Measurement of an excitonic wave function

Authors:
  • SDShuo Dong
    Shuo Dong
  • MPMichele Puppin
    Michele Puppin
  • TPTommaso Pincelli
    Tommaso Pincelli
  • SBSamuel Beaulieu
    Samuel Beaulieu
  • DCDominik Christiansen
    Dominik Christiansen
  • HHHannes Hubener
    Hannes Hubener
  • CNChristopher W. Nicholson
    Christopher W. Nicholson
  • RXR. Patrick Xian
    R. Patrick Xian
  • MDMaciej Dendzik
    Maciej Dendzik
  • YDYunpei Deng
    Yunpei Deng
  • YWYoav William Windsor
    Yoav William Windsor
  • MSMalte Selig
    Malte Selig
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Abstract
Excitons, Coulomb-bound electron-hole pairs, are the fundamental excitations governing optoelectronic properties of semiconductors. While optical signatures of excitons have been studied extensively, experimental access to the excitonic wave function itself has been elusive. Using multidimensional photoemission spectroscopy, we present a momentum-, energy- and time-resolved perspective on excitons in the layered semiconductor WSe$_2$. By tuning the excitation wavelength, we determine the energy-momentum signature of bright exciton formation and its difference from conventional single-particle excited states. The multidimensional data allows to retrieve fundamental exciton properties like the binding energy and the exciton-lattice coupling and to reconstruct the real-space excitonic wave function via Fourier transform. All quantities are in excellent agreement with microscopic calculations. Our approach provides a full characterization of the exciton wave function and is applicable to bright and dark excitons in semiconducting materials, heterostructures and devices.