Condensation Of Electron Pairs Research Articles

Impact of surface defects on a condensate of electron pairs in a quantum wire

We study the impact of surface defects on a condensate of electron pairs in a quantum wire. Based on previous results, we formulate a simple mathematical model accounting for such surface effects. For a system of noninteracting pairs, we prove the destruction of the condensate in the bulk. Finally, taking repulsive interactions between the pairs into account, we show that the condensate is recovered for pair densities greater than a critical density if the number of the surface defects is not too large.

Impact of surface defects on a condensate of electron pairs in a quantum wire

Исследуется влияние поверхностных дефектов на конденсат электронных пар в квантовом проводе. Для учета таких поверхностных эффектов на основе полученных ранее результатов сформулирована простая математическая модель. Для системы невзаимодействующих пар доказано, что объемный конденсат разрушается. Показано, что, когда число поверхностных дефектов не слишком велико, при учете отталкивания между парами конденсат восстанавливается при плотностях пар, больших критической.

Chiral superconductivity in heavy-fermion metal UTe2.

Spin-triplet superconductors are condensates of electron pairs with spin 1 and an odd-parity wavefunction1. An interesting manifestation of triplet pairing is the chiral p-wave state, which is topologically non-trivial and provides a natural platform for realizing Majorana edge modes2,3. However, triplet pairing is rare in solid-state systems and has not been unambiguously identified in any bulk compound so far. Given that pairing is usually mediated by ferromagnetic spin fluctuations, uranium-based heavy-fermion systems containing f-electron elements, which can harbour both strong correlations and magnetism, are considered ideal candidates for realizing spin-triplet superconductivity4. Here we present scanning tunnelling microscopy studies of the recently discovered heavy-fermion superconductor UTe2, which has a superconducting transition temperature of 1.6 kelvin5. We find signatures of coexisting Kondo effect and superconductivity that show competing spatial modulations within one unit cell. Scanning tunnelling spectroscopy at step edges reveals signatures of chiral in-gap states, which have been predicted to exist at the boundaries of topological superconductors. Combined with existing data that indicate triplet pairing in UTe2, the presence of chiral states suggests that UTe2 is a strong candidate for chiral-triplet topological superconductivity.

One-dimensional extended Hubbard model with spin-triplet pairing ground states

We show that the one-dimensional extended Hubbard model has saturated ferromagnetic ground states with the spin-triplet electron pair condensation in a certain range of parameters. The ground state wave functions with fixed electron numbers are explicitly obtained. We also construct two ground states in which both the spin-rotation and the gauge symmetries are broken, and show that these states are transferred from one to the other by applying the edge operators. The edge operators are reduced to the Majorana fermions in a special case. These symmetry breaking ground states are shown to be stabilized by a superconducting mean field Hamiltonian which is related to the Kitaev chain with the charge–charge interaction.

Mössbauer studies of two-electron centers with negative correlation energy in crystalline and amorphous semiconductors

The results of the study of donor U −-centers of tin and germanium in lead chalcogenides by Mossbauer emission spectroscopy are discussed. The published data regarding the identification of amphoteric U −-centers of tin in glassy binary arsenic and germanium chalcogenides using Mossbauer emission spectroscopy, and in multicomponent chalcogenide glasses using Mossbauer absorption spectroscopy are considered. Published data concerning the identification of two-atom U −-centers of copper in lattices of semimetal copper oxides by Mossbauer emission spectroscopy are analyzed. The published data on the detection of spatial inhomogeneity of the Bose-Einstein condensate in superconducting semiconductors and semimetal compounds, and on the existence of the correlation between the electron density in lattice sites and the superconducting transition temperature are presented. The principal possibility of using Mossbauer U −-centers as a tool for studying the Bose-Einstein condensation of electron pairs during the superconducting phase transition in semiconductors and semimetals is considered.

