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A First-principles Study of Weyl Nodal Loop and Multiple Sets of Weyl Points in Trigonal PtBi$_2$

Coexistence of surface superconductivity and Fermi arcs in trigonal $γ$-PtBi$_2$ has recently attracted attention for possible realization of topological superconductivity. The Fermi arcs on the two different (0001) surface terminations have been associated with the set of Weyl points just above the Fermi energy (E$_F$). Here using first-principles calculations to explore the band crossings over the full Brillouin zone between the nominally highest valence and lowest conduction bands in $γ$-PtBi$_2$, we find a Weyl nodal loop (WNL) and multiple sets of Weyl points (WPs). The main difference between the two reported experimental structural parameters is the magnitude of Bi-layer buckling. While the WNL, bulk gap region and the set of Weyl points just above the E$_F$ are robust, the number and location of the other sets of WPs depend sensitively on the structural parameters with different magnitude of Bi-layer buckling. Besides calculating the 2D Fermi surface with Fermi arcs and quasi-particle interference (QPI) around the E$_F$ in good agreements with ARPES and experimental QPI, we also predict new Fermi arc features at higher energy.