Electronic orbital responses of extended systems to static, homogeneous, electromagnetic fields

Abstract

We discuss theoretical methods with which the effects of static, homogenous, electromagnetic fields can be determined for systems that are extended and in the ultimate limit are infinite and periodic. We focus here on the finite field (FF) method, but there are obvious implications for perturbation theory approaches as well. The fact that including finite fields in electronic-structure calculations simultaneously introduces the coordinate r→ means that the translational invariance of the potential would be violated and therefore without modification this approach would be inapplicable to infinite, periodic systems. One such long-standing approach is to replace r→ by an operator that involves the derivative with respect to the crystal momentum k→. This is the primary procedure for electrostatic fields. For magnetostatic fields a number of suggestions have been made, all of which are or may be related to changing the gauge used to describe the fields. In the case of a large finite system, for non-vanishing electrostatic and/or magnetostatic field, the lowest energy orbitals are unbound. Thus, the bound states become resonances and the bound-state variational principle can no longer be applied. Instead, special methods for identifying the changes in the system properties due to the presence of these fields are evaluated. Our own simple method based on identifying those orbitals in the field-containing case that are most similar to the occupied orbitals in the field-free case seems to be a promising approach. Since methods for finite molecular systems exposed to static electromagnetic fields are more mature than those for the infinite, periodic crystals, an important issue is to establish that these methods give identical results when treating a crystal as being either large and finite or infinite and periodic. Finally it shall be mentioned that our presentation focuses on methods rather than results. Moreover, it concentrates on our own work that, in some cases, is not yet complete.