Condensation of fermion composite particles

The possibility of condensation of electron pairs has been established by Yang and Coleman. Recent observations of Bose-Einstein condensate (BEC) of alkali atoms, containing odd number of electrons, require some explanation, which also must be based on a correct permutational symmetry of a system, containing different types of fermions. In the framework of the same reduced density matrix formalism, it is proved that aggregates (atoms), containing even number 2f of fermions, can be condensed only in a mixed quantum state in contrast to elementary bosons because a natural occupation number λ is proved to be strictly smaller than their total sum. If fermions are absent in aggregates the reduction of sum of λ to one term becomes possible. The upper bound λ$_{max}$ for a macroscopic ensemble of n aggregates, built of m different sorts of fermions is shown to be $m^1[((2f-1)!!)^3 A/(2f)!!B]^{1/2}$ where A is the number of all possible aggregates in a system, B is the number of ways to form a given composition of an aggregate from 2f-fermions of m sorts; n is a macroscopic greatest common devisor of fermion numbers of all sorts. The bound λ$_{max}$ increases as $n^{f}$, while sum of λ grows as $n^{2f}$. The evenness of the total number of fermions 2f in an aggregate is a necessary and sufficient condition for BEC formation. In particular, the number N of neutrons in neutral atom must be even because of the integrity of f=Z+N/2. The extreme type wave function is built, for which λ is arbitrary close to n$^{f}$ that proves the sufficiency of this criterion. The occupation maximum is achieved when pairs of fermions (identical or different) are condensed independently. The possibility of condensation of bound aggregates only (atoms) is shown arising from nonoverlapping of wave functions of electron relative coordinates of different atoms. This conclusion is based on separation of the centers' of mass motion, which are proved behaving like a bosonic gas. The remaining product of identical atomic wave functions of relative coordinates, which determine main properties of condensate ingredients, is shown not requiring further antisymmetrization that makes condensation possible.

50 Years of Fluxoid Quantization: 2e or Not 2e

The year 2011 is quite remarkable because it allows us to celebrate not only the centennial of the discovery of superconductivity by Heike Kamerlingh-Onnes (The superconductivity of Mercury, Comm. Phys. Lab. Univ. Leiden, vols. 122, 124, 1911), but also the half-centennial of the discovery of what is referred to as fluxoid quantization in superconductors by Robert Doll and Martin Nabauer (Phys. Rev. Lett. 7:51, 1961; Z. Phys. 169:526, 1962), and, independently, by Bascom S. Deaver Jr. and William Fairbank (Phys. Rev. Lett. 7:43, 1961; Ph.D. Thesis, Stanford University, 1962). The experimental proof of the quantization of magnetic flux (or more accurately fluxoid) in hollow superconducting cylinders actually supports two important theoretical concepts. The form of the fluxoid quantum, on the one hand, which contains twice the elementary charge, allows for the conclusion, that the superconducting ground state can be viewed as a condensate of electron pairs, as predicted by the BCS theory of superconductivity (Bardeen et al. in Phys. Rev. 106:162, 1957; Phys. Rev. 108:1175, 1957). It can be viewed, on the other hand, as a quantum phenomenon seen on macroscopic scales and thus supports the concept of the bosonic macroscopic wave function, here applied to the description of (quasi-bosonic) fermion pair condensates. This review is devoted to a discussion of the physics behind the Doll-Nabauer, Deaver-Fairbank discoveries and is intended to review historically the chain of events which motivated these talented experimentalists and which led to their independent discoveries at quite remote points of the earth.

BCS-to-BEC evolution details

Sá de Melo replies: I thank D. M. Eagles for his comments. My statement concerning the evolution from Bardeen-Cooper-Schrieffer to Bose–Einstein condensation superfluids was about clarity and not who was the first to propose the idea. Although I appreciate Eagles’s work, I still think that Anthony Leggett’s papers 1 are the clearest presentation on the topic up to 1980.In his very interesting book written in 1964, John Blatt describes the BEC theory of superconductivity and its relation to the BCS theory. 2 As he recounts, the possibility of pairing without superconductivity and Bose condensation of electron pairs at a lower temperature was suggested as early as 1946 by Richard Ogg Jr. In 1954 and subsequent years, Max Schafroth developed a firm theoretical framework for such pairing, but it was not supported by experimental evidence: No preformed pairs were found, and the BEC temperature was much too high for known superconductors. Blatt’s book thoroughly documents a clear connection between a variational, fixed-number ground state comprising antisymmetrized products of pair wavefunctions and the BCS equations that Eagles used in his 1969 paper. Eagles noticed that the BCS and number equations at zero temperature could be used to describe the evolution from BCS to BEC superconductivity in low-carrier-density thin films or bulk materials for fixed (and sufficiently strong) interaction and changing carrier density. However, Blatt’s main interest was in metals with high carrier densities. If one reads the full statement in the box entitled “Feshbach resonances” on page 47 of my article, it is clear that I am talking about changing interactions for fixed density and not changing density for fixed interactions. I do not think it is currently possible in any superconductor to control the interactions between fermions. Thus my statement is accurate.In many instances the change in carrier concentration in thin films or three-dimensional (bulk) systems is made via chemical doping, which may introduce disorder or distortions in the crystal structure and thus change the system in more than the desired way. I have serious doubts that ceramic samples of zirconium-doped strontium titanate described in Eagles’s letter indeed show the BCS-to-BEC evolution; the references provided do not offer clear evidence of such a phenomenon.Since cuprate superconductors are known to be quasi-2D and have d-wave pairing symmetry, the evolution from BCS to BEC superconductivity for sufficiently strong fixed interactions and changing carrier density would be accompanied by a topological quantum phase transition 3 and would not be a crossover as in the s-wave case. However, as much as I might want such a transition to be found for the cuprates, current experimental evidence shows that their normal state and superconducting properties are more complicated than simple BCS-to-BEC theories would predict.The beauty of the observation of the BCS-to-BEC evolution in ultracold atoms is that many of the materials difficulties encountered in standard condensed matter can be avoided and the tuning of the interaction for fixed low density can be controlled. However, one should keep an open mind that a similar realization may appear elsewhere. For instance, if carrier density could be controlled and changed continuously via electrostatic doping in good-quality thin films or at the surface of bulk low-carrier-density superconductors like some titanates or cuprates, then there is a good chance of observing the BCS-to-BEC evolution as a function of carrier density as envisioned by Eagles in 1969.REFERENCESSection:ChooseTop of pageREFERENCES << REFERENCES 1. A. J. Leggett, in Modern Trends in the Theory of Condensed Matter: Proceedings of the XVI Karpacz Winter School of Theoretical Physics, February 19-March 3, 1979, Karpacz, Poland, A. Pekalski, J. Przystawa, eds., Springer, New York (1980) Google Scholar A. J. Leggett, J. Phys. Colloq. 41, C7–19 (1980). https://doi.org/10.1051/jphyscol:1980704 , Google ScholarCrossref2. J. M. Blatt, Theory of Superconductivity, Academic Press, New York (1964). Google Scholar3. L. S. Borkowski, C. A. R. Sá de Melo, http://arxiv.org/abs/cond-mat/9810370v1 , Google Scholar R. D. Duncan, C. A. R. Sá de Melo, Phys. Rev. B 62, 9675 (2000). https://doi.org/10.1103/PhysRevB.62.9675 , Google ScholarCrossref, ISI© 2009 American Institute of Physics.

