Lowering Of Kinetic Energy Research Articles

The role of references and the elusive nature of the chemical bond

Chemical bonding theory is of utmost importance to chemistry, and a standard paradigm in which quantum mechanical interference drives the kinetic energy lowering of two approaching fragments has emerged. Here we report that both internal and external reference biases remain in this model, leaving plenty of unexplored territory. We show how the former biases affect the notion of wavefunction interference, which is purportedly recognized as the most basic bonding mechanism. The latter influence how bonding models are chosen. We demonstrate that the use of real space analyses are as reference-less as possible, advocating for their use. Delocalisation emerges as the reference-less equivalent to interference and the ultimate root of bonding. Atoms (or fragments) in molecules should be understood as a statistical mixture of components differing in electron number, spin, etc.

A Universal Binding Mechanism in Molecular Covalent Bonding and Nucleon-Nucleon Interaction

In the hydrogen molecular ion, the kinetic energy lowering of the electron is associated with its delocalization due to electron exchange between the two protons of the molecule. This decrease in the kinetic energy of the exchanged electron in the hydrogen molecular ion and the decrease in the dynamical mass of the two exchanged pions in the nucleon-nucleon interaction are at the origin of the attraction mechanism in the molecular covalent bonding and in the nuclear interaction. Based on this unitary approach of the attraction mechanism, the formulas of molecular potential and central nucleon-nucleon potential were derived. The decrease in the mass of the exchanged pions in the nucleon-nucleon bound state, actually means the decrease in the mass of the nucleons. This nucleon mass decrease could be a manifestation of the partial chiral symmetry restoration in nuclear matter.

Spinning Superconductors and Ferromagnets

When a magnetic field is applied to a ferromagnetic body it starts to spin (Einstein-de Haas effect). This demonstrates the intimate connection between the electron's magnetic moment $\mu_B=e\hbar/2m_ec$, associated with its spin angular momentum $S=\hbar/2$, and ferromagnetism. When a magnetic field is applied to a superconducting body it also starts to spin (gyromagnetic effect), and when a normal metal in a magnetic field becomes superconducting and expels the magnetic field (Meissner effect) the body also starts to spin. Yet according to the conventional theory of superconductivity the electron's spin only role is to label states, and the electron's magnetic moment plays no role in superconductivity. Instead, within the unconventional theory of hole superconductivity, the electron's spin and associated magnetic moment play a fundamental role in superconductivity. Just like in ferromagnets the magnetization of superconductors is predicted to result from an aggregation of magnetic moments with angular momenta $\hbar/2$. This gives rise to a "Spin Meissner effect", the existence of a spin current in the ground state of superconductors. The theory explains how a superconducting body starts spinning when it expels magnetic fields, it provides a dynamical explanation for the Meissner effect, and it explains how supercurrents stop without dissipation, all of which we argue the conventional theory fails to explain. Essential elements of the theory of hole superconductivity are that superconductivity is driven by lowering of kinetic energy, which we have also proposed is true for ferromagnets], that the normal state charge carriers in superconducting materials are holes, and that the spin-orbit interaction plays a key role in superconductivity. The theory is proposed to apply to all superconductors.

Dynamic Hubbard model: kinetic energy driven charge expulsion, charge inhomogeneity, hole superconductivity and Meissner effect

