  Spacetime inversion symmetry can generate intriguing types of spinless
excitations in crystalline materials. Here, we propose a topological phase
protected by spacetime inversion symmetry - the crossed real nodal line (RNL)
in the phonon spectrum of gold monobromide (AuBr). In AuBr, there exist four
straight nodal lines, which are linked by a crossed nodal line formed by two
lower bands. Remarkably, each adjacent two of the four straight nodal lines is
a pair, forming a crossed RNL with nontrivial real Chern number. Such
configuration and pairing mode of RNL have never been reported. The crossed RNL
exhibits unique surface and hinge states distinguished from that of the
conventional RNLs. The symmetry protection and the transformation under the
symmetry-preserving strain of the crossed RNL are also investigated. Our
results open the door to a new class of topological states, and predict its
realization in experimentally synthesized material.
