Steady--State Current Signatures of Strong Light--Matter Coupling in Single--Molecule Junctions

Strong light-matter coupling offers exciting opportunities for controlling molecular properties, yet resolving single-molecule behavior from collective effects remains a challenge. Recent experiments in scanning tunneling microscope break junctions (STM-BJs) have demonstrated strong light-matter coupling at the single-molecule level. Because STM-BJs provide direct access to molecular-junction currents, we investigate whether strong coupling leaves a measurable fingerprint in transport, potentially probing polaritonic states beyond optical spectroscopy. Using a semiclassical mapping approach for nonequilibrium quantum transport, we find that steady-state current indeed carries a direct signature of single-molecule strong coupling. We test the robustness of this signature against electrode connectivity, nuclear motion, spatially structured electromagnetic modes, and solvent effects. While environmental factors and nuclear motion reshape the signature, the current is not a passive response but is actively influenced by coupled molecular dynamics. Our work establishes current as a tool to interpret and control strong light-matter interactions in nanoscale junctions.