Resonant enhancement of Raman scattering in a MoS${}_2$ nanotube

Abstract

The whispering-gallery modes confined in the wall of a multiwall MoS${}_2$ nanotube resonantly enhance the spontaneous Raman scattering by its own optical phonons. The enhancement is doubly resonant --- pump and Stokes waves hit two adjacent modes at one pump energy, and the signal scales as $(Q_{\mathrm{pump}}{Q}_{\mathrm{sc}}{)}^2$ - whenever a phonon energy matches the free spectral range of the mode ladder. Near the A exciton the excitonic dispersion compresses the ladder and sweeps its spacing through all intralayer phonon energies of MoS${}_2$, so the match, reached for $A_{1g}$ at $E_{\mathrm{pump}}=1551$~meV, requires no geometric tuning. A missed match splits the excitation peak into a pump- and a scattered-resonant doublet whose splitting measures the residual detuning. Selection rules confine the double resonance to the TM$\to$TM channel and exclude $E_{1g}$.