1993), and Cottbus (1994) on the initial studies on phase separation (PS) and charge inhomogeneity in cuprates carried out against the view of the majority of the scientific community at that time. Going over the years and passing through the charge density wave (CDW) instability of the correlated Fermi liquid (FL) and to the consequences of charge density fluctuations (CDFs), I end with a presentation of my current research activity on CDWs and the related two-dimensional charge density fluctuations (2D-CDFs). A scenario follows of the physics of cuprates, which includes the solution of the decades-long problem of the strange metal (SM) state.

Possible Occurrence of Superconductivity by the π-flux Dirac String Formation Due to Spin-Twisting Itinerant Motion of Electrons

We show that the Rashba spin-orbit interaction causes spin-twisting itinerant motion of electrons in metals and realizes the quantized cyclotron orbits of conduction electrons without an external magnetic field. From the view point of the Berry connection, the cause of this quantization is the appearance of a non-trivial Berry connection A fic = − ℏ 2 e ∇ χ ( χ is an angular variable with period 2 π ) that generates π flux (in the units of ℏ = 1 , e = 1 , c = 1 ) inside the nodal singularities of the wave function (a “Dirac string”) along the centers of spin-twisting. Since it has been shown in our previous work that the collective mode of ∇ χ is stabilized by the electron-pairing and generates supercurrent, the π -flux Dirac string created by the spin-twisting itinerant motion will be stabilized by the electron-pairing and produce supercurrent.

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 YBa₂Cu₃O_7-δ and Nd_{1+ x} Ba_{2- x} Cu₃O_7-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.

Multi-Band Superconductivity and the Steep Band/Flat Band Scenario

The basic features of multi-band superconductivity and its implications are derived. In particular, it is shown that enhancements of the superconducting transition temperature take place due to interband interactions. In addition, isotope effects differ substantially from the typical BCS scheme as soon as polaronic coupling effects are present. Special cases of the model are polaronic coupling in one band as realized e.g., in cuprates, coexistence of a flat band and a steep band like in MgB2, crossovers between extreme cases. The advantages of the multiband approach as compared to the single band BCS model are elucidated and its rather frequent realization in actual systems discussed.

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.

The Ancient Romans’ Route to Charge Density Waves in Cuprates

An account is given of the main steps that led the research group in Rome, to which the author belongs, to the formulation of the charge-density-wave scenario for high- T c superconducting cuprates. The early finding of the generic tendency of strongly correlated electron systems with short range interactions to undergo electron phase separation was subsequently contrasted with the homogenizing effect of the long-range Coulomb interaction. The two effects can find a compromise in the formation of incommensurate charge density waves. These charge density waves are inherently dynamical and are overdamped as a consequence of the possibility to decay in electron-hole pairs, yet tend to maintain a (quantum) critical character, which is mirrored in their marked momentum and frequency dependence and in their strong variation with temperature and doping. These dynamical incommensurate charge density waves act as mediators of pairing lading to high- T c superconductivity, and provide the scattering mechanism that produces the observed violation of the Fermi-liquid paradigm in the metallic phase.

Mechanism of High-Temperature Superconductivity in Correlated-Electron Systems

It is very important to elucidate the mechanism of superconductivity for achieving room temperature superconductivity. In the first half of this paper, we give a brief review on mechanisms of superconductivity in many-electron systems. We believe that high-temperature superconductivity may occur in a system with interaction of large-energy scale. Empirically, this is true for superconductors that have been found so far. In the second half of this paper, we discuss cuprate high-temperature superconductors. We argue that superconductivity of high temperature cuprates is induced by the strong on-site Coulomb interaction, that is, the origin of high-temperature superconductivity is the strong electron correlation. We show the results on the ground state of electronic models for high temperature cuprates on the basis of the optimization variational Monte Carlo method. A high-temperature superconducting phase will exist in the strongly correlated region.

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.

