Towards a theory of superconductivity based on collective Cooper pairs

Superconductivity could be seen as a Bose-Einstein condensation (BEC) of Cooper pairs. However, the creation and annihilation operators of Cooper pairs do not satisfy the bosonic commutation relations and then, the mentioned viewpoint has a weakness in its foundation. In this work, we introduce the concept of collective Cooper pairs (CCP) as linear combinations of Cooper pairs and prove their bosonic nature at the dilute limit. This bosonic nature is given rise from their diffuse character on the Cooper pairs, which permits the accumulation of many collective pairs at a single quantum state. Moreover, the superconducting ground state proposed by Bardeen, Cooper and Schrieffer (BCS) can be written in terms of these collective Cooper pairs, which means that the BCS theory is consistent with a possible BEC theory of superconductivity based on collective Cooper pairs. Finally, we calculate the energy spectra and the BEC critical temperature of CCP.     

Cross-over effects in heavy-fermion superconductors

The influence of correlation effects on superconductivity in lanthanide and actinide compounds is investigated theoretically. As driving mechanism for the formation of heavy-fermion Cooper pairs different electron-phonon interactions are considered and discussed within the Anderson lattice model. The elimination of the bare electron-phonon interactions and a BCS-like truncation procedure lead to the appearance of different types of Cooper pairs. The stability of these Cooper pairs in the Kondo lattice state is studied by using a semi-phenomenological parameter which effectively describes the correlation off electrons. It is found that hybrid pairing is less important and that superconductivity of conduction andf electrons always occurs simultaneously. Furthermore, in the case of strongly correlatedf electrons a cross-over takes place from mainly heavy-fermion superconductivity to conduction electron superconductivity.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Electromagnetic Meissner effect in spin-one color superconductors

It is shown that color-superconducting quark matter, where quarks of the same flavor form Cooper pairs with spin one, exhibits an electromagnetic Meissner effect. This is in contrast to spin-zero color superconductors where Cooper pairs consist of quarks with different flavors.     

Long-range superharmonic Josephson current

We consider a long superconductor-ferromagnet-superconductor junction with one spin-active region. It is shown that an odd number of Cooper pairs cannot have a long-range propagation when there is only one spin-active region. When the temperature is much lower than the Thouless energy, the coherent transport of two Cooper pairs becomes the dominant process and the superharmonic current-phase relation is obtained (I ∝ sin2?).     

Physical Mechanism of Photon Pairing in a Kerr Nonlinear Medium

We establish that Cooper instability of the ground state of a normal blackbody triggers the attractive photons to form the pairs. We next find that however small the effective interphoton attraction V ₀ is, Cooper pairs of photon always exist in the ground state of a Kerr nonlinear blackbody. It has been pointed out that there are the three fundamental properties of the Cooper pair of photon: the extremely large binding energy, the extremely small radius, and the extremely high critical temperature. These properties are reflected in the many-photon bound state described by the optical superfluid theory.     

“库柏对”的诞生

基于史料,阐述了库柏对产生的经过     

Bosonic nature of collective Cooper pairs

Superconductivity is not considered as a Bose-Einstein condensation, because the creation and annihilation operators of Cooper pairs do not satisfy bosonic commutation relations. However, collective pairs can be constructed by a linear combination of Cooper pairs and we demonstrate in this Letter that these collective Cooper pairs have bosonic nature. In addition, the Bardeen-Cooper-Schrieffer (BCS) superconducting ground state can be built by means of these pairs and in consequence, could be treated as a Bose-Einstein condensate.     

Single Cooper pair pump

We have operated a Cooper pair pump, a linear array of superconducting tunnel junctions in which single Cooper pairs are moved under the influence of ac signals applied to two gate electrodes. The pump is based on the Coulomb blockade of charge tunneling. Because of the small junction capacitance precisely one Cooper pair is transferred per ac cycle. The current-voltage characteristics of this device show current plateaus close to 2ef, wheref is the frequency of the ac voltages. Deviations are explained in terms of Zener tunneling, Cooper pair co-tunneling, and sporadic quasiparticle tunneling.     