Conventional Hubbard models do not take into account the fact that the wavefunction of an electron in an atomic orbital expands when a second electron occupies the orbital. Dynamic Hubbard models have been proposed to describe this physics. These models reflect the fact that electronic materials are generically not electron–hole symmetric, and they give rise to superconductivity driven by lowering of kinetic energy when the electronic energy band is almost full, with higher transition temperatures resulting when the ions are negatively charged. We show that the charge distribution in dynamic Hubbard models can be highly inhomogeneous in the presence of disorder, and that a finite system will expel negative charge from the interior to the surface, and that these tendencies are largest in the parameter regime where the models give rise to highest superconducting transition temperatures. High Tc cuprate materials exhibit charge inhomogeneity and they exhibit tunneling asymmetry, a larger tendency to emit electrons rather than holes in normal–insulating–superconducting tunnel junctions. We propose that these properties, as well as their high Tc, are evidence that they are governed by the physics described by dynamic Hubbard models. Below the superconducting transition temperature the models considered here describe a negatively charged superfluid and positively charged quasiparticles, unlike the situation in conventional Bardeen–Cooper–Schrieffer superconductors where quasiparticles are charge neutral on average. We examine the temperature dependence of the superfluid and quasiparticle charges and conclude that spontaneous electric fields should be observable in the interior and in the vicinity of superconducting materials described by these models at sufficiently low temperatures. We furthermore suggest that the dynamics of the negatively charged superfluid and positively charged quasiparticles in dynamic Hubbard models can provide an explanation for the Meissner effect observed in high Tc and low Tc superconducting materials.

Charge expulsion, charge inhomogeneity, and phase separation in dynamic Hubbard models

Dynamic Hubbard models are extensions of the conventional Hubbard model that take into account the fact that atomic orbitals expand upon double occupancy. It is shown here that systems described by dynamic Hubbard models have a tendency to expel negative charge from their interior to the surface, and to develop charge inhomogeneity and even phase separation in the bulk. These effects are associated with lowering of electronic kinetic energy. We propose that these models may explain the charge inhomogeneity and negatively charged grain boundaries observed in cuprate oxides and other materials.

Correcting 100 Years of Misunderstanding: Electric Fields in Superconductors, Hole Superconductivity, and the Meissner Effect

From the outset of superconductivity research it was assumed that no electrostatic fields could exist inside superconductors, and this assumption was incorporated into conventional London electrodynamics. Yet the London brothers themselves initially (in 1935) had proposed an electrodynamic theory of superconductors that allowed for static electric fields in their interior, which they unfortunately discarded a year later. I argue that the Meissner effect in superconductors necessitates the existence of an electrostatic field in their interior, originating in the expulsion of negative charge from the interior to the surface when a metal becomes superconducting. The theory of hole superconductivity predicts this physics, and associated with it a macroscopic spin current in the ground state of superconductors ("Spin Meissner effect"), qualitatively different from what is predicted by conventional BCS-London theory. A new London-like electrodynamic description of superconductors is proposed to describe this physics. Within this theory superconductivity is driven by lowering of quantum kinetic energy, the fact that the Coulomb repulsion strongly depends on the character of the charge carriers, namely whether electron- or hole-like, and the spin-orbit interaction. The electron-phonon interaction does not play a significant role, yet the existence of an isotope effect in many superconductors is easily understood. In the strong coupling regime the theory appears to favor local charge inhomogeneity. The theory is proposed to apply to all superconducting materials, from the elements to the high $T_c$ cuprates and pnictides, is highly falsifiable, and explains a wide variety of experimental observations.

Hole pairing from attraction of opposite-chirality spin vortices: Non-BCS superconductivity in underdoped cuprates

Within a gauge approach to the t-J model, we propose a new, non-BCS mechanism of superconductivity for underdoped cuprates. We implement the no-double occupancy constraint with a (semionic) slave-particle formalism. The dopant generates a vortex-like quantum distortion of the AF background centered on the empty sites, with opposite chirality for cores on the two N\'eel sublattices. Empty sites are described in terms of spinless fermionic holons and the long-range attraction between spin vortices on two opposite N\'eel sublattices is the holon pairing force, leading eventually to SC. The spin fluctuations are described by bosonic spinons with a gap generated by scattering on spin vortices. Due to the occupation constraint, there is a gauge attraction between holon and spinon, binding them into a physical hole. Through gauge interaction the spin vortex attraction induces the formation of spin-singlet RVB pairs reducing the spinon gap. Lowering T, there are two crossovers as precursors of the SC transition: at the higher one a gas of holon pairs appears, reducing the hole spectral weight, while at the lower one a gas of spinon pairs also appears, giving rise to a gas of incoherent preformed hole pairs with magnetic vortices in the plasma phase, supporting a Nernst signal. At an even lower T the hole pairs become coherent and SC appears beyond a critical doping. The proposed SC mechanism is not of the BCS-type, because it involves a gain in kinetic energy (lowering of spinon gap) and it is "almost" of the classical 3D XY-type. Since both the spinon gap and the holon pairing originate from the same term in the slave-particle representation of the t-J model, this approach incorporates a strong interplay between AF and SC, giving rise to a universal relation between Tc and the energy of the resonance mode, as observed in neutron scattering experiments.

