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Composite Boson Description of a Low-Density Gas of Excitons

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Abstract

Ground-state properties of a fermionic Coulomb gas are calculated using the fixed-node diffusion Monte Carlo method. The validity of the composite boson description is tested for different densities. We extract the exciton–exciton s-wave scattering length by solving the four-body problem in a harmonic trap and mapping the energy to that of two trapped bosons. The equation of state is consistent with the Bogoliubov theory for composite bosons interacting with the obtained s-wave scattering length. The perturbative expansion at low density has contributions physically coming from (a) exciton binding energy, (b) mean-field Gross–Pitaevskii interaction between excitons, and (c) quantum depletion of the excitonic condensate (Lee–Huang–Yang terms for composite bosons). In addition, for low densities we find a good agreement with the Bogoliubov bosonic theory for the condensate fraction of excitons. The equation of state in the opposite limit of large density is found to be well described by the perturbative theory including (a) mixture of two ideal Fermi gases and (b) exchange energy. We find that for low densities both energetic and coherent properties are correctly described by the picture of composite bosons (excitons).

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Acknowledgements

Pierbiagio Pieri and Alexander Fetter are acknowledged for useful discussions about the expansion of the equation of state for a weakly interacting Fermi gas. We acknowledge partial financial support from the MICINN (Spain) Grant No. FIS2014-56257-C2-1-P. Yu. E. Lozovik was supported by RFBR. The authors thankfully acknowledge the computer resources at MareNostrum and the technical support provided by Barcelona Supercomputing Center (FI-2017-2-0011). The authors gratefully acknowledge the Gauss Centre for Supercomputing 3.V. (www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (LRZ, www.lrz.de).

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Authors and Affiliations

  1. Yandex, ulitsa Lva Tolstogo 16, Moscow, Russia, 119021

    A. E. Golomedov

  2. Institute of Spectroscopy RAS, Troitsk, Moscow, Russia, 108840

    Yu. E. Lozovik

  3. Departament de Física, Universitat Politècnica de Catalunya, 08034, Barcelona, Spain

    G. E. Astrakharchik & J. Boronat

Authors
  1. A. E. Golomedov
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  2. Yu. E. Lozovik
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  3. G. E. Astrakharchik
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  4. J. Boronat
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Correspondence to G. E. Astrakharchik.

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Golomedov, A.E., Lozovik, Y.E., Astrakharchik, G.E. et al. Composite Boson Description of a Low-Density Gas of Excitons. J Low Temp Phys 189, 300–311 (2017). https://doi.org/10.1007/s10909-017-1814-y

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  • DOI: https://doi.org/10.1007/s10909-017-1814-y

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