Cooper Molecules: Second Pairing of Cooper Pairs in Gapless Superconductor CeCoIn_5

We establish a quantum field theory of phase transitions in gapless superconductor CeCoIn5.It is found that uniform Cooper pair gases with pure gradient interactions with negative coefficient can undergo a BardeenCooper-Schrieffer (BCS) condensation below a critical temperature.In the BCS condensation state,bare Cooper pairs with opposite wave vectors are bound into Cooper molecules,and uncoupled bare Cooper pairs are transformed into a new kind of quasiparticle,i.e.,the dressed particles.The Cooper molecule s.ystem is a condensate or a superfluid,and the dressed particle s.ystem is a normal fluid.The critical temperature is derived anal.yticall.y.The critical temperature of the superconductor CeCoIn5 is obtained to be T_c = 2.289 K,which approaches the experimental data.The transition from the BCS condensation state to the normal state is a first-order phase transition.     

约瑟夫森器件中的宏观量子现象及超导量子计算

超导体中的电子结成库珀对，凝聚到可以用一个宏观波函数来描绘的能量基态，该波函数的位相是代表了成百万库珀对集体运动的宏观变量．以约瑟夫森结为基础元件的超导约瑟夫森器件，使人们能够控制并测量一个超导体的位相和库珀对数目，因此是研究宏观量子现象的理想系统．文章回顾了约瑟夫森器件中的宏观量子现象研究的发展历程，介绍了当前超导约瑟夫森器件在量子计算中的重要应用，并对它们的未来作了简要的展望．     

两库柏对相互作用问题的研究

在文中给出了库柏对的两种不同表达形式。发现用由对算符组成的哈密顿量来计算更方便,用这些对算符对易性质,而不是把它们看成费米子算符的组合产物。这样一来,研究的库柏对相互作用问题也把库柏对看成对算符。文中解决了两个库柏对相互作用问题,并讨论了推广到多库柏系统的情况。     

Normal processes which inhibit superconductivity

The effective interaction strength for the establishment of Cooper pairs in a degenerate Fermion gas is shown to be reduced by a second-order exchange process. In physical terms, the reduction is a consequence of the normal polarization clouds surrounding the individual Fermions. Because of the Pauli exclusion principle, these polarization clouds block the approach of further quasi-particles and thereby tend to prevent Cooper pairing. The effect is related to but simpler than that studied byHenley andWilets in connection with the energy gap of nuclear matter. The second-order suppressive effect is considerable for strong interaction and large state density, and may even prevent the superconducting transition from occurring at all.     

Coboson formalism for Cooper pairs and its application to Richardson’s equations

We propose a many-body formalism for Cooper pairs which has similarities to the one we recently developed for composite boson excitons (coboson in short). Its Shiva diagram representation evidences that N Cooper pairs differ from N single pairs through electron exchange only: no direct coupling exists due to the very peculiar form of the reduced BCS potential. As a first application, we here use this formalism to derive Richardson’s equations for the exact eigenstates of N Cooper pairs. This derivation gives hints on why the N(N-1)N(N-1) dependence of the N-pair ground state energy we recently obtained by solving Richardson’s equations analytically in the low density limit, stays valid up to the dense regime. No higher order dependence exists under large overlap, a surprising result hard to accept at first. We also briefly question the BCS wave function ansatz compared to Richardson’s exact form, in the light of our understanding of coboson many-body effects.     

Conductance spectroscopy of spin-triplet superconductors

We propose a novel experiment to identify the symmetry of superconductivity on the basis of theoretical results for differential conductance of a normal metal connected to a superconductor. The proximity effect from the superconductor modifies the conductance of the remote current depending remarkably on the pairing symmetry: spin singlet or spin triplet. The clear-cut difference in the conductance is explained by symmetry of Cooper pairs in a normal metal with respect to frequency. In the spin-triplet case, the anomalous transport is realized due to an odd-frequency symmetry of Cooper pairs.     

Overall picture of the cascade gamma decay of neutron resonances within a modified practical model

The intensities of two-step cascades in 43 nuclei of mass number in the range of 28 ≤ A ≤ 200 were approximated to a high degree of precision within a modified version of the practical cascade-gammadecay model introduced earlier. In this version, the rate of the decrease in the model-dependent density of vibrational levels has the same value for any Cooper pair undergoing breakdown. The most probable values of radiative strength functions both for E1 and for M1 transitions are determined by using one or two peaks against a smooth model dependence on the gamma-transition energy. The statement that the thresholds for the breaking of Cooper pairs are higher for spherical than for deformed nuclei is a basic result of the respective analysis. The parameters of the cascade-decay process are now determined to a precision that makes it possible to observe the systematic distinctions between them for nuclei characterized by different parities of neutrons and protons.     

