  Trapping of microspheres with a single focused laser beam is usually limited
to materials with relative refractive indexes slightly larger than one. We show
that directional light scattering can be employed to optically trap high-index
materials. For this purpose, we propose a material platform to achieve zero
backward scattering (ZBS), also known as the first Kerker condition, in a
composite media containing spherical inclusions of silica embedded in a SiC
microsphere. By tuning the volume filling fraction of inclusions and the
microsphere radius, stable trapping can be achieved, provided that ZBS is
combined with the condition for destructive interference between the fields
reflected at the external and internal interfaces of the microsphere when
located at the focal point. We show that our proposal also holds even in the
presence of a significant amount of spherical aberration, which is a common
condition in most optical tweezers setups. In this case, achieving ZBS is
essential for trapping high-index materials.