KINETIC ENERGY DRIVEN SUPERCONDUCTIVITY AND SUPERFLUIDITY

The theory of hole superconductivity proposes that superconductivity is driven by lowering of quantum kinetic energy and is associated with expansion of electronic orbits and expulsion of negative charge from the interior to the surface of superconductors and beyond. This physics provides a dynamical explanation of the Meissner effect. Here we propose that similar physics takes place in superfluid helium 4. Experimental manifestations of this physics in 4 He are the negative thermal expansion of 4 He below the λ point and the "Onnes effect", the fact that superfluid helium will creep up the walls of the container and escape to the exterior. The Onnes effect and the Meissner effect are proposed to originate in macroscopic zero point rotational motion of the superfluids. It is proposed that this physics indicates a fundamental inadequacy of conventional quantum mechanics.

KINETIC ENERGY DRIVEN SUPERCONDUCTIVITY, THE ORIGIN OF THE MEISSNER EFFECT, AND THE REDUCTIONIST FRONTIER

Is superconductivity associated with a lowering or an increase of the kinetic energy of the charge carriers? Conventional BCS theory predicts that the kinetic energy of carriers increases in the transition from the normal to the superconducting state. However, substantial experimental evidence obtained in recent years indicates that in at least some superconductors the opposite occurs. Motivated in part by these experiments many novel mechanisms of superconductivity have recently been proposed where the transition to superconductivity is associated with a lowering of the kinetic energy of the carriers. However none of these proposed unconventional mechanisms explores the fundamental reason for kinetic energy lowering nor its wider implications. Here I propose that kinetic energy lowering is at the root of the Meissner effect, the most fundamental property of superconductors. The physics can be understood at the level of a single electron atom: kinetic energy lowering and enhanced diamagnetic susceptibility are intimately connected. We propose that this connection extends to superconductors because they are, in a very real sense, "giant atoms". According to the theory of hole superconductivity, superconductors expel negative charge from their interior driven by kinetic energy lowering and in the process expel any magnetic field lines present in their interior. Associated with this we predict the existence of a macroscopic electric field in the interior of superconductors and the existence of macroscopic quantum zero-point motion in the form of a spin current in the ground state of superconductors (spin Meissner effect). In turn, the understanding of the role of kinetic energy lowering in superconductivity suggests a new way to understand the fundamental origin of kinetic energy lowering in quantum mechanics quite generally. This provides a new understanding of "quantum pressure", the stability of matter and the origin of fermion anticommutation relations, it leads to the prediction that spin currents exist in the ground state of aromatic ring molecules, and that the electron wavefunction is double-valued, requiring a reformulation of conventional quantum mechanics.

Electromotive Forces and the Meissner Effect Puzzle

In a voltaic cell, positive (negative) ions flow from the low (high) potential electrode to the high (low) potential electrode, driven by an `electromotive force' which points in opposite direction and overcomes the electric force. Similarly in a superconductor charge flows in direction opposite to that dictated by the Faraday electric field as the magnetic field is expelled in the Meissner effect. The puzzle is the same in both cases: what drives electric charges against electromagnetic forces? I propose that the answer is also the same in both cases: kinetic energy lowering, or `quantum pressure'.

