Theory of High Temperature Superconductivity in Cuprates and Other Doped Polar Insulators

In the last two decades, there have been tremendous attempts to build an adequate theory of high-temperature superconductivity. Most studies used some model Hamiltonians with input parameters not directly related to the material. The dielectric response function of electrons in strongly correlated high-temperature superconductors is a priori unknown. Hence, one has to start with the generic Hamiltonian including unscreened Coulomb and Fr?hlich electron?Cphonon interactions operating on the same scale since any ad-hoc assumption on their range and relative magnitude might fail. Using such a generic Hamiltonian, the analytical theory of high-temperature superconductivity in doped polar insulators predicting the critical temperature in excess of a hundred Kelvin without any adjustable parameters has been built. The many-particle electron system is described by an analytically solvable polaronic t?CJ _p Hamiltonian with reduced hopping integral, t, allowed double on-site occupancy, large phonon-induced antiferromagnetic exchange, J _p >t, and a high-temperature superconducting state of small superlight bipolarons protected from clustering. Here, major steps of the theory are outlined suggesting that the true origin of high-temperature superconductivity is found in a proper combination of strong electron?Celectron correlations with a significant finite-range (Fr?hlich) EPI, and that the theory is fully compatible with the key experiments.     

High Temperature Superconductivity Due to a Long-Range Electron–Phonon Interaction, Application to Isotope Effects, Thermomagnetic Transport and Nanoscale Heterogeneity in Cuprates

Strong electron–phonon (e–ph) interaction in cuprates and other high-temperature superconductors has gathered support over the last decade in a large number of experiments. I briefly review the “Fröhlich–Coulomb” multi-polaron model of high-temperature superconductivity, which includes strong onsite repulsive correlations and the long-range Coulomb and e–ph interactions. The extension of the BCS theory to the strong-coupling regime with a long-range unscreened e–ph interaction naturally explains the isotope effects, unconventional thermomagnetic transport, and checkerboard modulations of the tunnelling density of states (DOS) in cuprates.     

Unconventional Pairs Glued by Conventional Phonons in Cuprate Superconductors

It has gone almost unquestioned that superexchange in the t−J (or Hubbard) model, and not phonons, is responsible for the unconventional (“d-wave”) pairing symmetry of cuprate superconductors. However, a number of advanced numerical studies have not found superconductivity in the Hubbard (or t−J) model. On the other hand, compelling experimental evidence for a strong electron–phonon interaction (EPI) has currently arrived. Here I briefly review some phonon-mediated unconventional pairing mechanisms. In particular the anisotropy of sound velocity makes the phonon-mediated attraction of electrons non-local in space providing unconventional Cooper pairs with a non-zero orbital momentum already in the framework of the conventional BCS theory with weak EPI. In the opposite limit of strong EPI rotational symmetry breaking appears as a result of a reduced Coulomb repulsion between unconventional bipolarons. Using the variational Monte Carlo method we have found that a relatively weak finite-range EPI induces a d-wave BCS state also in doped Mott–Hubbard insulators or strongly-correlated metals. These results tell us that poorly screened EPI with conventional phonons is responsible for the unconventional pairing in cuprate superconductors.      

Scanning tunnelling microscopy imaging of symmetry-breaking structural distortion in the bismuth-based cuprate superconductors

A complicating factor in unravelling the theory of high-temperature (high-T(c)) superconductivity is the presence of a 'pseudogap' in the density of states, the origin of which has been debated since its discovery. Some believe the pseudogap is a broken symmetry state distinct from superconductivity, whereas others believe it arises from short-range correlations without symmetry breaking. A number of broken symmetries have been imaged and identified with the pseudogap state, but it remains crucial to disentangle any electronic symmetry breaking from the pre-existing structural symmetry of the crystal. We use scanning tunnelling microscopy to observe an orthorhombic structural distortion across the cuprate superconducting Bi(2)Sr(2)Ca(n-1)Cu(n)O(2n+4+x) (BSCCO) family tree, which breaks two-dimensional inversion symmetry in the surface BiO layer. Although this inversion-symmetry-breaking structure can impact electronic measurements, we show from its insensitivity to temperature, magnetic field and doping, that it cannot be the long-sought pseudogap state. To detect this picometre-scale variation in lattice structure, we have implemented a new algorithm that will serve as a powerful tool in the search for broken symmetry electronic states in cuprates, as well as in other materials.     