Holes localized on a Skyrmion in a doped antiferromagnet on the honeycomb lattice: Symmetry analysis

Using the low-energy effective field theory for hole-doped antiferromagnets on the honeycomb lattice, we study the localization of holes on Skyrmions, as a potential mechanism for the preformation of Cooper pairs. In contrast to the square lattice case, for the standard radial profile of the Skyrmion on the honeycomb lattice, only holes residing in one of the two hole pockets can get localized. This differs qualitatively from hole pairs bound by magnon exchange, which is most attractive between holes residing in different momentum space pockets. On the honeycomb lattice, magnon exchange unambiguously leads to f$f$-wave pairing, which is also observed experimentally. Using the collective-mode quantization of the Skyrmion, we determine the quantum numbers of the localized hole pairs. Again, f$f$-wave symmetry is possible, but other competing pairing symmetries cannot be ruled out.     

Superconducting nanofilms: molecule-like pairing induced by quantum confinement

Quantum confinement of the perpendicular motion of electrons in single-crystalline metallic superconducting nanofilms splits the conduction band into a series of single-electron subbands. A distinctive feature of such a nanoscale multi-band superconductor is that the energetic position of each subband can vary significantly with changing nanofilm thickness, substrate material, protective cover and other details of the fabrication process. It can occur that the bottom of one of the available subbands is situated in the vicinity of the Fermi level. We demonstrate that the character of the superconducting pairing in such a subband changes dramatically and exhibits a clear molecule-like trend, which is very similar to the well-known crossover from the Bardeen-Cooper-Schrieffer regime to Bose-Einstein condensation (BCS-BEC) observed in trapped ultracold fermions. For Pb nanofilms with thicknesses of 4 and 5 monolayers (MLs) this will lead to a spectacular scenario: up to half of all the Cooper pairs nearly collapse, shrinking in the lateral size (parallel to the nanofilm) down to a few nanometers. As a result, the superconducting condensate will be a coherent mixture of almost molecule-like fermionic pairs with ordinary, extended Cooper pairs.     

Finite-bias Cooper pair splitting

In a device with a superconductor coupled to two parallel quantum dots (QDs) the electrical tunability of the QD levels can be used to exploit nonclassical current correlations due to the splitting of Cooper pairs. We experimentally investigate the effect of a finite potential difference across one quantum dot on the conductance through the other completely grounded QD in a Cooper pair splitter fabricated on an InAs nanowire. We demonstrate that the nonlocal electrical transport through the device can be tuned by electrical means and that the energy dependence of the effective density of states in the QDs is relevant for the rates of Cooper pair splitting (CPS) and elastic cotunneling. Such experimental tools are necessary to understand and develop CPS-based sources of entangled electrons in solid-state devices.     

Enhanced photon generation in a Nb/n-InGaAs/p-InP superconductor/semiconductor-diode light emitting device

We experimentally demonstrate Cooper pairs' drastic enhancement of the band-to-band radiative recombination rate in a semiconductor. Electron Cooper pairs injected from a superconducting electrode into an active layer by the proximity effect recombine with holes injected from a p-type electrode. The recombination of a Cooper pair with p-type carriers dramatically increases the photon generation probability of a light-emitting diode in the optical-fiber communication band. The measured radiative decay time rapidly decreases with decreasing temperature below the superconducting transition temperature of the niobium electrodes. Our results indicate the possibility to open up new interdisciplinary fields between superconductivity and optoelectronics.     

电-声超导电性的对称理论

利用新的库珀对平均汤近似，导出了电－声系统中声子－库珀对有效作用，证明了声子通过交换虚的库珀对能够产生一个有效的吸引力，导致两动量相反的声子配对并构成稳定的声超导态。发现电子超导态与声子超导态的直积能构成稳定的电－声对称的高温超导基态。在声子－库珀对弱耦合极限下，基态对称破缺成为传统的ＢＣＳ基态。