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, i.e., remnant currents, have applications in petahertz logical gates. The remnant currents' strength strongly depends on the pulse shape. We develop an analytical formula that allows one to optimize the pulse shape for remnant current production; we predict remnant currents exceeding the values observed so far by up to five orders of magnitude. This can be achieved by using single-cycle pulses instead of the previously employed multicycle pulses. In fact, remnant currents can be almost as strong as the peak current under irradiation.