Difficulties in operator-based formulation of the bulk quadrupole moment

Abstract

Electric multipole moments are the most fundamental properties of insulating materials. However, the general formulation of bulk multipoles has been a long-standing problem. The solution for the electric dipole moment was provided decades ago by King-Smith, Vanderbilt, and Resta. Recently, there have been attempts at generalizing Resta's formula to higher-order multipoles. We point out several issues in the recent proposals.