  The pyrochlore lattice, a three-dimensional network of corner-sharing
tetrahedra, is a promising material playground for correlated topological
phases arising from the interplay between spin-orbit coupling (SOC) and
electron-electron interactions. Due to its geometrically frustrated lattice
structure, exotic correlated states on the pyrochlore lattice have been
extensively studied using various spin Hamiltonians in the localized limit. On
the other hand, the topological properties of the electronic structure in the
pyrochlore lattice have rarely been explored, due to the scarcity of pyrochlore
materials in the itinerant paramagnetic limit. Here, we explore the topological
electronic band structure of pyrochlore superconductor RbBi$_{2}$ using
angle-resolved photoemission spectroscopy. Thanks to the strong SOC of the Bi
pyrochlore network, we experimentally confirm the existence of
three-dimensional (3D) massless Dirac fermions enforced by nonsymmorphic
symmetry, as well as a 3D quadratic band crossing protected by cubic
crystalline symmetry. Furthermore, we identify an additional 3D linear Dirac
dispersion associated with band inversion protected by threefold rotation
symmetry. These observations reveal the rich non-trivial band topology of
itinerant pyrochlore lattice systems in the strong SOC regime. Through
manipulation of electron correlations and SOC of the frustrated pyrochlore
lattices, this material platform is a natural host for exotic phases of matter,
including the fractionalized quantum spin Hall effect in the topological Mott
insulator phase, as well as axion electrodynamics in the axion insulator phase.