Theory of High Temperature Superconductivity Beyond BCS with Realistic Coulomb and Fröhlich Interactions

Along with some other researches we have realised that the true origin of high-temperature superconductivity is found in the strong Coulomb repulsion combined with a significant electron–phonon interaction. Both interactions are strong (on the order of 1 eV) compared with the low Fermi energy of doped carriers which makes the conventional BCS-Eliashberg theory inapplicable in cuprates and related doped insulators. Based on our recent analytical and numerical results we argue that high-temperature superconductivity from repulsion alone is impossible for any strength of the Coulomb interaction. Major steps of the alternative polaron theory are outlined starting from the generic Hamiltonian including the unscreened (bare) Coulomb and electron–phonon interactions. The theory accounts for high superconducting critical temperatures, unconventional isotope effects and reconciles tunnelling, photoemission and quantum oscillation data.     

Phase Separation of Electrons Strongly Coupled with Phonons in Cuprates and Manganites

Recent advanced Monte Carlo simulations have not found superconductivity and phase separation in the Hubbard model with on-site repulsive electron–electron correlations. We argue that microscopic phase separations in cuprate superconductors and colossal magnetoresistance (CMR) manganites originate from a strong electron–phonon interaction (EPI) combined with unavoidable disorder. Attractive electron correlations, caused by an almost unretarded EPI, are sufficient to overcome the direct inter-site Coulomb repulsion in these charge-transfer Mott–Hubbard insulators, so that low energy physics is that of small polarons and small bipolarons (real-space electron (hole) pairs dressed by phonons). They form clusters localized by disorder below the mobility edge, but propagate as the Bloch states above the mobility edge. I identify the Fröhlich finite-range EPI with optical phonons as the most essential for pairing and phase separation in superconducting layered cuprates. The pairing of oxygen holes into heavy bipolarons in the paramagnetic phase (current-carrier density collapse (CCDC)) explains also CMR of doped manganites due to magnetic break-up of bipolarons in the ferromagnetic phase. Here I briefly present an explanation of high- and low-resistance phase coexistence near the ferromagnetic transition as a mixture of polaronic ferromagnetic and bipolaronic paramagnetic domains due to unavoidable disorder in doped manganites.     

Complex Lattice and Charge Inhomogeneity Favoring Quantum Coherence in High-Temperature Superconductors

The presence of two components in the electron fluid of high-temperature superconductors and the complex charge and lattice inhomogeneity have been the hot topics of the international conference of the superstripes series, SUPERSTRIPES 2015, held in Ischia in 2015. The debate on the mechanisms for reaching room-temperature superconductors has been boosted by the discovery of superconductivity with the highest critical temperature in pressurized sulfur hydride. Different complex electronic and structural landscapes showing up in superconductors which resist to the decoherence effects of high temperature have been discussed. While low-temperature superconductors described by the BCS approximation are made of a single condensate in the weak coupling, the high-temperature superconductors are made of coexisting multiple condensates (in different spots of the k-space and the real space) some in the BCS-BEC crossover regime and others in the BCS regime. The role of “shape resonance” in the exchange interaction between these different condensates, like “the Fano-Feshbach resonance” in ultracold gasses, is emerging as a key term for high-temperature superconductivity.     

