Theory Of high-Tc Superconductivity Research Articles

Searching for high-temperature superconductivity: from Mendeleev to Seiberg–Witten via Madelung and beyond

Abstract Recently, noticeable progress has been achieved in the area of high-temperature superconductors. Maximum temperatures Tc of 250 K (−23○ C) for LaH10 and 288 K (+15○ C) for CSH8 have been reported at megabar pressures. The highest possible Tcs were achieved by employing hydrides of chemical elements. Empirically, many of these are made of Madelung-exceptional atoms. Here, the theoretical background is provided to explain this observation. The, thus far empirical, Madelung rule controls Mendeleev’s law of periodicity. Although the majority of elements do obey this rule, there are some exceptions. Thus, it is of interest to derive it and its exceptions theoretically in view of experimental findings. As a by-product, such a study yields a plausible explanation of the role of Madelung-exceptional atoms in the design of high-Tc superconductors. Thus far the atoms obeying the Madelung rule and its exceptions have been studied with help of relativistic Hartree–Fock calculations. In this work we reobtain both the rule and the exceptions analytically. The newly developed methods are expected to be of value in quantum many-body theory and, in particular, in the theory of high-Tc superconductivity. Ultimately, the new methods involve some uses of the Seiberg–Witten theory known as the extended Ginzburg–Landau theory of superconductivity. Using results of Sieberg–Witten theory, the difference between Madelung-regular and Madelung-exceptional atoms is explained in terms of the topological transition. The extension of this single-atom result to solids of the respective elements is also discussed.

Nematic order driven by superconducting correlations

The interplay of nematicity and superconductivity has been observed in a wide variety of quantum materials. To explore this interplay, we consider a two-dimensional (2D) array of nematogens, local droplets with Z3 nematicity, coupled to a network of Josephson junction wires. Using finite temperature classical Monte Carlo simulations, we elucidate the phase diagram of this model and show that the development of superconducting correlations and the directional delocalization of Cooper pairs can promote nematogen ordering, resulting in long-range nematic order. We obtain the transport properties of our model within an effective resistor network picture. We discuss these ideas in the context of the 2D electron gas at the (111) KTaO3 interface and the doped topological insulators NbxBi2Se3 and CuxBi2Se3. Our work makes contact with Phil Anderson’s numerous contributions to broken symmetries driven by the saving of kinetic energy, including double exchange ferromagnetism and the interlayer tunneling theory of high Tc superconductivity.

Superconducting and Antiferromagnetic Phases of Space-Time

A correspondence between the SO5 theory of high-TC superconductivity and antiferromagnetism, put forward by Zhang and collaborators, and a theory of gravity arising from symmetry breaking of a SO5 gauge field is presented. A physical correspondence between the order parameters of the unified SC/AF theory and the generators of the gravitational gauge connection is conjectured. A preliminary identification of regions of geometry, in solutions of Einstein’s equations describing charged-rotating black holes embedded in de Sitter space-time, with SC and AF phases is carried out.

Ba1−xKxMn2As2: An Antiferromagnetic Local-Moment Metal

The compound BaMn2As2 with the tetragonal ThCr2Si2 structure is a local-moment antiferromagnetic insulator with a Néel temperature T(N)=625 K and a large ordered moment μ=3.9μ(B)/Mn. We demonstrate that this compound can be driven metallic by partial substitution of Ba by K while retaining the same crystal and antiferromagnetic structures together with nearly the same high T(N) and large μ. Ba(1-x)K(x)Mn2As2 is thus the first metallic ThCr2Si2-type MAs-based system containing local 3d transition metal M magnetic moments, with consequences for the ongoing debate about the local-moment versus itinerant pictures of the FeAs-based superconductors and parent compounds. The Ba(1-x)K(x)Mn2As2 class of compounds also forms a bridge between the layered iron pnictides and cuprates and may be useful to test theories of high T(c) superconductivity.

Theory of high-TC superconductivity: transition temperature

It is demonstrated that the transition temperature (TC) ofhigh-TC superconductors is determined by their layered crystal structure, bondlengths, valency properties of the ions, and Coulomb coupling betweenelectronic bands in adjacent, spatially separated layers. Analysis of 31 high-TC materials (cuprates, ruthenates, ruthenocuprates, iron pnictides, organics) yields theuniversal relationship for optimal compounds, kBTC0 = β/ℓζ, where ℓ is related to the mean spacing between interacting charges in the layers,ζ is the distance between interacting electronic layers,β is a universalconstant and TC0 is the optimal transition temperature (determined to within an uncertainty of ± 1.4 K by this relationship). Non-optimum compounds, in which sample degradation is evident, e.g. bybroadened superconducting transitions and diminished Meissner fractions, typically exhibit reducedTC < TC0. It is shownthat TC0 may be obtained from an average of the Coulomb interaction forces between the two layers.

