There are many materials which can show both battery and supercapacitor behavior and the study of these two application together is called supercapattery. The main aim of supercapattery is to match the performance between the supercapacitor and battery with optimized energy and power densities . The energy and power densities are key parameters to evaluate the performance of energy storage devices. The energy density value mainly depends on capacitance and potential window as well as the internal resistance of the device, which is represented in the following equation.
E=12CV2E=12CV2
where, E is the energy density and C and V are the capacitance and potential window of the device, respectively.
One of my material which I have studied for battery application is well known supercapacitor material. The paper is attached here.