Pseudo-gap and Vertex Correction of Electron–Phonon Interaction in High Transition-Temperature Superconductors

The strong-coupling Eliashberg theory plus vertex correction is used to calculate the maps of transition temperature (T _c) in parameter-space characterizing superconductivity. Based on these T _c maps, complex crossover behaviors are found when electron?Cphonon interaction increases from weak-coupling region to strong-coupling region. The doping-dependent T _c of cuprate superconductors and most importantly the emergence of pseudo-gap region can be explained as the effects of vertex correction.     

High Temperature Interface Superconductivity

We use atomic-layer-by-layer molecular beam epitaxy (ALL-MBE) to deposit atomically smooth films of cuprate superconductors and other complex oxides. Bilayers, multilayers, and superlattices are grown with atomic precision and virtually perfect interfaces. This has allowed a discovery and in-depth study of high-temperature interface superconductivity, which is briefly reviewed here.     

Vitaly Ginzburg and High-Temperature Superconductivity

Vitaly L. Ginzburg has contributed in many areas of physics. One of these is the field of high-temperature superconductivity (HTSC). I have benefited from his insight in this field and have enjoyed his friendship and support over a period of almost 40 years. I present some personal reminiscences of these interactions and discuss recent progress towards the understanding of the mechanism responsible for the superconductivity of the high T _c cuprate superconductors, its relation to our earlier work, and what lies ahead.     

Non-linear Localized Lattice Mode Coupling Mechanism and the Pseudogap in High-temperature Superconducting Cuprates

The pseudo-gap phenomena in high-temperature cuprate superconductors is an outstanding puzzle with no consensus yet on its physical origin. A previous suggestion on the role of non-linear local lattice instability modes on the microscopic pairing mechanism in high temperature cuprate superconductors is re-examined to investigate whether unusual lattice mechanisms could cause a pseudo-gap. By assuming an electron predominantly interacting with a non-linear Q ₂ mode of the oxygen clusters in the CuO₂ planes, we show that the interaction has explicit d-wave symmetry and leads to an indirect coupling of d-wave symmetry between electrons. We show that the polaron formation by the non-linear mode can cause a pseudo-gap of d-wave symmetry before the onset of coherence in the superconducting pairing. We suggest a simple phenomenological explanation of the pseudo-gap crossover temperature and the Fermi arcs. The discussion may be relevant for the pseudo-gap in non-superconducting giant magnetoresistive manganites.     

Bose–Einstein Condensation in the Pseudogap Phase of Cuprate Superconductors

We have identified the unscreened Fröhlich electron–phonon interaction (EPI) as the most essential for pairing in cuprate superconductors as now confirmed by isotope substitution, recent angle-resolved photoemission (ARPES), and some other experiments. Low-energy physics is that of mobile lattice polarons and bipolarons in the strong EPI regime. Many experimental observations have been predicted or explained in the framework of our “Coulomb–Fröhlich” model, which fully takes into account the long-range Coulomb repulsion and the Fröhlich EPI. They include pseudo-gaps, unusual isotope effects and upper critical fields, the normal state Nernst effect, diamagnetism, the Hall–Lorenz numbers, and a giant proximity effect (GPE). These experiments along with the parameter-free estimates of the Fermi energy and the critical temperature support a genuine Bose–Einstein condensation of real-space lattice bipolarons in the pseudogap phase of cuprates. On the contrary, the phase fluctuation (or vortex) scenario is incompatible with the insulating-like in-plane resistivity and the magnetic-field dependence of orbital magnetization in the resistive state of underdoped cuprates.     

Magnetic Field Dependence of Penetration Depth in Kinetic Energy Driven Cuprate Superconductors

Within the kinetic energy driven superconductivity, the magnetic field dependent penetration depth in cuprate superconductors is studied in the linear response approach. The electromagnetic response kernel is evaluated by considering both couplings of the electron charge and electron magnetic momentum with a weak magnetic field and employed to calculate the penetration depth based on the specular reflection model, then the main features of the magnetic field dependent penetration depth are well reproduced.     