Optical integral in the cuprates and the question of sum-rule violation

Much attention has been given to a possible violation of the optical sum rule in the cuprates and the connection this might have to kinetic energy lowering. The optical integral is composed of a cutoff-independent term (whose temperature dependence is a measure of the sum-rule violation), plus a cutoff-dependent term that accounts for the extension of the Drude peak beyond the upper bound of the integral. We find that the temperature dependence of the optical integral in the normal state of the cuprates can be accounted for solely by the latter term, implying that the dominant contribution to the observed sum-rule violation in the normal state is due to the finite cutoff. This cutoff-dependent term is well modeled by a theory of electrons interacting with a broad spectrum of bosons.

Novel Orientational Ordering and Reentrant Metallicity inKxC60Monolayers for3≤x≤5

STM studies on K(x)C(60) monolayers reveal new behavior over a wide range of the phase diagram. As x increases from 3 to 5 K(x)C(60) monolayers undergo metal-insulator-metal reentrant phase transitions and exhibit a variety of novel orientational orderings, including a complex 7-molecule, pinwheel-like structure. The proposed driving mechanism for the orientational ordering is the lowering of electron kinetic energy by maximizing the overlap of neighboring molecular orbitals. In insulating (metallic) K(x)C(60) this gives rise to orbital versions of the superexchange (double-exchange) interaction.

NUMERICAL STUDY OF HOLE CORRELATION IN THE t-J MODEL WITH FOUR HOLES ON A 32-SITE LATTICE

We solve the t-J model with four holes on a 32-site lattice using exact diagonalization. This is the largest scale calculation ever reported for this model. The size of the matrix involved in this problem is about 3×109 by 3×109. We find that at the realistic parameter J/t = 0.3, holes in the ground state of this system are unbound. They have short range repulsion due to lowering of kinetic energy. The electron momentum distribution function resembles hole pockets. We show that in case antiferromagnetic order is strong, holes form d-wave bound pairs and there is mutual repulsion among the holes. This presumably will occur at low doping level.

Hole correlation and antiferromagnetic order in thet−Jmodel

We study the t-J model with four holes on a 32-site square lattice using exact diagonalization. This system corresponds to doping level x=1/8. At the ``realistic'' parameter J/t=0.3, holes in the ground state of this system are unbound. They have short range repulsion due to lowering of kinetic energy. There is no antiferromagnetic spin order and the electron momentum distribution function resembles hole pockets. Furthermore, we show evidence that in case antiferromagnetic order exists, holes form d-wave bound pairs and there is mutual repulsion among hole pairs. This presumably will occur at low doping level. This scenario is compatible with a checkerboard-type charge density state proposed to explain the ``1/8 anomaly'' in the LSCO family, except that it is the ground state only when the system possesses strong antiferromagnetic order.

The fundamental role of charge asymmetry in superconductivity

Neither BCS theory nor London theory contain any charge asymmetry. However it is an experimental fact that a rotating superconductor always exhibits a magnetic field parallel, never antiparallel, to its angular velocity. This and several other experimental observations point to a special role of charge asymmetry in superconductivity, which is the foundation of the theory of hole superconductivity. The theory describes heavy dressed {\it positive} hole carriers in the normal state that undress by pairing and become light undressed {\it negative} electron carriers in the superconducting state. Superconductivity is driven by kinetic energy lowering rather than by electron-phonon coupling as in BCS. In quantum mechanics, kinetic energy lowering is associated with $expansion$ of the electronic wave function, and hence we predict: (1) Superconductors expel $negative$ charge from their interior which consequently becomes $positively$ charged; (2) Macroscopic electrostatic fields exist in the interior of superconductors always, and in certain cases also outside near the surface; (3) Macroscopic spin currents exist in the superconducting state; (4) Superconductors are 'rigid' with respect to their response to applied longitudinal electric fields. These predictions apply to all superconductors and are testable but are as yet untested. The theory predicts highest $T_c$'s for materials for which normal state transport occurs through $(positive)$ holes in $negatively$ charged anions.

