Distinguishing finite-momentum superconducting pairing states with two-electron photoemission spectroscopy

We show theoretically that double photoemission ($2e$-ARPES) may be used to identify the pairing state in superconductors in which the Cooper pairs have a nonzero center-of-mass momentum, ${\mathbf{q}}_{\mathrm{cm}}$. We theoretically evaluate the $2e$-ARPES counting rate ${P}^{(2)}$ for the cases of a ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductor, a pair-density-wave (PDW) phase, and a Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) phase. We show that ${P}^{(2)}$ provides direct insight into the center-of-mass momentum and spin state of the superconducting condensate, and thus can distinguish between these three different superconducting pairing states. In addition, ${P}^{(2)}$ can be used to map out the momentum dependence of the superconducting order parameter. Our results identify $2e$-ARPES as an ideal tool for identifying and probing ${\mathbf{q}}_{\mathrm{cm}}\ensuremath{\ne}0$ superconducting pairing states in superconductors.