Mapping High-Temperature Superconductors—A Scientometric Approach

This study has been carried out to analyze the research field of high-temperature superconductivity and to demonstrate the potential of modern databases and search systems for generating meta-information. The alkaline earth (A2) rare earth (RE) cuprate high-temperature superconductors as a typical inorganic compound family and the corresponding literature were analyzed by scientometric methods. The time dependent overall number of articles and patents and of the publications related to specific compound subsets and subject categories are given. The data reveal a significant decrease of basic research activity in this research field. The A2 RE cuprate species covered by the CAS compound file were analyzed with respect to the occurrence of specific elements in order to visualize known and unknown substances and to identify characteristic patterns. The quaternary and quinternary cuprates were selected and the number of compound species as a function of specific combinations of A2 and RE elements is given. The Cu/O and RE/A2 ratios of the quaternary cuprate species as a function of A2 and RE atoms are shown. In addition, the research landscape of the MgB₂ related publications was established using STN AnaVist, an analysis tool recently developed by STN International.     

On the Role of Polarization of Oxygen Ions and Mechanism of Superconductivity in Cuprate Superconductors

A new approach to the valence electron state in cuprate superconductors leading to a new mechanism of high-temperature superconductivity is considered. The approach takes into account specific features of the outer electron shells of the compound-forming elements and polarization of anions by cations. The polarization of anions by copper cations results in sharing of a valence electron by every two neighboring ions, which gives rise to a highly correlated state of the valence electrons and formation of a localized spin-ordered electron lattice responsible for dielectric and magnetic properties of an undoped material. It is also shown that asymmetric polarization of an anion by cations with inert gas shells transforms an unshared anion electron pair into a superconducting one by exciting it into a hybrid state. The superconducting state of the material itself results from formation and delocalization of one-dimensional Wigner crystals of the excited pairs.     

Determination of pairing symmetry using phase-sensitive tunneling in tricrystal cuprates

An unambiguous determination of the pairing symmetry in cuprate superconductors is important in order to understand the origin of high-temperature superconductivity. By making use of the effects of pair tunneling and flux quantization, we have designed and implemented several tricrystal experiments for phase-sensitive determination of the order parameter symmetry in high-Tc superconductors such as YBa₂Cu₃O₇ Tl₂Ba₂CuO₆, GdBa₂Cu₃O₇, and Bi₂Sr₂CaCu₂O₈. By using a high-resolution scanning SQUID microscope, we have made the first direct observation of spontaneously generated half-flux quanta at the tricrystal point. The half-integer flux quantum effect in various specially designed tricrystal cuprate systems provides strong evidence for d-wave pairing in high-T_c cuprates. Our various tricrystal experiments have demonstrated that this effect can be used as a general probe of the microscopic phase of the pair wavefunction in unconventional superconductors.     

Superdiamagnetics and the high-temperature superconductivity problem

The superdiamagnetism observed in CuCl and CdS, with its special features, can be explained by the electron localization in grains of polycrystalline specimens. The similarity in behavior between superdiamagnetics and high-temperature superconductors with transition temperatures near room temperature prompts one to assume that the superconductivity in the latter is connected with electron localization in grains of ceramics.     

Design of New Superconducting Materials, and Point-Contact Spectroscopy as a Probe of Strong Electron Correlations

At this centenary of the discovery of superconductivity, the design of new and more useful superconductors remains as enigmatic as ever. These materials play crucial roles both for fundamental science and applications, and they hold great promise in addressing our global energy challenge. The recent discovery of a new class of high-temperature superconductors has made the community more enthusiastic than ever about finding new superconductors. Historically, these discoveries were almost completely guided by serendipity, and now, researchers in the field have grown into an enthusiastic global network to find a way, together, to predictively design new superconductors. After a short history of discoveries of superconducting materials, we share our own guidelines for searching for high-temperature superconductors. Finally, we show how point-contact spectroscopy (PCS) is used to detect strong correlations in the normal state, with a focus on the normal state region of the Fe-based superconductors, defining a new region in the phase diagram of Ba(Fe_1?x Co _x )₂As₂.