Hidden topological number of quadratic Dirac fermions in β-PbO2

Gapless topological phase, including Weyl, Dirac, and nodal line semimetals, has become an attractive research field in recent years. Some of them have been studied in elementary particle physics, while nodal line and quadratic Dirac semimetals are beyond. Among the latter category, nodal line semimetals have been well studied in the past decade, however, the quadratic Dirac semimetals are less discovered by experiments or first-principles calculations, and how to analyze the topological properties of a Dirac node itself remains elusive while highly desirable. In this work, we developed a new method to unravel a hidden topological invariance of quadratic Dirac fermion of β - Pb O 2 . Through density functional theory (DFT) and k ⋅ p model in this new approach, we predict that β - Pb O 2 hosts the quadratic Dirac node (QDN) with mirror Chern number 2 when spin–orbit coupling is included, surpassing previous studies of topological semimetals. Our work paves the route toward a new class of topological matter.