Weakly damped bosons and precursor gap in the vicinity of an antiferromagnetic metallic transition

We study the electronic spectral function of a metal in the vicinity of an antiferromagnetic (AFM) quantum critical point, focusing on a situation where the bare bandwidth of the spin fluctuations is significantly smaller than the Fermi energy. In this limit, we identify a range of energies where the fermionic quasiparticles near the "hot spots"on the Fermi surface are strongly scattered by the quantum critical fluctuations, whereas the damping of the AFM fluctuations by the electrons is negligible. Within a one-loop approximation, there is a parameter range where the T=0 spectral function at the hot spots has a "precursor gap"feature, with a local maximum at a finite frequency. However, we find that the ratio of the bare spin-wave velocity to the Fermi velocity required to obtain a precursor gap is smaller by about an order of magnitude than the value in the electron-doped cuprate superconductors. Hence, our results cannot easily account for the recent angle-resolved photoemission experiments in this system [He, Proc. Natl. Acad. Sci. USA 116, 3449 (2019)0027-842410.1073/pnas.1816121116]. At lower frequencies, the Landau damping of the AFM fluctuations becomes important, and the electronic spectral function has the familiar ω-1/2 singularity. Our one-loop perturbative results are supported by a numerical Monte Carlo simulation of electrons coupled to an undamped, nearly critical AFM mode.