Quantitative Characterization of the Nanoscale Local Lattice Strain Induced by Sr Dopants in La_{1.92}Sr_{0.08}CuO_{4}

The nanometer scale lattice deformation brought about by the dopants in the high temperature superconducting cuprate La_{2-x}Sr_{x}CuO_{4} (x=0.08) was investigated by measuring the associated x-ray diffuse scattering around multiple Bragg peaks. A characteristic diffuse scattering pattern was observed, which can be well described by continuum elastic theory. With the fitted dipole force parameters, the acoustic-type lattice deformation pattern was reconstructed and found to be of similar size to lattice thermal vibration at 7 K. Our results address the long-term concern of dopant introduced local lattice inhomogeneity, and show that the associated nanometer scale lattice deformation is marginal and cannot, alone, be responsible for the patched variation in the spectral gaps observed with scanning tunneling microscopy in the cuprates.

The flux dynamics behavior of the two competing high temperature superconducting phases in underdoped LaCuO4.06

In complex transition metal oxides (TMO) an arrested electronic phase separation (PS) appears by tuning the system near a Lifshitz transition in multiband Hubbard models. The PS in La2CuO4+y near insulator to metal transition (IMT) is made of short range Charge Density Wave (CDW) order inhomogeneity coexisting with quenched lattice disorder. While at high doping y = 0.1 percolation gives a single superconducting phase, near the IMT at y = 0.06 two coexisting superconducting phases appear: the first one with a critical temperature Tc1 = 16 K and the second one with Tc2 = 29 K. It is known that the two superconducting phases are characterized by two different space geometry because of two different spatial distributions of both CDW order and dopants self-organization. Here we show that these two phases show different flux dynamic regimes using alternating current (AC) multi-harmonic susceptibility experiments. This is a unique technique capable to investigate multi-phase superconductors and characterize their transport properties in a percolative scenario. Results point out that the low critical temperature phase is well described by a bulk-like flux pinning with a 2D geometry while the phase with higher critical temperature shows a 'barrier pinning' mechanism providing direct evidence of two different superconducting vortex dynamics in different complex geometrical spaces.

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.

Antiperovskite Chalco-Halides Ba3(FeS4)Cl, Ba3(FeS4)Br, and Ba3(FeSe4)Br with Spin Super-Super Exchange

Perovskite-related materials have received increasing attention for their broad applications in photovoltaic solar cells and information technology due to their unique electrical and magnetic properties. Here we report three new antiperovskite chalco-halides: Ba₃(FeS₄)Cl, Ba₃(FeS₄)Br, and Ba₃(FeSe₄)Br. All of them were found to be good solar light absorbers. Remarkably, although the shortest Fe-Fe distance exceeds 6 Å, an unexpected anti-ferromagnetic phase transition near 100 K was observed in their magnetic susceptibility measurement. The corresponding complex magnetic structures were resolved by neutron diffraction experiments as well as investigated by first-principles electronic structure calculations. The spin-spin coupling between two neighboring Fe atoms along the b axis, which is realized by the Fe-S···S-Fe super-super exchange mechanism, was found to be responsible for this magnetic phase transition.

Inhomogeneity of charge-density-wave order and quenched disorder in a high-Tc superconductor

It has recently been established that the high-transition-temperature (high-Tc) superconducting state coexists with short-range charge-density-wave order and quenched disorder arising from dopants and strain. This complex, multiscale phase separation invites the development of theories of high-temperature superconductivity that include complexity. The nature of the spatial interplay between charge and dopant order that provides a basis for nanoscale phase separation remains a key open question, because experiments have yet to probe the unknown spatial distribution at both the nanoscale and mesoscale (between atomic and macroscopic scale). Here we report micro X-ray diffraction imaging of the spatial distribution of both short-range charge-density-wave 'puddles' (domains with only a few wavelengths) and quenched disorder in HgBa2CuO4 + y, the single-layer cuprate with the highest Tc, 95 kelvin (refs 26-28). We found that the charge-density-wave puddles, like the steam bubbles in boiling water, have a fat-tailed size distribution that is typical of self-organization near a critical point. However, the quenched disorder, which arises from oxygen interstitials, has a distribution that is contrary to the usually assumed random, uncorrelated distribution. The interstitial-oxygen-rich domains are spatially anticorrelated with the charge-density-wave domains, because higher doping does not favour the stripy charge-density-wave puddles, leading to a complex emergent geometry of the spatial landscape for superconductivity.

