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We present a relativistic tight-binding (TB) approximation method that is applicable to actual crystalline materials immersed in a uniform magnetic field. The magnetic Bloch theorem is used to make the dimensions of the Hamiltonian matrix finite. In addition, by means of the perturbation theory, the magnetic hopping integral that appears in the Hamiltonian matrix is reasonably approximated as the relativistic hopping integral multiplied by the magnetic-field-dependent phase factor. In order to calculate the relativistic hopping integral, the relativistic version of the so-called Slater-Koster table is also given in an explicit form. We apply the present method to crystalline silicon immersed in a uniform magnetic field, and reveal its energy-band structure that is defined in the magnetic first Brillouin zone. It is found that the widths of energy-bands increase with increasing the magnetic field, which indicates the magnetic-field dependence of the appropriateness of the effective mass approximation. The recursive energy spectrum, which is the so-called butterfly diagram, can also be seen in the k-space plane perpendicular to the magnetic field.

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The experimentally predicted narrowing in the bandwidth of sodium is interpreted in terms of the nonlocal self-energy effect on quasiparticle energies of the electron liquid. The calculated self-energy correction is an increasing function of the wave number variable. The usual analysis of angle-resolved photoemission experiments assumes the final-state energies on the nearly free-electron-like model and hence incorrectly ascribes the nonlocal self-energy correction to the final-state energies to occupied-state energies, seemingly leading to a narrowing in the bandwidth.

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We present a density-functional scheme for calculating the pair density ͑PD͒ by means of the correlated wave function. The Jastrow wave function is adopted as the correlated wave function. By using the lowestorder approximation to the Jastrow wave function PDs, the search region for the ground-state PD is substantially extended as compared with our previous theory ͓Physica B 387, 117 ͑2007͔͒. The variational principle results in simultaneous equations that are practicable to calculate the ground-state PD.

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