Phonon assisted absorption in Transition Metal Dichalcogenide heterostructures

Abstract

The coupling of atomic vibrations to electronic excitations - traditionally understood to be a source of energy loss in semiconductors - has recently been explored in photosynthetic light harvesting as a means to circumvent dissipation by harnessing quantum vibronic coherence. Motivated by recent photocurrent measurements of vibronic sidebands in WSe$_2$/MoSe$_2$ optoelectronic devices, we present a nonperturbative theoretical framework for phonon-assisted absorption in van der Waals heterostructures. Using a polaron transformation, a closed-form expression for the optical absorption spectrum at arbitrary temperatures is presented. Our model includes both intraband and interband electron--phonon coupling. Detailed analysis shows that the observed periodic sidebands originate from the strong coupling between interlayer excitons and nearly dispersionless optical phonon modes. Comparing two limiting cases - one involving only intraband couplings, and another incorporating coherent interband processes - we show that interband phonon-assisted transitions are needed to account for the observed data. Beyond enabling the direct estimation of vibronic coupling strengths from spectroscopic data, these findings have profound consequences for our understanding of optical and optoelectronic responses: coherent interband coupling of atomic vibrations to excitons is essential to quantifying photoresponse in transition metal dichalcogenide heterostructures.

Figures (6)

• Figure 1: (a) Schematic of interlayer excitons formed via $K\rightarrow K$ and $\Gamma\rightarrow K$ transitions in WSe$_2$/MoSe$_2$ heterostructure. (b) Device layout showing layered structure, graphene gate, and contacts. Reproduced with permission from Ref. [PhononData].
• Figure 2: Photocurrent spectra revealing periodic vibronic sidebands. (a) Spectrum associated with $K \rightarrow K$ interlayer excitons, showing a series of regularly spaced absorption peaks separated by approximately 30 meV. (b) Gate-dependent photocurrent $I_{\text{PC}}$ near the $\Gamma \rightarrow K$ interlayer exciton resonance, also exhibiting periodic sidebands with similar spacing. Reproduced with permission from Ref. [PhononData].
• Figure 3: Phonon band structure of the heterostructure. The boxed region highlights nearly dispersionless optical phonon modes around 30 meV, which mediate electron–phonon coupling. Reproduced with permission from Ref. [PhononData].
• Figure 4: Schematic interaction vertices for electron–phonon coupling processes relevant to our models. (a) Model I includes only intraband phonon-assisted processes, where electrons scatter within the conduction or valence band at fixed valley while emitting or absorbing a phonon. (b) Model II additionally incorporates interband phonon-assisted transitions between the conduction and valence bands near either the $K$ or $\Gamma$ point. The Hermitian conjugate process is implied but not shown.
• Figure 5: (a) Weight functions $W(\theta)$ for various $\widetilde{G}$ values. (b) Contour plot of $\widetilde{G}$ in the $(T/\Omega,|g|)$ plane. Here $T$ and $\Omega$ are both measured in eV.