We report the magnetoresistance (MR), de Haas–van Alphen (dHvA) oscillations, and first-principles calculation studies on topological semimetal candidates ${\mathrm{Ba}X}_4$ $(X=\mathrm{Ga}, \mathrm{In})$. Large unsaturated MR that reaches $3\times {10}^3\%$ in ${\mathrm{BaGa}}_4$ and $4\times {10}^4\%$ in ${\mathrm{BaIn}}_4$ are observed, which is due to the carrier compensations and high mobility. Evident dHvA oscillations are detected with $B//\left[001\right]$ configuration, from which the quantum mobilities are extracted. The light cyclotron effective masses are extracted from the fitting of the thermal damping term in the LK formula. According to the first-principles calculations, ${\mathrm{Ba}X}_4$ possesses several Dirac points in the absence of spin-orbit coupling (SOC), some of which open negligible gaps when SOC is considered. The $Z_2$ invariants of ${\mathrm{Ba}X}_4$ are equal to 1, indicating the nontrivial topological properties.

• Received 13 April 2021
• Accepted 25 October 2021

DOI:https://doi.org/10.1103/PhysRevB.104.205119