Current- and spin-density-functional theory for inhomogeneous electronic systems in strong magnetic fields

We formulate the current- and spin-density-functional theory for electronic systems in arbitrarily strong magnetic fields. A set of single-particle self-consistent equations which determine, in addition to the ground-state energy, the density, the spin density, the current density, and the spin-current density, is derived and is proved to be gauge invariant and to satisfy various physical requirements, including the continuity equation. For a magnetic field of constant direction in space, we prove that the exchange-correlation energy functional E_xc[n_↑,n_↓,j_p↑,j_p↓] n_mT (↓)r) is the ↑ (↓) component of the density and j_p↑ (↓)(r) is the ↑ (↓) component of the ‘‘paramagnetic’’ current density] is actually a functional of n_↑(r), n_↓(r), ν_↑(r)≡∇×j_p↑(r)/n_↑(r), and ν_↓(r)≡∇×j_p↓(r)/n_↓(r). An explicit form of E_xc, which is local in ν_↑(r) and ν_↓(r), is derived from linear-response theory. The generalizations to finite-temperature ensembles and to magnetic fields of arbitrarily varying directions are presented.