A trion is a localized excitation which consists of three charged particles. A negative trion consists of two electrons and one hole and a positive trion consists of two holes and one electron. The trion itself is a quasiparticle and is somewhat similar to an exciton, which is a complex of one electron and one hole. The trion has a ground singlet state (spin S = 1/2) and an excited triplet state (S = 3/2). Here singlet and triplet degeneracies originate not from the whole system but from the two identical particles in it. The half-integer spin value distinguishes trions from excitons in many phenomena; for example, energy states of trions, but not excitons, are split in an applied magnetic field. Trion states were predicted theoretically in 1958;[1] they were observed experimentally in 1993 in CdTe/Cd1−xZnxTe quantum wells,[2] and later in various other optically excited semiconductor structures.[3][4] There are experimental proofs of their existence in nanotubes[5] supported by theoretical studies.[6] Despite numerous reports of experimental trion observations in different semiconductor heterostructures, there are serious concerns on the exact physical nature of the detected complexes. The originally foreseen 'true' trion particle has a delocalized wavefunction (at least at the scales of several Bohr radii) while recent studies reveal significant binding from charged impurities in real semiconductor quantum wells.[7]

Trions have been observed in atomically thin two-dimensional (2D) transition-metal dichalcogenide semiconductors.[8][9] In 2D materials the form of the interaction between charge carriers is modified by the nonlocal screening provided by the atoms in the layer. The interaction is approximately logarithmic at short range and of Coulomb 1/r form at long range.[10] The diffusion Monte Carlo method has been used to obtain numerically exact results for the binding energies of trions in 2D semiconductors within the effective mass approximation.[11][12][13]

References

  1. ^ Lampert, Murray A. (1958). "Mobile and Immobile Effective-Mass-Particle Complexes in Nonmetallic Solids". Physical Review Letters. 1 (12): 450–453. Bibcode:1958PhRvL...1..450L. doi:10.1103/PhysRevLett.1.450.
  2. ^ Kheng, K.; Cox, R. T.; d' Aubigné, Merle Y.; Bassani, Franck; Saminadayar, K.; Tatarenko, S. (1993). "Observation of negatively charged excitons X− in semiconductor quantum wells". Physical Review Letters. 71 (11): 1752–1755. Bibcode:1993PhRvL..71.1752K. doi:10.1103/PhysRevLett.71.1752. PMID 10054489.
  3. ^ Moskalenko, S. A.; et al. (2000). Bose-Einstein condensation of excitons and biexcitons: and coherent nonlinear optics with excitons. Cambridge University Press. p. 140. ISBN 0-521-58099-4.
  4. ^ Bimberg, Dieter (2008). Semiconductor Nanostructures. Springer. pp. 243–245. ISBN 978-3-540-77898-1.
  5. ^ Matsunaga, R.; Matsuda, K.; Kanemitsu, Y. (2011). "Observation of Charged Excitons in Hole-doped Carbon Nanotubes Using Photoluminescence and Absorption Spectroscopy". Phys. Rev. Lett. 106 (37404): 1. arXiv:1009.2297. Bibcode:2011PhRvL.106c7404M. doi:10.1103/PhysRevLett.106.037404. PMID 21405298. S2CID 19049386.
  6. ^ Marchenko, Sergey (2012). "Stability of Trionic States in Zigzag Carbon Nanotubes". Ukr. J. Phys. 57: 1055–1059. arXiv:1211.5754. Bibcode:2012arXiv1211.5754M.
  7. ^ Solovyev, V.V.; Kukushkin, I.V. (2009). "Measurement of binding energy of negatively charged excitons in GaAs/Al0.3Ga0.7As quantum wells". Phys. Rev. B. 79 (23): 233306. arXiv:0906.5612. Bibcode:2009PhRvB..79w3306S. doi:10.1103/PhysRevB.79.233306. S2CID 119099596.
  8. ^ Ross, J.S.; et al. (2013). "Electrical control of neutral and charged excitons in a monolayer semiconductor". Nat. Commun. 4: 1474. arXiv:1211.0072. Bibcode:2013NatCo...4.1474R. doi:10.1038/ncomms2498. PMID 23403575. S2CID 9872370.
  9. ^ Mak, K.F.; et al. (2013). "Tightly bound trions in monolayer MoS2". Nat. Mater. 12 (3): 207–211. arXiv:1210.8226. Bibcode:2013NatMa..12..207M. doi:10.1038/nmat3505. PMID 23202371. S2CID 205408065.
  10. ^ Keldysh, L.V. (1979). "Coulomb interaction in thin semiconductor and semimetal films". JETP. 29: 658.
  11. ^ Ganchev, B.; et al. (2015). "Three-Particle Complexes in Two-Dimensional Semiconductors". Phys. Rev. Lett. 114 (10): 107401. arXiv:1408.3981. Bibcode:2015PhRvL.114j7401G. doi:10.1103/PhysRevLett.114.107401. PMID 25815964. S2CID 36635305.
  12. ^ Mayers, M.Z.; et al. (2015). "Binding energies and spatial structures of small carrier complexes in monolayer transition-metal dichalcogenides via diffusion Monte Carlo". Phys. Rev. B. 92 (16): 161404. arXiv:1508.01224. Bibcode:2015PhRvB..92p1404M. doi:10.1103/PhysRevB.92.161404. S2CID 118607038.
  13. ^ Szyniszewski, M.; et al. (2017). "Binding energies of trions and biexcitons in two-dimensional semiconductors from diffusion quantum Monte Carlo calculations". Phys. Rev. B. 95 (8): 081301(R). arXiv:1701.07407. Bibcode:2017PhRvB..95h1301S. doi:10.1103/PhysRevB.95.081301. S2CID 17859387.
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