Swallowtail band structure of the superfluid Fermi gas in an optical lattice

We investigate the energy band structure of the superfluid flow of ultracold dilute Fermi gases in a one-dimensional optical lattice along the BCS to Bose-Einstein condensate (BEC) crossover within a mean-field approach. In each side of the crossover region, a loop structure (swallowtail) appears in the Bloch energy band of the superfluid above a critical value of the interaction strength. The width of the swallowtail is largest near unitarity. Across the critical value of the interaction strength, the profiles of density and pairing field change more drastically in the BCS side than in the BEC side. It is found that along with the appearance of the swallowtail, there exists a narrow band in the quasiparticle energy spectrum close to the chemical potential, and the incompressibility of the Fermi gas consequently experiences a profound dip in the BCS side, unlike in the BEC side.     

Superfluid states in β-stable nuclear matter

Two superfluid states of nuclear matter, which are supposed to play an important role in neutron stars, are discussed: the first one due to the proton-proton ¹ S ₀ pairing in β-equilibrium nuclear matter; the second one due to the anisotropic neutron-neutron ³ PF ₂ pairing in neutron matter. Since the two phases appear at high density of nuclear matter, the three-body forces were added to the pairing interaction and the strong correlation effects in the single-paricle spectrum. The energy gaps, obtained solving the extended BCS equations, significantly deviate from the values without medium effects so as to limit the role of these two superfluid states in the interpretation of phenomena occurring in the neutron-star core.     

Exact quantum critical points and phase separation instabilities in Betts Hubbard nanoclusters

Spontaneous phase separation instabilities with the formation of various types of charge and spin pairing (pseudo)gaps in U>0 Hubbard model including the next nearest neighbor coupling are calculated with the emphasis on the two-dimensional (square) lattices generated by 8- and 10-site Betts unit cells. The exact theory yields insights into the nature of quantum critical points, continuous transitions, dramatic phase separation instabilities and electron condensation in spatially inhomogeneous systems. The picture of coupled antiparallel (singlet) spins and paired charged holes suggests full Bose condensation and coherent pairing in real space at zero temperature of electrons complied with the Bose-Einstein statistics. Separate pairing of charge and spin degrees at distinct condensation temperatures offers a new route to superconductivity different from the BCS scenario. The conditions for spin liquid behavior coexisting with unsaturated and saturated Nagaoka ferromagnetism due to spin-charge separation are established. The phase separation critical points and classical criticalities found at zero and finite temperatures resemble a number of inhomogeneous, coherent and incoherent nanoscale phases seen near optimally doped high-T_c cuprates, pnictides and CMR nanomaterials.     

Cooper pair and electron-hole pair instabilities in a quasi-one dimensional system

We calculate for an almost half-filled tight-binding band, the mean field ground state energy differences between the charge-density-wave (CDW) and BCS paired states for a truncated model Hamiltonian with zero-range instantaneous electron-electron interactions. The CDW pairing is found to be always unstable vis-à-vis BCS for a static lattice distortion of wave vector Q = (2k_F, π, π).     

Self-consistency in the projected shell model

The projected shell model is a shell-model theory built up over a deformed BCS mean field. Ground state and excited bands in even-even nuclei are obtained through diagonalization of a pairing plus quadrupole Hamiltonian in an angular momentum projected 0-, 2-, and 4-quasiparticle basis. The residual quadrupole-quadrupole interaction strength is fixed self-consistently with the deformed mean field and the pairing constants are the same used in constructing the quasiparticle basis. Taking ¹⁶⁰Dy as an example, we calculate low-lying states and compare them with experimental data. We exhibit the effect of changing the residual interaction strengths on the spectra. It is clearly seen that there are many J^π = 0⁺, 1⁺, 4⁺ bandheads whose energies can only be reproduced using the self-consistent strengths. It is thus concluded that the projected shell model is a model with essentially no free parameters. The predicted energy of the 2⁺ bandhead lies however in nearly twice the experimental value.     

Multi-quasiparticle isomers and rotational bands in 178W

The high spin structure of the nucleus ¹⁷⁸W has been studied following the ¹⁷⁰Er(¹³C,5n) reaction. Many previously unidentified rotational bands are seen based on high-K, 2-, 4-, 6- and 8-quasiparticle structures, some of which are isomeric. The excitation energies of the multi-quasiparticle bandheads are compared with BCS calculations, including residual interactions. The bands show substantial increases in moments-of-inertia with increasing quasiparticle number. These are examined in terms of pairing blocking. The effect of blocked pairing is also taken into account in the calculation of g-factors, which supports the configuration assignments. The K^π = 25⁺, 8-quasiparticle band forms the yrast line from its bandhead upwards. This bandhead is a 220 ns isomer whose decay is strongly hindered, compared to the decay of the four- and six-quasiparticle structures.     

