Sideband fingerprint of the Leggett mode in terahertz two-dimensional coherent spectroscopy of multiband superconductors

Abstract

Collective modes of the superconducting condensate encode fundamental information on the pairing interaction, yet their direct detection remains experimentally challenging. In multiband superconductors, the Leggett mode, i.e., a coherent oscillation of the relative phase between two condensates, is Raman-active and couples to light only nonlinearly in ordinary situations. Here we show theoretically that terahertz two-dimensional coherent spectroscopy (2DCS) provides a direct fingerprint of the Leggett mode (with frequency $ω_L$) through sideband emission at the detection frequency $ω_t = ω_L\pmΩ$ ($Ω$ is the central frequency of the incident pulses) in the nonlinear 2D spectrum. The key insight is that the finite duration of the THz pulses is the physical mechanism that makes the mode accessible: the broad spectral content of a finite pulse provides the nonlinear frequency combinations needed to resonantly excite the mode at ωL without any prior knowledge of its value or tuning of external parameters. We demonstrate robustness of this signature against temperature and quasiparticle relaxation, and show that sweeping $Ω$ allows unambiguous identification of the Leggett mode.