Lithium sulfur batteries are described, especially ones that are flexible for wearing about an appendage of a wearer. Such batteries have a lithium metal anode, a sulfur cathode comprising sulfur, a conductive carbon, a lithium supertonic solid-state conductor, and a dendritic or hyperbranched polymer binder, an electrolyte layer between the lithium metal anode and the sulfur cathode, and a current collector positioned on the sulfur cathode opposite the electrolyte layer.