Hourglasslike nodal net semimetal in Ag2BiO3

Based on first-principles calculations and analysis of crystal symmetries, we propose a kind of hourglasslike nodal net (HNN) semimetal in centrosymmetric Ag2BiO3 that is constructed by two hourglasslike nodal chains 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 HNNs [T. Bzdugek et al., Nature (London) 538, 75 (2016)] where the SOC and double group 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 toruslike electron pocket and a toruslike 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 a weak-SOC effect is taken into consideration, this HNN structure will be slightly broken, leaving a pair of hourglasslike Dirac points at the twofold screw axis. This type of hourglasslike Dirac semimetal is symmetry enforced and does not need band inversion anymore. Our discovery provides a platform to study novel topological semimetal states from nonsymmorphic symmetries.