A rechargeable alkali metal-sulfur cell selected from lithium-sulfur cell, sodium-sulfur cell, or potassium-sulfur cell The alkali metal-sulfur cell comprises an anode active material layer, an optional anode current collector supporting the anode active material layer, a cathode active material layer, an electrolyte with an optional porous separator layer in ionic contact with the anode active material layer and the cathode active material layer, and an optional cathode current collector supporting the cathode active material layer, wherein the cathode active material layer contains a graphite or carbon material having expanded inter-graphene planar spaces with an inter-planar spacing d002 from 0.43 nm to 2.0 nm, as measured by X-ray diffraction, and 1%-95% by weight of sulfur or a metal polysulfide residing in these expanded inter-graphene planar spaces. This battery exhibits an excellent combination of high sulfur content, high sulfur utilization efficiency, high energy density, and long cycle life.