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We performed comprehensive theoretical and experimental studies of theelectronic structure and the Fermi surface topology of two novel quantummaterials, MoSi$_2$ and WSi$_2$. The theoretical predictions of the electronicstructure in the vicinity of the Fermi level was verified experimentally bythorough analysis of the observed quantum oscillations in both electricalresistivity and magnetostriction. We established that the Fermi surface sheetsin MoSi$_2$ and WSi$_2$ consist of 3D dumbbell-shaped hole-like pockets androsette-shaped electron-like pockets, with nearly equal volumes. Based on thisfinding, both materials were characterized as almost perfectly compensatedsemimetals. In conjunction, the magnetoresistance attains giant values of$10^4$ and $10^5\,\%$ for WSi$_2$ and MoSi$_2$, respectively. In turn, theanisotropic magnetoresistance achieves $-95$ and $-98\,\%$ at $T=2\,$K and in$B=14\,$T for WSi$_2$ and MoSi$_2$, respectively. Furthermore, for bothcompounds we observed the Shoenberg effect in their Shubnikov-de Haasoscillations that persisted at as high temperature as $T=25\,$K in MoSi$_2$ and$T=12\,$K in WSi$_2$. In addition, we found for MoSi$_2$ a rarely observedspin-zero phenomenon. Remarkably, the electronic structure calculationsrevealed type-II Dirac cones located near 480 meV and 710 meV above the Fermilevel in MoSi$_2$ and WSi$_2$, respectively.

physical review. b./physical review. b

Giant magnetoresistance, Fermi surface topology, Shoenberg effect and  vanishing quantum oscillations in type-II Dirac semimetal candidates MoSi$_2$  and WSi$_2$