Corrigendum for Foreword for special issue of philosophical magazine on: topological correlated insulators and SmB₆

This article refers to:

Foreward for special issue of philosophical magazine on: topological correlated insulators and SmB6

J.W. Allen, Foreword for special issue of philosophical magazine on: topological correlated insulators on SmB₆, Philos Mag 96 (2016), pp. 3227–3238.

The Foreword pointed out the ‘apparent coincidence’ that the lowest six single particle 4f excitations of SmB₆ have the same symmetry properties when analysed either with a single-electron band model based on the spin-orbit split j = 5/2 and j = 7/2 4f Sm orbitals, or a many-body model based on the lowest lying multiplets of 4f⁵ and 4f⁶. Maurits Haverkort has pointed out [1] that the coincidence is actually systematic and occurs for electron removal from and addition to any empty or filled atomic shell. The entirely filled j = 5/2 orbitals of the Sm f⁶ configuration act as a filled shell.

As an illustration of the basic general argument, for a fully filled shell the local many electron ground state belongs to the fully symmetric A_1g irreducible representation of the relevant local point group. Adding or removing an electron of a particular orbital representation (x) leads to a many body state belonging to the x * A_1g = X representation. For the Sm f⁶ ground state (⁷F₀) electron removal of a j = 5/2 electron leads to a lowest lying J = 5/2 multiplet state (⁶H_5/2).