A numerical framework to calculate the height and potential of the vacuum inner gap of pulsars is presented here. The results demonstrate that small mountains on a pulsar’s polar cap tend to significantly influence the properties of the inner vacuum gap, making it easier for sparks to form. In this scenario, the magnetospheric activity observed from the pulsars PSR J0250+5854 and PSR J2144−3933, which lie below the traditional pulsar death line, and some single-pulse modulation phenomena could also then be understood. Furthermore, the presence of small mountains should depend on the puzzling state of supranuclear matter inside pulsars. In order to sustain stable mountains on the surface, pulsars might be made of solid strangeon matter, which is favored by both the charge neutrality and the flavor symmetry of quarks.