Description of the New Nuclide 259Db and Its α-Decay Chain in Relativistic Mean Field Theory

The new nuclide ²⁵⁹Db and its α decay chain are systematically studied in the framework of the relativistic mean field (RMF) theory with NL3 and TM1 effective interactions. The nuclide ²⁵⁹Db and its α-decay daughter nuclei are calculated in a RMF framework with and without the pairing correlation. With the pairing gaps obtained from the RCHB, the deformed RMF+BCS has been carried out for these nuclei. It has been found that the DRMF+BCS well reproduces the data and implies that the new nuclide ²⁵⁹Db and its α decay daughter nuclei are highly deformed. The α-decay energy Q_α for different channel has been given and it seems that the ground state to ground state Q_α values from DRMF+BCS reproduce the data well. Furthermore the single particle levels of the α decay chain are studied carefully and the explanation for the stability is also presented.     

Electron coherent and incoherent pairing instabilities in inhomogeneous bipartite and nonbipartite nanoclusters

Exact calculations of collective excitations and charge/spin (pseudo) gaps in an ensemble of bipartite and nonbipartite clusters yield level crossing degeneracies, spin-charge separation, condensation and recombination of electron charge and spin driven by interaction strength, inter-site couplings and temperature. Near crossing degeneracies, the electron configurations of the lowest energies control the physics of electronic pairing, phase separation and magnetic transitions. Rigorous conditions are found for the smooth and dramatic phase transitions with competing stable and unstable inhomogeneities. Condensation of electron charge and spin degrees at various temperatures offers a new mechanism of pairing and a possible route to superconductivity in inhomogeneous systems, different from the BCS scenario. Small bipartite and frustrated clusters exhibit charge and spin inhomogeneities in many respects typical for nano and heterostructured materials. The calculated phase diagrams in various geometries may be linked to atomic scale experiments in high Tc cuprates, manganites and other concentrated transition metal oxides.     

Effect of hybridization and dispersion of quasiparticles on the coexistent state of superconductivity and antiferromagnetism in <Emphasis Type="Italic">R</Emphasis>Ni<Subscript>2</Subscript>B<Subscript>2</Subscript>C

The effect of hybridization of conduction electrons and f-level on superconductivity (SC) and antiferromagnetism (AFM) in the coexistent phase of rare-earth nickel borocarbide superconductors (RNi₂B₂C) is reported. The Hamiltonian of the system is a mean field one and has been solved by writing equations of motion for the single-particle Green functions. It is assumed that superconductivity arises due to BCS pairing mechanism in the presence of antiferromagnetism in nickel lattices of Ni₂B₂ plane. The expressions for superconducting and antiferromagnetic order parameters are derived using double time electron Green functions. The quasiparticle energy bands are plotted and the nature of band dispersion of the quasiparticles is studied.     

On the influence of shell structure and matrix element fluctuations on the pairing correlation in nuclei

The uniform model for the nuclear pairing-force problem is extended to take into account the effect of fluctuations in nucleon orbital level densityρ and in pairing matrix elementsG _vv′. Simple formulas for the average dependence of level density on energy are presented, and alternative ways of estimating effects of shell bunching on the pairing correlation are derived. It is argued also that the pairing constantG might be systematically overestimated in the usual BCS numerical calculations; a semiconstant pairing force with diagonal elements larger than off-diagonal is thus suggested.     

Statistical description of a paired nucleus with the inclusion of angular momentum

The effect of angular momentum on an excited paired nucleus has been studied. The BCS Hamiltonian, modified to include the z-projection of angular momentum has been diagonalized and expressed in terms of the quasiparticle occupation numbers. The grand partition function and all the relevant thermodynamical functions as well as the level-density expression have been derived for the general case of an arbitrary set of single-particle levels. Furthermore, the formalism has been applied to the uniform model and, whenever possible, analytical expressions have been derived. In particular the zero-temperature angular momentum dependence of the gap parameter, the critical angular momentum as well as the yrast line have been calculated. The critical temperature as a function of angular momentum, which defines the phase transition between paired and unpaired systems, has been calculated. A new effect called the thermally assisted pairing correlation, involving an increase of pairing with increasing temperature has been predicted. The completeness of the formalism as applied to spherical or deformed nuclei has been discussed.     