Consistent theory of underdoped cuprates: Evolution of the resonating valence bond state from half filling

We have been able to resolve two long-standing issues that are central to the theory of high Tc superconductivity: (1) How is the physics of the doped region connected to that of the Mott insulator? (2) What is the origin of the two-dimensionality of the normal state? Specifically, based on the t-J model, we derive a renormalized Hamiltonian to describe the properties of underdoped cuprates. The theory is constrained to agree with the behavior at half filling, which is well described by the bosonic RVB state of Arovas and Auerbach. Moving holes are assumed to destroy long-range magnetic order, which leads to a gap in the spinon spectrum. The presence of the spin gap allows us to derive a constrained Hamiltonian which describes sublattice-preserving hopping by renormalized holons and holon pairs, accompanied by spinon singlet backflows. Below the singlet condensation, i.e, the psudogap (as distinct from the spin gap), temperature T*, holons form a spinless Fermi liquid without an observable small Fermi surface. Above T* holons are localized, giving rise to a (gauge) insulator, which we identify with the strange metal phase. Holon pair hopping leads to a robust d-wave superconductor, its symmetry determined primarily by the symmetry of the RVB state at half filling. The predictions of the theory are shown to be consistent with the results of nmr, tunneling and transport experiments. Remarkably, the existence of the spin gap provides a natural explanation for the two-dimensionality of the normal state. The marked asymmetry between hole-doped and electron-doped cuprates is also easily explained.

Superconductivity and Structure

The degree of the isolation of the CuO2 planes (e.g. distance or bond valence to the apical coordination) has been shown by quantitative algorithms to be the major factor in determining aspects of the doping curves. They include the magnitude of the optimal number of doped holes (hop) and the corresponding Tcop. It is shown that the roots of these phenomenological laws lie in a related structural dependence of super-exchange. The latter is expressed in the pseudo-gap or Neel temperature of the undoped parent compound. A fruitful language can be developed which deals with a buildup of complex quantum chemical features by bringing two holes into vicinity of a super-exchange O, forming a “local” Cu2O7 pair. Structural considerations also dictate that stress is relieved by alternate orthogonal pair orientation. This leads to plaid patterns with primary and secondary channels of charge. The presence of these two types of charge channels is involved in the mechanism of superconducting charge transport. Similar structuring of doped charge into plaid patterns of “local” pairs has been proposed for “all” high Tc superconductivity. STM now gives pictorial representation of the remnants of such an electronic crystal structure. The response of these bond-ordering motifs to structural details is further discussed. These ideas supply organization to the manifold experimental situation and provide opportunities for a unifying theory for high Tc superconductivity in terms of real space structuring of “local” pairs, largely on crystal-chemical principles.

ON THE ORIGIN OF d-WAVE PAIR FUNCTIONS IN HIGH-Tc SUPERCONDUCTIVITY

We argue that the usual Hubbard's model produces only s-wave pairing functions and, even then, only at unphysically large values of the lumped parameter J≡4t2/U. It follows that a reliable theory of high-Tc superconductivity has to include additional features if it is to reproduce the d-wave gap. We test the effects of an alternating potential caused by a charge stripe, on the ground state of the Hubbard model in strong-coupling. If we "fine tune" we do find the d-waves. However, a better-formulated version of a three-band model yields a sturdier theory of pair formation in high-Tc superconductivity. The coupling constant g1=t2/V factors out, hence it serves only to establish the unit of energy; the underlying Hamiltonian is universal. We outline the principal properties of this model, including the intimate relation between charge-density stripes and the d-wave pair function, its rejection of 45° stripes (checkerboard pattern), and other concerns.

Spinless Excitons Implicit in SO(5) Theory**The project supported by National Natural Science Foundation of China and Shanghai Research Center of Applied Physics

A pair of up-down operators are constructed explicitly for S.C. Zhang's SO(5) theory of high Tc superconductivity. From them two good quantum numbers are derived. The up-down operators are related to the spin-independent excitons which are not considered before.

Magnetic correlation functions in SO(5) theory of high-Tc superconductivity

In this paper we present analytical calculations of a variety of magnetic correlation functions within Zhang's SO(5) quantum rotor theory of high-${T}_{c}$ superconductivity. Using the spherical approach for three-dimensional quantum rotors we derived explicit analytical formulas for variety of dynamic spin susceptibilities related to the lattice version of the SO(5) nonlinear quantum-sigma model. We show in detail the frequency dependence of these quantities for various settings of relevant control parameters (like temperature, quantum fluctuations) in normal and superconducting state. We found the results in overall qualitative agreement with basic phenomenology of high-${T}_{c}$ cuprates.

Non-Abelian Holonomy of BCS and SDW Quasiparticles

In this work we investigate properties of fermions in theSO(5) theory of highTcsuperconductivity. We show that the adiabatic time evolution of aSO(5) superspin vector leads to a non-AbelianSU(2) holonomy of theSO(5) spinor states. Physically, this non-trivial holonomy arises from the non-zero overlap between the SDW and BCS quasiparticle states. While the usual Berry's phase of aSO(3) spinor is described by a Dirac magnetic monopole at the degeneracy point, the non-Abelian holonomy of aSO(5) spinor is described by a Yang monopole at the degeneracy point and is deeply related to the existence of the second Hopf map fromS7toS4. We conclude this work by extending the bosonicSO(5) nonlinearσmodel to include the fermionic states around the gap nodes as 4 component Dirac fermions coupled toSU(2) gauge fields in 2+1 dimensions.