Mössbauer U − centers as tools for studying the Bose condensation in semiconductors

It is shown that the Mossbauer two-electron centers with negative correlation energy are efficient tools for studying the processes of Bose condensation of electron pairs in superconducting phase transition. The corresponding probes are sensitive to two-electron processes and determine their high sensitivity to a variation in the electron density at the phase transition. It is shown that a variation in the electron density in the case of a phase transition depends on the critical temperature T c and is different for different sublattices.

Ferromagnetic pairing states on two-coupled chains

We propose a concrete model which exhibits ferromagnetism and electron-pair condensation simultaneously. The model is defined on two chains and consists of the electron hopping term, the on-site Coulomb repulsion and a ferromagnetic interaction which describes ferromagnetic coupling between two electrons, one on a bond in a chain and the other on a site in the other chain. It is rigorously shown that the model has fully-polarized ferromagnetic pairing ground states. The higher dimensional version of the model is also presented.

Exact Electron-Pairing Ground States of Tight-Binding Models with Local Attractive Interactions

We present a class of exactly solvable models of correlated electrons. The models are defined in any dimension d and consist of electron-hopping terms and local attractive interactions between electrons. For each even number of electrons less than or equal to 1/( d +1)-filling, we find the exact ground state in which all electrons form pairs of a certain type, and thus the models exhibit an electron-pair condensation.

Statistical mechanics of the electron-phonon system

The electron-phonon system has received considerable attention in connection with the phenomenon of superconductivity, where the condensation of electron pairs is believed to arise from the attraction produced by the phonons () The system is usually described by the Frolich Hamiltonian (), where the phonons are represented by a scalar field coupled to the electron density. Although this interaction has been widely used for approximate calculations, it has never been proved that it provides a statistical mechanical description in the usual sense, in particular that it allows the infinite volume limit to be taken for the thermodynamic quantities. Here, we shall consider this problem, concentrating on the statistical mechanics of the electrons. We therefore us the method of Feynman (), in which the statistical operator of the electrons is given by a path integral representation and the phonon field is eliminated at the expense of introducing a non instantaneous interaction between the electrons. Except for this last feature, the situation is then similar to the one encountered in the case of quantum systems with instantaneous potentials (). The Hamiltonian we start from is

The Meissner Effect in the Quasi-Chemical Equilibrium Theory of Superconductivity

Based on the quasi-chemical equilibrium theory of superconductivity, an explicitly gage-invariant proof of the Meissrer-Ochserfeld effect (magnetic field expulsion from a superconductor) is given. The essential condition for a Heissner effect is the Bose-Einstein condensation of electron pairs. Other aspects of the problem, such as the energy gap and plasma waves, are not necessary for the Meissner effect and do not appear in the calculation. The random-phase approximation was not used. (auth)