Unconventional Superconductivity, Spontaneous Time-Reversal Symmetry Breaking and Lowering of Kinetic Energy in Doped, Short-Range Antiferromagnets

Unconventional Superconductivity, Spontaneous Time-Reversal Symmetry Breaking and Lowering of Kinetic Energy in Doped, Short-Range Antiferromagnets

Pairing-induced kinetic energy lowering in doped antiferromagnets

We analyse lowering of the kinetic energy in doped antiferromagnets at the transition to thesuperconducting state. Measurements of optical conductivity indicate that suchunconventional behaviour takes place in underdoped Bi-2212. We argue thatthe definition of the operator representing the kinetic energy is determined byexperimental conditions. The thermodynamic average of that operator is related to theintegrated spectral weight of the optical conductivity and thus depends on the cut-offfrequency limiting that integral. If the upper limit of the integral lies below thecharge transfer gap the spectral weight represents the average of the hoppingterm in the space restricted to the energy range below the gap. We show thatthe kinetic energy is indeed lowered at the superconducting transition in thet–J model(tJM),which is an effective model defined in the restricted space. That result is in agreement withexperimental observations and may be attributed to the formation of spin polarons and thechange of roles which are played by the kinetic and the potential energy in thetJM and in some effective model for spin polarons. The total spectral weight represents thekinetic energy in a model defined in a broader space if the upper limit in the integral of theoptical conductivity is set above the gap. We demonstrate that the kinetic energy in theHubbard model is also lowered in the superconducting state. That result doesnot agree with experimental observations, indicating that the spectral weight isconserved for all temperatures if the upper limit of the integral is set above thecharge transfer gap. This discrepancy suggests that a single band model is notcapable of describing in some respects the physics of excitations across the gap.

Equation of state and correlation energy of dense plasmas

In this paper, the method of thermodynamic Green's functions is applied to investigate thermodynamic properties of dense weakly coupled plasmas. First, we present results for the equation of state for fully ionized hydrogen and compare our results with path integral Monte Carlo simulation data. Densities and temperatures are considered where correlations as well as Fermi statistics have to be taken into account. Then, the correlation energy and the mean value of the kinetic energy of dense plasmas are considered. Usually one finds that the kinetic energy is larger than that of an ideal system due to the interaction. However, in agreement with results from quantum simulations, we found, for certain densities and temperatures, a lowering of the kinetic energy.

Optical sum rule violation, superfluid weight, and condensation energy in the cuprates

The model of hole superconductivity predicts that the superfluid weight in the zero-frequency $\ensuremath{\delta}$ function in the optical conductivity has an anomalous contribution from high frequencies, due to lowering of the system's kinetic energy upon entering the superconducting state. The lowering of kinetic energy, mainly in-plane in origin, accounts for both the condensation energy of the superconductor as well as an increased potential energy due to larger Coulomb repulsion in the paired state. It leads to an apparent violation of the conductivity sum rule, which in the clean limit we predict to be substantially larger for in-plane than for c-axis conductivity. However, because cuprates are in the dirty limit for c-axis transport, the sum rule violation is found to be greatly enhanced in the c direction. The model predicts the sum rule violation to be largest in the underdoped regime and to decrease with doping, more rapidly in the c direction than in the plane. So far, experiments have detected sum rule violation in c-axis transport in several cuprates, as well as a decrease and disappearance of this violation for increasing doping, but no violation in plane. We explore the predictions of the model for a wide range of parameters, both in the absence and in the presence of disorder, and the relation with current experimental knowledge.

Superconductivity and ferromagnetism from effective mass reduction

Within a simple model Hamiltonian, both superconductivity and metallic ferromagnetism can be understood as arising from lowering of kinetic energy as the ordered state develops, due to a reduction in the carriers effective mass, or equivalently, a bandwidth expansion. Experimental manifestation of this physics has been detected in both high Tc superconductors and large magnetoresistance ferromagnets, as an anomalous transfer of spectral weight in optical absorption from high to low frequencies as the ordered state develops. It is proposed that this general principle is common to the essential physics of superconductivity and ferromagnetism in nature, and hence that these effects in optical properties, although often smaller in magnitude, should exist in all superconductors and metallic ferromagnets.