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.

arXiv comment7 pages, 4 figures, 4 table; v3: the version to appear in Phys. Rev. B

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