Stripe-like nanoscale structural phase separation in superconducting BaPb(1-x)Bi(x)O3

The phase diagram of BaPb(1-x)Bi(x)O3 exhibits a superconducting dome in the proximity of a charge density wave phase. For the superconducting compositions, the material coexists as two structural polymorphs. Here we show, via high-resolution transmission electron microscopy, that the structural dimorphism is accommodated in the form of partially disordered nanoscale stripes. Identification of the morphology of the nanoscale structural phase separation enables determination of the associated length scales, which we compare with the Ginzburg-Landau coherence length. We find that the maximum Tc occurs when the superconducting coherence length matches the width of the partially disordered stripes, implying a connection between the structural phase separation and the shape of the superconducting dome.

Phase diagram of cuprate high-temperature superconductors described by a field theory based on anharmonic oxygen degrees of freedom

In high temperature superconductors, although some phenomena such as the Mott transition (MT) at low doping are clearly driven by electron correlations, recent experimental data imply that anharmonic oxygen degrees of freedom-characteristic of perovskite materials-are playing a significant role. A key test of the role of anharmonic oxygen is to reproduce the complex cuprate phase diagram from a simple model. Here, we show that a field theory based on nonlinear coupling to anharmonic oxygens, parametrized from ab initio calculations, quantitatively reproduces the cuprate phase diagram for dopings above the MT. Pairing is mediated by renormalized oxygen vibrations transmuted into excitations of the pseudogap. The observed strong dependence of gap to transition temperature ratio on Tc also emerges from this field theory. This work suggests that including vibrational degrees of freedom is key to developing a complete understanding of the cuprates.

Superconducting pairing and the pseudogap in the nematic dynamical stripe phase of La2-xSrxCuO4

Fully absorption coefficient corrected Raman spectra were obtained in La2-xSrxCuO4. The B1g spectra have a Fleury-Loudon type two-magnon peak (resonant term) whose energy decreases from 3180 cm(-1) (394 meV) to 440 cm(-1) (55 meV) on increasing the carrier density from x = 0 to 0.25, while the B2g spectra have a 1000-3500 cm(-1) (124-434 meV) hump (hill) whose lower-edge energy increases from x = 0 to 0.115 and then stays constant to x = 0.25. The B2g hump is assigned to the electronic scattering (non-resonant term) of the spectral function with magnetic self-energy. The completely different carrier density dependence arises from anisotropic magnetic excitations of spin-charge stripes. The B1g spectra were assigned to the sum of k ∥  and k⊥ stripe excitations and the B2g spectra to k⊥ stripe excitations according to the calculation by Seibold and Lorenzana (2006 Phys. Rev. B 73 144515). The k ∥  and k⊥ stripe excitations in fluctuating spin-charge stripes were separately detected for the first time. The appearance of only k⊥ stripe excitations in the electronic scattering arises from the charge hopping perpendicular to the stripe. This is the same direction as the Burgers vector of the edge dislocation in metal. The successive charge hopping in the Burgers vector direction across the charge stripes may cause Cooper pairs as predicted by Zaanen et al (2004 Ann. Phys. 310 181). Indeed, this is supported by the experimental fact that the superconducting coherent length coincides with the inter-charge stripe distance in the wide carrier density range. The one-directional charge hopping perpendicular to the stripe causes the flat Fermi surface and the pseudogap near (π,0) and (0,π), but the states around (π/2,π/2) cannot be produced. The low-energy Raman scattering disclosed that the electronic states at the Fermi arc around (π/2,π/2) are coupled to the A1g soft phonon of the tetragonal-orthorhombic phase transition. This suggests that the Fermi arc is produced by the electron-phonon interaction. All the present Raman data suggest that Cooper pairs are formed at moving edge dislocations of dynamical charge stripes.

