Pair-density-wave superconductivity constitutes a novel electronic condensate proposed to be realized in certain unconventional superconductors. Establishing its potential existence is important for our fundamental understanding of superconductivity in correlated materials. Here we compute the dynamical magnetic susceptibility in the presence of a pair-density-wave ordered state and study its fingerprints on the spin-wave spectrum including the neutron resonance. In contrast to the standard case of $d$-wave superconductivity, we show that the pair-density-wave phase exhibits neither a spin gap nor a magnetic resonance peak, in agreement with a recent neutron scattering experiment on underdoped ${\mathrm{La}}_{1.905}{\mathrm{Ba}}_{0.095}{\mathrm{CuO}}_4$ [Z. Xu et al., Phys. Rev. Lett. 113, 177002 (2014)].

• Received 13 January 2016

DOI:https://doi.org/10.1103/PhysRevLett.116.167001