  Topology establishes a unifying framework for a diverse range of scientific
areas including particle physics, cosmology, and condensed matter physics. One
of the most fascinating manifestations of topology in the context of condensed
matter is the topological Hall effect, and its relative: the Skyrmion Hall
effect. Skyrmions are stable vortex-like spin configurations in certain chiral
magnets, and when subject to external electric currents can drift in the
transverse direction to the current. These quasi-particles are characterised by
a conserved topological charge which in the Skyrmion Hall effect plays the role
of electric charges in the ordinary Hall effect. Recently, it has been shown
that liquid crystals endowed with chiral properties serve as an ideal testbed
for the fundamental investigation of topological solitons, including their two-
and three-dimensional realisations. Here, we show experimentally and
numerically that three-dimensional solitons aka "torons" exhibit a Hall-like
effect when driven by shear flows: the torons are deflected in the direction
perpendicular to the shear plane. The experimental results are rationalised in
terms of the dynamic Ericksen-Leslie equations, which predict the emergence of
the transverse component of the net mass flow, the magnitude of which scales as
the 3rd power of the shear rate. The perturbation analysis highlights an
interplay of the viscous and chiral elastic torques as the mechanism for the
emergence of net transverse currents. Numerical simulations demonstrate,
however, that torons are not merely dragged by the flow but move with their own
transverse speed, much larger than the average flow velocity in the transverse
direction. Our findings may enable responsive microfluidic applications relying
on soft topological solitons.
