Condensation state of ultra-cold Bose atomic gases with pure gradient interactions with negative coefficient

Within the framework of quantum field theory, we find that uniform Bose atomic gases with pure gradient interactions with negative coefficient can undergo a Bardeen-Cooper-Schrieffer (BCS) condensation below a critical temperature. In the BCS condensation state, bare atoms with opposite wave vectors are bound into pairs, and unpaired bare atoms are transformed into a new kind of quasi-particle, i.e. the dressed atom. The atom-pair system is a condensate or a superfluid and the dressed-atom system is a normal fluid. At absolute zero temperature the condensate possesses a lowest negative energy. When the total interaction strength of atoms is large enough, the energy of the condensate is a monotonically increasing function of temperature and interaction strength. The critical temperature and the effective mass of dressed atoms are derived analytically. The transition from the BCS condensation state to the normal state is a first-order phase transition.     

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.     

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.     

Normal phase and superconducting instability in the attractive Hubbard model: a DMFT(NRG) study

We study the normal (nonsuperconducting) phase of the attractive Hubbard model within the dynamical mean field theory (DMFT) using the numerical renormalization group (NRG) as an impurity solver. A wide range of attractive potentials U is considered, from the weak-coupling limit, where superconducting instability is well described by the BCS approximation, to the strong-coupling region, where the superconducting transition is described by Bose condensation of compact Cooper pairs, which are formed at temperatures much exceeding the superconducting transition temperature. We calculate the density of states, the spectral density, and the optical conductivity in the normal phase for this wide range of U, including the disorder effects. We also present the results on superconducting instability of the normal state dependence on the attraction strength U and the degree of disorder. The disorder influence on the critical temperature T _c is rather weak, suggesting in fact the validity of Anderson’s theorem, with the account of the general widening of the conduction band due to disorder.     

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．     

Observation of spin susceptibility enhancement in the possible Fulde-Ferrell-Larkin-Ovchinnikov state of CeCoIn(5)

We report (115)In nuclear magnetic resonance measurements of the heavy-fermion superconductor CeCoIn(5) in the vicinity of the superconducting critical field H(c2) for a magnetic field applied perpendicular to the ? axis. A possible inhomogeneous superconducting state, the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, is stabilized in this part of the phase diagram. In an 11 T applied magnetic field, we observe clear signatures of the two phase transitions: the higher temperature one to the homogeneous superconducting state and the lower temperature phase transition to a FFLO state. We find that the spin susceptibility in the putative FFLO state is significantly enhanced as compared to the value in a homogeneous superconducting state. The implications of this finding for the nature of the low temperature phase are discussed.     

Pre-formed Cooper pairs and Bose-Einstein condensation in cuprate superconductors

A two-dimensional (2D) assembly of noninteracting, temperature-dependent, pre-formed Cooper pairs in chemical/thermal equilibrium with unpaired fermions is examined in a binary boson-fermion statistical model as the Bose-Einstein condensation (BEC) singularity temperature T_c is approached from above. Compared with BCS theory (which is not a BEC theory) substantially higher T_cs are obtained without any adjustable parameters, that fall roughly within the range of empirical T_cs for quasi-2D cuprate superconductors.     

Stable and resonant Cooper pairs

A Bethe-Salpeter treatment of Cooper pairs (CPs) based on an ideal Fermi gas (IFG) ‘sea’ yields the familiar stable negative-energy, infinite-lifetime two-particle bound-state if two-hole CPs are ignored. Otherwise, it gives purely imaginary energies and thus unphysical solutions. However, a Bogoliubov transformation to the BCS ground state yields the trivial sound solution plus a nontrivial one. The latter are two-fermion ‘moving CPs’ as positive-energy stable objects for zero center-of-mass momentum (CMM), and finite-lifetime resonant ones for nonzero CMM with a linear dispersion leading term. Hence, Bose-Einstein condensation of such pairs may occur in exactly two dimensions as it cannot with quadratic dispersion.     

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。     

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。     

Josephson current through a half metal at low temperatures

We study the Josephson effect in the superconductor/diffusive half metal/superconductor junctions by using the recursive Green function method. In the presence of spin-flip scatterings at the interface, odd-frequency spin-triplet Cooper pairs penetrate deeply into a half metal and carry Josephson current. The critical Josephson current increases with decreasing temperatures near the transition temperature. At low temperatures, however, the critical current decreases with decreasing temperatures. Such reentrant behavior is unusual in the case of s-wave superconductor junctions. The penetration of odd-frequency pairs modifies quasiparticle density of states in a half metal near the Fermi energy, which is responsible for the nonmonotonic temperature dependence of critical Josephson current.     

