Generating functional approach for spontaneous coherence in semiconductor electron-hole-photon systems

Makoto Yamaguchi, Ryota Nii, Kenji Kamide, Tetsuo Ogawa, and Yoshihisa Yamamoto
Phys. Rev. B 91, 115129 – Published 16 March 2015

Abstract

Electrons, holes, and photons in semiconductors are interacting fermions and bosons. In this system, a variety of ordered coherent phases can be formed through the spontaneous phase symmetry breaking because of their interactions. The Bose-Einstein condensation (BEC) of excitons and polaritons is one of such coherent phases, which can potentially cross over into the Bardeen-Cooper-Schrieffer (BCS) type ordered phase at high densities under quasiequilibrium conditions, known as the BCS-BEC crossover. In contrast, one can find the semiconductor laser, superfluorescence (SF), and superradiance as relevant phenomena under nonequilibrium conditions. In this paper, we present a comprehensive generating functional theory that yields nonequilibrium Green's functions in a rigorous way. The theory gives us a starting point to discuss these phases in a unified view with a diagrammatic technique. Comprehensible time-dependent equations are derived within the Hartree-Fock approximation, which generalize the Maxwell-semiconductor-Bloch equations under the relaxation time approximation. With the help of this formalism, we clarify the relationship among these cooperative phenomena and we show theoretically that the Fermi-edge SF is directly connected to the e-h BCS phase. We also discuss the emission spectra as well as the gain-absorption spectra.

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  • Received 11 December 2014
  • Revised 13 February 2015

DOI:https://doi.org/10.1103/PhysRevB.91.115129

©2015 American Physical Society

Authors & Affiliations

Makoto Yamaguchi1,2,*, Ryota Nii1, Kenji Kamide3, Tetsuo Ogawa1,4, and Yoshihisa Yamamoto5,6

  • 1Department of Physics, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043, Japan
  • 2Center for Emergent Matter Science, RIKEN, Wakoshi, Saitama, 351-0198, Japan
  • 3Institute for Nano Quantum Information Electronics (NanoQuine), University of Tokyo, Tokyo 153-8505, Japan
  • 4Photon Pioneers Center, Osaka University, 2-1 Yamada-oka, Suita, Osaka 565-0871, Japan
  • 5E. L. Ginzton Laboratory, Stanford University, Stanford, California 94305, USA
  • 6ImPACT Program, Japan Science and Technology Agency, 7 Gobancho, Chiyoda-ku, Tokyo 102-0076, Japan

  • *makoto.yamaguchi@riken.jp

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Vol. 91, Iss. 11 — 15 March 2015

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