Nanoscale structure and atomic disorder in the iron-based chalcogenides

The multiband iron-based superconductors have layered structure with a phase diagram characterized by a complex interplay of charge, spin and lattice excitations, with nanoscale atomic structure playing a key role in their fundamental electronic properties. In this paper, we briefly review nanoscale structure and atomic disorder in iron-based chalcogenide superconductors. We focus on the Fe(Se,S)1-x Te x (11-type) and K0.8Fe1.6Se2 (122-type) systems, discussing their local structure obtained by extended x-ray absorption fine structure. Local structure studies on the Fe(Se,S)1-x Te x system reveal clear nanoscale phase separation characterized by coexisting components of different atomic configurations, similar to the case of random alloys. In fact, the Fe-Se/S and Fe-Te distances in the ternary Fe(Se,S)1-x Te x are found to be closer to the respective distances in the binary FeSe/FeS and FeTe systems, showing significant divergence of the local structure from the average one. The observed features are characteristic of ternary random alloys, indicating breaking of the local symmetry in these materials. On the other hand, K0.8Fe1.6Se2 is known for phase separation in an iron-vacancy ordered phase and an in-plane compressed lattice phase. The local structure of these 122-type chalcogenides shows that this system is characterized by a large local disorder. Indeed, the experiments suggest a nanoscale glassy phase in K0.8Fe1.6Se2, with the superconductivity being similar to the granular materials. While the 11-type structure has no spacer layer, the 122-type structure contains intercalated atoms unlike the 1111-type REFeAsO (RE = rare earth) oxypnictides, having well-defined REO spacer layers. It is clear that the interlayer atomic correlations in these iron-based superconducting structures play an important role in structural stability as well as superconductivity and magnetism.

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.

Temperature-dependent local structure of NdFeAsO(1-x)F(x) system using arsenic K-edge extended x-ray absorption fine structure

Local structure of NdFeAsO(1-x)F(x) (x = 0.0, 0.05, 0.15 and 0.18) high temperature iron-pnictide superconductor system is studied using arsenic K-edge extended x-ray absorption fine structure measurements as a function of temperature. Fe-As bond length shows only a weak temperature and F-substitution dependence, consistent with the strong covalent nature of this bond. The temperature dependence of the mean square relative displacements of the Fe-As bond length are well described by the correlated Einstein model for all the samples, but with different Einstein temperatures for the superconducting and non-superconducting samples. The results indicate distinct local Fe-As lattice dynamics in the superconducting and non-superconducting iron-pnictide systems.

Local structural studies of Ba(1-x)K(x)Fe2As2 using atomic pair distribution function analysis

Systematic local structural studies of the Ba(1-x)K(x)Fe(2)As(2) system are undertaken at room temperature using atomic pair distribution function analysis. The local structure of the Ba(1-x)K(x)Fe(2)As(2) is found to be well described by the long-range structure extracted from diffraction experiments, but with anisotropic atomic vibrations of the constituent atoms (U11 = U22 not equal U33). The crystal unit cell parameters, the FeAs(4) tetrahedral angle and the pnictogen height above the Fe-plane are seen to show systematic evolution with K doping, underlining the importance of the structural changes, in addition to the charge doping, in determining the properties of Ba(1-x)K(x)Fe(2)As(2).

Spectral and optical properties in the antiphase stripe phase of the cuprate superconductors

We investigate the superconducting order parameter, the spectral and optical properties in a stripe model with spin-(charge-) domain-derived scattering potential V(s) (V(c)). We show that the charge-domain-derived scattering is less effective than the spin scattering on the suppression of superconductivity. For [Formula: see text], the spectral weight concentrates on the (π,0) antinodal region and a finite energy peak appears in the optical conductivity with the disappearance of the Drude peak. But for V(s)≈V(c), the spectral weight concentrates on the (π/2,π/2) nodal region and a residual Drude peak exists in the optical conductivity without the finite energy peak. These results consistently account for the divergent observations in the ARPES and optical conductivity experiments in several high- T(c) cuprates and suggest that the 'insulating' and 'metallic' properties are intrinsic to the stripe state, depending on the relative strength of the spin- and charge-domain-derived scattering potentials.

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.

Setup for optimized grazing incidence x-ray absorption experiments on thin films on substrates

We present a state-of-the-art experimental apparatus and a proper setup to perform x-ray absorption spectroscopy (XAS) experiments in grazing incidence mode. This geometry is appropriate for doped thin films or interfaces buried at moderate depth in a thick matrix, whenever the scattering and/or fluorescence from the matrix has to be strongly attenuated. Both the calculation and the experimental data demonstrate that the specific setup that consists in a grazing incidence and grazing collection geometry is extremely advantageous. In fact, with respect to the standard geometry used to perform XAS experiments in fluorescence mode, the present setup allows an enhancement in the interesting fluorescence signal from the surface layer without a corresponding increase in the elastic scattering contribution from the matrix. The sample holder especially designed for this kind of experiment can work in vacuum and at low temperature. An easy and quick automatic sample alignment procedure is detailed.

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.

