  Weak topological insulators and Dirac semimetals are gapped and nodal phases
with distinct topological properties, respectively. Here, we propose a novel
topological phase that exhibits features of both and is dubbed composite Dirac
semimetal (CDSM). In its bulk, the CDSM has a pair of Dirac points and a pair
of bands inverted along a high-symmetry path. At side surfaces, a pair of Fermi
arcs connecting the projected Dirac points coexist with a pair of Fermi loops
traversing the surface Brillouin zone. A nonsymmorphic symmetry dictates
degeneracies between the Fermi arcs and the Fermi loops. We characterize the
CDSM by multiple topological invariants and show that, under a transition
without breaking any symmetry, it deforms into a topological crystalline
insulator hosting two pairs of surface Fermi loops. We demonstrate the CDSM in
two models and predict its realization in the KAuTe-family materials.
