  Charge profiles in liquid electrolytes are of crucial importance for
applications, such as supercapacitors, fuel cells, batteries, or the
self-assembly of particles in colloidal or biological settings. However,
creating localised (screened) charge profiles in the bulk of such electrolytes,
generally requires the presence of surfaces -- for example, provided by
colloidal particles or outer surfaces of the material -- which poses a
fundamental constraint on the material design. Here, we show that topological
defects in nematic electrolytes can perform as regions for local charge
separation, forming charged defect cores and in some geometries even electric
multilayers, as opposed to the electric double layers found in isotropic
electrolytes. Using a Landau-de Gennes-Poisson-Boltzmann theoretical framework,
we show that ions highly effectively couple with the topological defect cores
via ion solvability, and with the local director-field distortions of the
defects via flexoelectricity. The defect charging is shown for different defect
types -- lines, points, and walls -- using geometries of ionically screened
flat isotropic-nematic interfaces, radial hedgehog point defects and
half-integer wedge disclinations in the bulk and as stabilised by (charged)
colloidal particles. More generally, our findings are relevant for possible
applications where topological defects act as diffuse ionic capacitors or as
ionic charge carriers.