Recent developments in the SO(5) theory of high Tc superconductivity

This paper outlines the general strategy behind the SO(5) theory of high T c superconductivity. Progress is reviewed in the direction of exact SO(5) models, numerical exact diagonalization and possible experimental tests. Criticisms raised recently against the SO(5) theory are also addressed and directions for future exploration are indicated.

The Theory of Superconductivity in the High‐Tc Cuprates

This book is P. W. Anderson's long-awaited full presentation of his theory of high-Tc superconductivity in the cuprates. He realized that this striking new phenomenon needed for its explanation not just a new mechanism or gimmick but a radical reworking of the electronic theory of metals, especially those of low dimension. The many fundamentally new ideas that are first fully presented here will require a rewriting of the textbooks of many-body theory, which may take decades. The book incorporates full discussions of the experimental situation in these complex materials, both the normal and the superconducting states. The latest advances are contained in a selection of re-and pre-prints of recent work by Anderson and collaborators. The fundamental insight contained in the book is that the conditions for validity of the renormalized quasiparticle theory of metals (Fermi Liquid Theory) are much more restrictive than had been thought, and are not satisfied in the CuO2 planes of high-Tc materials (among, probably, many other examples). This requires a new state of matter to be invented, new transport theories, and new mechanisms for superconductivity. This book will supersede all theoretical discussions of superconductivity that are now available in book form. Originally published in 1997. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

The SO(5) theory of high Tc superconductivity

This paper gives a simple introduction to the SO(5) theory of high T c superconductivity. Current status and relation to experiments are summarized.

Two new developments in the theory of high Tc superconductivity

Abstract Two new developments in the theory of high Tc superconductivity which explain experimental anomalies are described: First, an explanation of some striking anomalies in the angle resolved photoemission excitation spectrum provides experimental evidence for the composite nature of electronic excitations; and secondly, a gap equation for the superconducting state, which allows detailed calculations using phonon plus interlayer coupling, allows calculation of the large anisotropy of the gap, of the isotope effect, and of estimates of Tc and its dependence upon structure.

Electron Spectrum and Dieleclric Susceptibility of the Hubbard Model with Local Lattice Anharmonicity

1. The model with local anharmonicity (Műller model) [1] involving Hub. bard-type electron correlations as well as interaction between electrons and vibrational modes which can be represented in terms of pseudospin variables, is one of the used in the theory of high-Tc superconductivity. Vibrations of apex oxygen Ow possess anharmonicity in the case of YBaCuO-type systems. Their possible importance for charge transfer to or from the CuO layers, superconducting pairing of electrons and connection with observed high values of dielectric permittivity ezz was mentioned in several papers [2, 3]. 2. Hamiltonian of the model [1] has the following form:

Two new developments in the theory of high T c superconductivity

Abstract Two new developments in the theory of high Tc superconductivity which explain experimental anomalies are described: First, an explanation of some striking anomalies in the angle resolved photoemission excitation spectrum provides experimental evidence for the composite nature of electronic excitations; and secondly, a gap equation for the superconducting state, which allows detailed calculations using phonon plus interlayer coupling, allows calculation of the large anisotropy of the gap, of the isotope effect, and of estimates of Tc and its dependence upon structure.

Acoustic plasmon exchange in multilayered systems: II. application to high-Tc superconductors

For pt.I see ibid., vol.4, p.1799, 1992. A theory for high-Tc superconductivity has been developed using the Eliashberg model on the basis that the attractive interaction is provided by the Plasmon-mediated effective interaction between the charge carriers. Calculation of Tc using these interactions, presented in paper I, shows that Tc should rise, with a saturation effect, with the number of CuO layers per unit cell, which is in agreement with observations in the Tl- and Bi-based compounds. Furthermore, this theory shows that a short coherence length is an essential requirement for superconductivity at high temperature.

A phenomenological theory of high Tc superconductivity

The essential features of a new phenomenological theory (the s-channel theory of superconductivity) are presented. The relations between small coherence length, Bose-Einstein condensation and high Tc are emphasized. Applications to the μsR and other experiments are discussed.

A theory of high- Tc superconductivity

For high- T c superconductors such as YBa 2Cu 3O 6.5 + 6 z , the Cu 3d x 2− y 2 and O 2p energy levels may be close together ( ϵ d− ϵ p ∼ 0). For z0, holes are created in the upper oxygen band. The oxygen Hubbard parameter U′ is important for this upper Hubbard band. For sufficiently large z-dependence of U′, there may be attraction due to the electron density fluctuations on the oxygen sites; hence high- T c superconductivity may develop. A BCS-like Hamiltonian may be used for this attraction. The BCS theory may then be adapted to calculate T c . The theoretical results are consistent with the experimental data. It appears that the crucial criteria are: (a) ϵ d− ϵ p ∼ 0 and (b) sufficiently large z-dependence of U′.