Experimental measurement of the intrinsic excitonic wave function

Michael K L Man; Julien Madéo; Chakradhar Sahoo; Kaichen Xie; Marshall Campbell; Vivek Pareek; Arka Karmakar; E Laine Wong; Abdullah Al-Mahboob; Nicholas S Chan; David R Bacon; Xing Zhu; Mohamed M M Abdelrasoul; Xiaoqin Li; Tony F Heinz; Felipe H da Jornada; Ting Cao; Keshav M Dani

doi:10.1126/sciadv.abg0192

Experimental measurement of the intrinsic excitonic wave function

Sci Adv. 2021 Apr 21;7(17):eabg0192. doi: 10.1126/sciadv.abg0192. Print 2021 Apr.

Authors

Michael K L Man¹, Julien Madéo¹, Chakradhar Sahoo^{1

2}, Kaichen Xie³, Marshall Campbell⁴, Vivek Pareek¹, Arka Karmakar¹, E Laine Wong¹, Abdullah Al-Mahboob¹, Nicholas S Chan¹, David R Bacon¹, Xing Zhu¹, Mohamed M M Abdelrasoul¹, Xiaoqin Li⁴, Tony F Heinz^{5

6}, Felipe H da Jornada⁷, Ting Cao^{3

5}, Keshav M Dani⁸

Affiliations

¹ Femtosecond Spectroscopy Unit, Okinawa Instittute of Science and Technology Graduate University, Onna, Okinawa, Japan 904 0495.
² School of Physics, University of Hyderabad, Gachibowli, Hyderabad, 500046 Telangana, India.
³ Department of Materials Science and Engineering, University of Washington, Seattle, WA 98195, USA.
⁴ Physics Department, Center for Complex Quantum System, The University of Texas at Austin, Austin, TX 78712, USA.
⁵ Department of Applied Physics, Stanford University, Stanford, CA 94305, USA.
⁶ SLAC National Accelerator Laboratory, Menlo Park, CA 94720, USA.
⁷ Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305, USA.
⁸ Femtosecond Spectroscopy Unit, Okinawa Instittute of Science and Technology Graduate University, Onna, Okinawa, Japan 904 0495. kmdani@oist.jp.

Abstract

An exciton, a two-body composite quasiparticle formed of an electron and hole, is a fundamental optical excitation in condensed matter systems. Since its discovery nearly a century ago, a measurement of the excitonic wave function has remained beyond experimental reach. Here, we directly image the excitonic wave function in reciprocal space by measuring the momentum distribution of electrons photoemitted from excitons in monolayer tungsten diselenide. By transforming to real space, we obtain a visual of the distribution of the electron around the hole in an exciton. Further, by also resolving the energy coordinate, we confirm the elusive theoretical prediction that the photoemitted electron exhibits an inverted energy-momentum dispersion relationship reflecting the valence band where the partner hole remains, rather than that of conduction band states of the electron.

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