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Pressure-induced concomitant topological and metal-insulator quantum phase transitions in Ce$_3$Pd$_3$Bi$_4$

The electronic property and magnetic susceptibility of Ce$_3$Pd$_3$Bi$_4$ were systemically investigated from 18 K to 290 K for varying values of cell-volume using dynamic mean-field theory coupled with density functional theory. By extrapolating to zero temperature, the ground state of Ce$_3$Pd$_3$Bi$_4$ at ambient pressure is found to be a correlated semimetal due to insufficient hybridization. Upon applying pressure, the hybridization strength increases and a crossover to Kondo insulator is observed at finite temperatures. The characteristic temperature signaling the formation of Kondo singlet, as well as the characteristic temperature associated with $f$-electron delocalization-localization change, simultaneously vanishes around a critical volume of 0.992$V_0$, suggesting that such metal-insulator transition is possibly associated with a quantum critical point. Finally, the Wilson's loop calculations indicate that the Kondo insulating side is topologically trivial, thus a topological transition also occurs across the quantum critical point.