Critical behavior in type-II superconductors

The high-field critical behavior of type-II superconductors with weak disorder is dominated by the Landau levels of Cooper pairs. The macroscopic degeneracy of Landau manifolds suppresses phase coherence and eliminates the Abrikosov transition in dimensions two and three. A novel phase transition, unrelated to the conventional Abrikosov transition, is predicted to take its place. At this transition the normal state is unstable to the charge-density wave of Cooper pairs. The nature of this new state is discussed. This phase should be most readily observable in layered materials at fields > 1–10T.     

Energy of N Cooper pairs by analytically solving the Richardson-Gaudin equations for conventional superconductors

This Letter provides the solution to a yet unsolved basic problem of solid state physics: the ground state energy of an arbitrary number of Cooper pairs interacting via the Bardeen-Cooper-Schrieffer potential. We here break a 50?yr old math problem by analytically solving Richardson-Gaudin equations which give the exact energy of these N pairs via N parameters coupled through N nonlinear equations. Our result fully supports the standard BCS result obtained for a pair number equal to half the number of states feeling the potential. More importantly, it shows that the interaction part of the N-pair energy depends on N as N(N-1) only from N=1 to the dense regime, a result which evidences that Cooper pairs interact via Pauli blocking only.     

Energy-gap dynamics of superconducting NbN thin films studied by time-resolved terahertz spectroscopy

Using time-domain terahertz spectroscopy we performed direct studies of the photoinduced suppression and recovery of the superconducting gap in a conventional BCS superconductor NbN. Both processes are found to be strongly temperature and excitation density dependent. The analysis of the data with the established phenomenological Rothwarf-Taylor model enabled us to determine the bare quasiparticle recombination rate, the Cooper pair-breaking rate and the electron-phonon coupling constant, λ=1.1±0.1, which is in excellent agreement with theoretical estimates.     

Isotropically gapped strong-coupling superconductivity in the beta-pyrochlore KOs2O6: evidence from penetration depth measurements

We report on measurements of the temperature dependence of the magnetic penetration depth down to 0.04 K in a high-quality sample of the beta-pyrochlore KOs2O6 (Tc=9.65 K) with a spin-frustrated lattice. We observe temperature-independent behavior below T approximately 0.3Tc, which is firm evidence for the presence of an isotropic superconducting gap in this material. In the whole temperature range the superfluid density is very well described, without the need of adjustable parameters, by a strong-coupling extension of the BCS model for an isotropic gap. Thus, the penetration depth results indicate that KOs2O6 is a strong-coupling superconductor with a fully developed energy gap. No effect of the second phase transition taking place at Tp=7.5 K was observed on the penetration depth, which suggests that the Cooper pairs remain unperturbed across this transition.     

First-order superconducting phase transition in CeCoIn5

The superconducting phase transition in heavy fermion CeCoIn5 (T(c)=2.3 K in zero field) becomes first order when the magnetic field H parallel [001] is greater than 4.7 T, and the transition temperature is below T0 approximately 0.31T(c). The change from second order at lower fields is reflected in strong sharpening of both specific heat and thermal expansion anomalies associated with the phase transition, a strong magnetocaloric effect, and a steplike change in the sample volume. This effect is due to Pauli limiting in a type-II superconductor, and was predicted theoretically in the mid-1960s.     

Field dependence of the ground state in the exotic superconductor CeCoIn5: a nuclear magnetic resonance investigation

We report 115In nuclear magnetic resonance (NMR) measurements in CeCoIn5 at low temperature (T approximately 70 mK) as a function of the magnetic field (H0) from 2 to 13.5 T applied perpendicular to the c axis. A NMR line shift reveals that below 10 T the spin susceptibility increases as sqrt[H0]. We associate this with an increase of the density of states due to the Zeeman and Doppler-shifted quasiparticles extended outside the vortex cores in a d-wave superconductor. Above 10 T a new superconducting state is stabilized, possibly the modulated phase predicted by Fulde, Ferrell, Larkin, and Ovchinnikov. This phase is clearly identified by a strong and linear increase of the NMR shift with the field, before a jump at the first order transition to the normal state.     

First and second order quantum phase transitions in multi-band superconductors

In multi-band and inter-metallic materials superconductivity can be destroyed by applying external pressure in these systems. In many cases the critical temperature is driven continuously to zero, the superconducting to normal transition being associated with a superconducting quantum critical point (SQCP). In this paper we propose a model for this type of SQCP based on the increase of hybridization as pressure is applied in the material. We study a two-band superconductor with hybridization V between these bands. We use a BCS approximation and include both inter- and intra-band attractive interactions. We show that for negligible inter-band interactions, as hybridization increases there is a second order phase transition from a superconductor to a normal state at zero temperature at a critical value of the hybridization V_c. This SQCP can be reached by pressure, since this external parameter controls hybridization in the system. We also find discontinuous transitions at zero temperature and the appearance of a gapless superconducting (GS) phase in a certain range of hybridization in the case of inter-band interactions being dominant.