Density-functional theory in strong magnetic fields

Abstract

We formulate the current-density--functional theory for systems in arbitrarily strong magnetic fields. A set of self-consistent equations comparable to the Kohn-Sham equations for ordinary density-functional theory is derived, and proved to be gauge invariant and to satisfy the continuity equation. We prove that the exchange-correlation energy functional ${\mathrm{E}}_{\mathrm{xc}[\mathrm{n}}$,${\mathrm{j}}_{\mathrm{p}}$] [n(r) is the density and ${\mathrm{j}}_{\mathrm{p}}$(r) is the ``paramagnetic'' current density] depends on the current via the combination \ensuremath{\nu}(r)=\ensuremath{\nabla}\ifmmode\times\else\texttimes\fi{}${[\mathrm{j}}_{\mathrm{p}}$(r)/n(r)]. An explicit formula for ${\mathrm{E}}_{\mathrm{xc}}$ is derived, which is local in \ensuremath{\nu}(r).