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Bond-breaking Induced Lifshitz Transition in Robust Dirac Semimetal $\mathbf{VAl_3}$

Topological electrons in semimetals are usually vulnerable to chemical doping and environment change, which restricts their potential application in future electronic devices. In this paper we report that the type-II Dirac semimetal $\mathbf{VAl_3}$ hosts exceptional, robust topological electrons which can tolerate extreme change of chemical composition. The Dirac electrons remain intact even after a substantial part of V atoms have been replaced in the $\mathbf{V_{1-x}Ti_xAl_3}$ solid solutions. This Dirac semimetal state ends at $x=0.35$ where a Lifshitz transition to $p$-type trivial metal occurs. The V-Al bond is completely broken in this transition as long as the bonding orbitals are fully depopulated by the holes donated from Ti substitution. In other words, the Dirac electrons in $\mathbf{VAl_3}$ are protected by the V-Al bond whose molecular orbital is their bonding gravity center. Our understanding on the interrelations among electron count, chemical bond and electronic properties in topological semimetals suggests a rational approach to search robust, chemical-bond-protected topological materials.