A new approach to the treatment of uniform electric fields

It has been known for a long time that the treatment of an external uniform electric field in a periodic system presents conceptual and practical difficulties. At the heart of these difficulties lies the fact that, when a uniform electric field is present, the ground state does not exist: thus one is faced with the dilemma of either breaking the periodicity by a scalar potential or making the problem time-dependent by a vector potential. Within the context of density functional theory this seems to imply that the conventional description of many-body effects in terms of the time-dependent density should be abandoned in favor of a description in terms of the current density.$^1$ However, we will show that it is possible to describe the uniform electric field without leaving the framework of ordinary time-dependent DFT, by passing to a non-inertial reference frame. By leaving the distances invariant, this transformation preserves the periodicity of the lattice, and at the same time the appearance of an ``inertial force" compensates for the vector potential. Thus, we end up with a system subjected to a periodic time-dependent external potential -- a perfectly legitimate candidate for the application of TDDFT.\\ 1. N.T. Maitra, I. Souza, and K. Burke, Phys. Rev. B. {\bf 68}, 045019, (2003).