New BCS and renormalized QRPA formalism with application to double beta decay

A new analysis of the renormalized proton–neutron quasiparticle random phase approximation based on simultaneous recalculation of the one-body density matrix and the pairing tensor has been used to study the double beta decay. We demonstrated that inclusion of the quasiparticle correlations at the BCS level reduces ground state correlations in the particle–particle channel of the proton–neutron interaction. We also simplified the RQRPA equations significantly obtaining a low-dimensioned set of linear equations for the quasiparticle densities. The formalism was applied to the double beta decay of ⁷⁶Ge. Received: 4 January 1999 / Revised version: 29 March 1999     

The mass parameters for the average mean-field potential

Starting from a mean-field hamiltonian with pairing interaction, we use the generator coordinate method (GCM) and a generalized gaussian overlap approximation to derive a multidimensional collective hamiltonian for large-amplitude motion. Numerical calculations are performed for Nilsson and Woods-Saxon potentials with BCS pairing. The BCS wave function is taken as the generator function and the deformation parameters of the single-particle mean field are used as the generator coordinates. We find that the GCM mass parameters on the average are smaller than those of the cranking (+ BCS) model by a factor of $\text{～}\text{2}\text{3}$. In the present approach, the zero-point energy correction to the collective potential is shown to vanish identically.     

Conventional BCS,unconventional BCS,and non-BCS hidden dineutron phases in neutron matter

The nature of pairing correlations in neutron matter is re-examined. Working within the conventional approximation in which the nn pairing interaction is provided by a realistic bare nn potential fitted to scattering data, it is demonstrated that the standard BCS theory fails in regions of neutron number density, where the pairing constant λ, depending crucially on density, has a non-BCS negative sign. We are led to propose a non-BCS scenario for pairing phenomena in neutron matter that involves the formation of a hidden dineutron state. In low-density neutron matter, where the pairing constant has the standard BCS sign, two phases organized by pairing correlations are possible and compete energetically: a conventional BCS phase and a dineutron phase. In dense neutron matter, where λ changes sign, only the dineutron phase survives and exists until the critical density for termination of pairing correlations is reached at approximately twice the neutron density in heavy atomic nuclei.     

Effect of quasiparticle spectral weight and consistency of energy gaps obtained from STM and ARPES spectra for underdoped superconductor Bi2Sr2CaCu2O8 + δ

By comparing the recently obtained superconducting energy gaps from the scanning tunneling microscopy (STM) and the angle-resolved photoemission spectroscopy (ARPES) for underdoped superconductor Bi₂Sr₂CaCu₂O_8 + δ, significant distinctions were observed. By properly taking the effect of quasiparticle spectral weight in the STM spectra into account, good consistency between both energy gaps obtained by STM and ARPES is unveiled.     

Integer and fractional quantum Hall effects in bilayer electron systems

Integer and fractional quantum Hall (QH) effects are studied in bilayer electron systems both theoretically and experimentally, especially, at ν=2 and 2/3. Due to the spin and layer degrees of freedom, the SU(4) symmetry underlies the integer QH states, where quantum coherence develops spontaneously and quasiparticles are coherent excitations. It is intriguing that a pair of skyrmions makes one quasiparticle at ν=2. In the fractional QH regime, on the other hand, the composite-fermion cyclotron gap competes with the Zeeman and tunneling gaps, bringing in new phases and excitations. At ν=2/3 our experimental data suggest that a quasiparticle is not a coherent excitation but simply a composite fermion.     

Finite Fermi systems theory and self-consistency relations

The self-consistent theory of the finite Fermi systems is outlined. This approach is based on the same Fermi liquid theory principles as the familiar theory for finite Fermi systems (FFS) by Migdal. We show that the basic Fermi system properties can be evaluated in terms of the quasiparticle Lagrangian L_q which incorporates the energy dependency effects. This Lagrangian is defined so that the corresponding Lagrange equations should coincide with the FFS theory equations of motion of the quasiparticles. The quasiparticle energy E_q defined in the terms of t he quasiparticle Lagrangian L_q according to the usual canonical rules is shown to be equal to the binding energy E_o of the system. For a given Lagrangian L_q the particle densities in nuclei, the nuclear single-particle spectra, the low-lying collective states (LCS) properties, and the amplitude of the interquasiparticle interaction are also evaluated. The suggested approach is compared with the Hartree-Fock theory with effective forces.