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A delicate tension complicates the relationship between the topologicalmagnetoelectric effect in three-dimensional $\mathbb{Z}_2$ topologicalinsulators (TIs) and time-reversal symmetry (TRS). TRS underlies a particular$\mathbb{Z}_2$ topological classification of the electronic ground state of abulk insulator and the associated quantization of the magnetoelectriccoefficient calculated using linear response theory, but according to standardsymmetry arguments simultaneously forbids any physically meaningfulmagnetoelectric response. This tension between theories of magnetoelectricresponse in bulk and finite-sized materials originates from the distinctapproaches required to introduce notions of polarization and orbitalmagnetization in those fundamentally different environments. In this work weargue for a modified interpretation of the bulk linear response calculations innon-magnetic TIs that is more plainly consistent with TRS, and use thisinterpretation to discuss the effect's observation - still absent over a decadeafter its prediction. Our analysis is reinforced by microscopic bulk and thinfilm calculations carried out using a simplified but still realistic model forthe well established V$_2$VI$_3$ (V $=$ (Sb,Bi) and VI $=$ (Se,Te)) family ofnon-magnetic $\mathbb{Z}_2$ TIs. We conclude that the topologicalmagnetoelectric effect in non-magnetic $\mathbb{Z}_2$ TIs is activated bymagnetic surface dopants, and that the charge density response to magneticfields and the orbital magnetization response to electric fields in a givensample are controlled in part by the configuration of those dopants.

Reconciling magnetoelectric response and time-reversal symmetry in non-magnetic $\mathbb{Z}_2$ topological insulators