Experimental indications have been reported suggesting that laser pulses shining on materials with relativistic dispersion can produce currents that survive long after the illumination has died out. Such residual currents ('remnants') have applications in petahertz logical gates. The remnants' strength strongly depends on the pulse-shape. We develop an analytical formula that allows to optimize the pulse-shape for remnant production; we predict remnants exceeding the values observed so far by orders of magnitude. In fact, remnants can be almost as strong as the peak current under irradiation.