  Based on first-principles calculation and analysis of crystal symmetries, we
propose a kind of hourglass-like nodal net (HNN) semimetal in centrosymmetric
Ag2BiO3 that is constructed by two hourglass-like nodal chains (HNCs) at
mutually orthogonal planes in the extended Brillouin zone (BZ) when the weak
spin-orbit coupling (SOC) mainly from the 6s orbital of Bi atoms is ignored.
The joint point in the nodal net structure is a special double Dirac point
located at the BZ corner. Different from previous HNN [Bzdusek et al., Nature
538, 75 (2016)] where the SOC and double groups nonsymmorphic symmetries are
necessary, and also different from the accidental nodal net, this HNN structure
is inevitably formed and guaranteed by spinless nonsymmorphic symmetries, and
thus robust against any symmetry-remaining perturbations. The Fermi surface in
Ag2BiO3 consisting of a torus-like electron pocket and a torus-like hole pocket
may lead to unusual transport properties. A simple four-band tight-binding
model is built to reproduce the HNN structure. For a semi-infinite Ag2BiO3 ,
the "drumhead" like surface states with nearly flat dispersions are
demonstrated on (001) and (100) surfaces, respectively. If such weak SOC effect
is taken into consideration, this HNN structure will be slightly broken, left a
pair of hourglass-like Dirac points at the two-fold screw axis. This type of
hourglass-like Dirac semimetal is symmetry-enforced and does not need band
inversion anymore. Our discovery provides a new platform to study novel
topological semimetal states from nonsymmorphic symmetries.
