The present disclosure includes a sulfur-carbon nanotube composite comprising a sheet of carbon nanotubes and sulfur nucleated upon the carbon nanotubes, and methods for synthesizing the same. In some embodiments, the sulfur-carbon composite may further be binder-free and include a sheet of carbon nanotubes, rendering a binder and a current collector unnecessary. In other embodiments of the present disclosure, a cathode comprising the sulfur-carbon nanotube composite is disclosed. In additional embodiments of the present disclosure, batteries may include the cathodes described herein. Those batteries may achieve high rate capabilities.