  In this paper we study the effects of a topological Weyl semimetal (WSM) upon
the ground state and polarization of an hydrogen-like atom near its surface.
The WSM is assumed to be in the equilibrium state and at the neutrality point,
such that the interaction between the atomic charges and the material is fully
described (in the non retarded regime) by axion electrodynamics, which is an
experimentally observable signature of the anomalous Hall effect in the bulk of
the WSM. The atom-WSM interaction provides additional contributions to the
Casimir-Polder potential thus modifying the energy spectra and wave function,
which now became distance dependent. Using variational methods, we solve the
corresponding Schr\"{o}dinger equation for the atomic electron. The ground
state and the polarization are analyzed as a function of the atom-surface
distance, and we directly observe the effects of the nontrivial topology of the
material by comparing our results with that of a topologically trivial sample.
We also study the impact of the medium's permittivity by assuming a hydrogen
atom in vacuum, and a donor impurity in the semiconductors gallium arsenide
(GaAs) and gallium phosphide (GaP). We found that the topological interaction
behaves as an effective-attractive charge so that the electronic cloud tends to
be polarized to the interface of materials. Moreover, the loss of wave-function
normalization is interpreted as a critical location from below which the bound
state is broken.
