1S0 Pairing Gaps, Chemical Potentials and Entrainment Matrix in Superfluid Neutron-Star Cores for the Brussels–Montreal Functionals

Temperature and velocity-dependent 1S0 pairing gaps, chemical potentials and entrainment matrix in dense homogeneous neutron–proton superfluid mixtures constituting the outer core of neutron stars, are determined fully self-consistently by solving numerically the time-dependent Hartree–Fock–Bogoliubov equations over the whole range of temperatures and flow velocities for which superfluidity can exist. Calculations have been made for npeμ in beta-equilibrium using the Brussels–Montreal functional BSk24. The accuracy of various approximations is assessed and the physical meaning of the different velocities and momentum densities appearing in the theory is clarified. Together with the unified equation of state published earlier, the present results provide consistent microscopic inputs for modeling superfluid neutron-star cores.

Numerical solution of large scale Hartree-Fock-Bogoliubov equations

The Hartree-Fock-Bogoliubov (HFB) theory is the starting point for treating superconducting systems. However, the computational cost for solving large scale HFB equations can be much larger than that of the Hartree-Fock equations, particularly when the Hamiltonian matrix is sparse, and the number of electrons $N$ is relatively small compared to the matrix size $N_{b}$. We first provide a concise and relatively self-contained review of the HFB theory for general finite sized quantum systems, with special focus on the treatment of spin symmetries from a linear algebra perspective. We then demonstrate that the pole expansion and selected inversion (PEXSI) method can be particularly well suited for solving large scale HFB equations. For a Hubbard-type Hamiltonian, the cost of PEXSI is at most $\Or(N_b^2)$ for both gapped and gapless systems, which can be significantly faster than the standard cubic scaling diagonalization methods. We show that PEXSI can solve a two-dimensional Hubbard-Hofstadter model with $N_b$ up to $2.88\times 10^6$, and the wall clock time is less than $100$ s using $17280$ CPU cores. This enables the simulation of physical systems under experimentally realizable magnetic fields, which cannot be otherwise simulated with smaller systems.

The effect of quasiparticle self-energy on Cd2Re2O7 superconductor

The magnitude and the temperature dependence of the superconducting order parameter Δ(T) of single crystals of Cd2Re2O7 (Tc = 1.02 K) was measured using point-contact spectroscopy. To fit the conductance spectra and to extract the order parameter at different temperatures we generalized the Blonder–Tinkham–Klapwijk theory by including the self-energy of the quasiparticles into the Bogoliubov equations. This modification enabled excellent fits of the conductance spectra. Δ(T) increases steeply below the superconducting transition temperature of 1.02 K and levels off below ∼0.8 K at a value of 0.22(1) meV, ≈40% larger than the BCS value. Our results indicate the presence of a strong electron–phonon interaction and an enhanced quasiparticle damping and may be related to a possible phase transition within the superconducting region at ∼0.8 K.