Topological Kondo insulators are a rare example of an interaction-enabled topological phase of matter in three-dimensional crystals - making them an intriguing but also hard case for theoretical studies. Here, we aim to advance their theoretical understanding by solving the paradigmatic two-band model for topological Kondo-insulators using a fully spin-rotation invariant slave-boson treatment. Within a mean-field approximation, we map out the magnetic phase diagram and characterize both antiferromagnetic and paramagnetic phases by their topological properties. Among others, we identify an antiferromagnetic insulator that shows, for suitable crystal terminations, topologically protected hinge modes. Furthermore, Gaussian fluctuations of the slave boson fields around their mean-field value are included in order to establish the stability of the mean-field solution through computation of the full dynamical susceptibility.
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