Giant magnetoresistance, Fermi-surface topology, Shoenberg effect, and vanishing quantum oscillations in the type-II Dirac semimetal candidates <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>MoSi</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>WSi</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>

We performed comprehensive theoretical and experimental studies of the electronic structure Fermi surface topology two novel quantum materials, MoSi$_2$ WSi$_2$. The predictions in vicinity level was verified experimentally by thorough analysis observed oscillations both electrical resistivity magnetostriction. established that sheets WSi$_2$ consist 3D dumbbell-shaped hole-like pockets rosette-shaped electron-like pockets, with nearly equal volumes. Based on this finding, materials were characterized as almost perfectly compensated semimetals. In conjunction, magnetoresistance attains giant values $10^4$ $10^5\,\%$ for MoSi$_2$, respectively. turn, anisotropic achieves $-95$ $-98\,\%$ at $T=2\,$K $B=14\,$T Furthermore, compounds we Shoenberg effect their Shubnikov-de Haas persisted high temperature $T=25\,$K $T=12\,$K addition, found a rarely spin-zero phenomenon. Remarkably, calculations revealed type-II Dirac cones located near 480 meV 710 above WSi$_2$,