Spin vortices in cuprate superconductors: fictitious magnetic field, fictitious electric field, and persistent current

We theoretically investigate loop currents generated by a Berry phase that arises from spin vortices and argue that a coherent collection of them forms a supercurrent in cuprate superconductors. First, we explain enhanced Nernst signals in cuprates using a fictitious electric field that arises from flow of spin vortices with their centers at sites where lattice-distortion-clad holes (small polaronic holes) reside. Assuming the coexistence of holes in large and small polaron forms, the magnitude of the Nernst signal is shown to be proportional to density and mobility of small polarons, and expressed as e(N) = c(3)T(-1)e(-0.5W(p)/k(B)T)/(1 + (2pim*k(B)T)/(n(s)h(2))e(-W(p)/k(B)T)), where c(3) is a constant, W(p) is the small polaron formation energy, n(s) is the surface density of sites, and m* is the effective mass of the large polaron; by treating unknown parameters as fitting parameters, this formula follows the experimental temperature dependence very well. From the obtained W(p) value, it is indicated that superconductivity occurs at temperatures where almost all of the holes become small polarons; thus, the conventional current generation mechanism is ineffective at temperatures around T(c); however, loop current generation by the spin Berry phase is effective. We calculate the superconducting transition temperature as an order-disorder transition temperature of the loop currents. The doped hole concentration, x, dependence of the transition temperature is obtained as T(c) = T(0) ln x/x(0) and agrees with experimental data, where T(0) and x(0) are treated as fitting parameters. Lastly, we briefly mention an artificial nanostructure that generates a persistent current by utilizing the spin Berry phase.

Strong and complex electron-lattice correlation in optimally doped Bi2Sr2CaCu2O8+delta

We discuss the nature of electron-lattice interaction in optimally doped Bi_{2}Sr_{2}CaCu_{2}O_{8+delta} samples, using the isotope effect (IE) in angle resolved photoemission spectroscopy (ARPES) data. The IE in the ARPES linewidth and the IE in the ARPES dispersion are both quite large, implying a strong electron-lattice correlation. The strength of the electron-lattice interaction is "intermediate," i.e., stronger than the Migdal-Eliashberg regime but weaker than the small polaron regime, requiring a more general picture of the ARPES kink than the commonly used Migdal-Eliashberg picture. The two IEs also imply a complex interaction, due to their strong momentum dependence and their differing sign behaviors. In sum, we propose an intermediate-strength coupling of electrons to localized lattice vibrations via charge density fluctuations.

Structural matters in HTSC: the origin and form of stripe organization and checkerboarding

The paper deals with the controversial charge and spin self-organization phenomena in the HTSC cuprates, of which neutron, x-ray, STM and ARPES experiments give complementary, sometimes apparently contradictory glimpses. The examination has been set in the context of the boson-fermion, negative-U understanding of HTSC advocated over many years by the author. Stripe models are developed which are 2-q in nature and diagonal in form. For such a geometry to be compatible with the data rests upon both the spin and charge arrays being face-centred. Various special doping concentrations are closely looked at, in particular p = 0.1836 or 9/49, which is associated with the maximization of the superconducting condensation energy and the termination of the pseudogap regime. The stripe models are dictated by real space organization of the holes, whereas the dispersionless checkerboarding is interpreted in terms of correlation driven collapse of normal Fermi surface behaviour and response functions. The incommensurate spin diffraction below the 'resonance energy' is seen as in no way expressing spin-wave physics or Fermi surface nesting, but is driven by charge and strain (Jahn-Teller) considerations, and it stands virtually without dispersion. The apparent dispersion comes from the downward dispersion of the resonance peak, and the growth of a further incoherent commensurate peak pursuant upon the falling level of charge stripe organization under excitation.

Polaronic behavior of undoped high-T(c) cuprate superconductors from angle-resolved photoemission spectra

We present angle-resolved photoemission spectroscopy (ARPES) data on undoped La2CuO4, indicating polaronic coupling between bosons and charge carriers. Using a shell model, we calculate the electron-phonon coupling and find that it is strong enough to give self-trapped polarons. We develop an efficient method for calculating ARPES spectra in undoped systems. Using the calculated couplings, we find the width of the phonon sideband in good agreement with experiment. We analyze reasons for the observed dependence of the width on the binding energy.