An energy storage stack of at least two surface-mediated cells (SMCs) internally connected in parallel or in series. The stack includes: (A) At least two SMC cells, each consisting of (i) a cathode comprising a porous cathode current collector and a cathode active material; (ii) a porous anode current collector; and (iii) a porous separator disposed between the cathode and the anode; (B) A lithium-containing electrolyte in physical contact with all the electrodes, wherein the cathode active material has a specific surface area no less than 100 m2/g in direct physical contact with the electrolyte to receive lithium ions therefrom or to provide lithium ions thereto; and (C) A lithium source. This new-generation energy storage device exhibits the highest power densities of all energy storage devices, much higher than those of all the lithium ion batteries, lithium ion capacitors, and supercapacitors.