Relative stability of excitonic complexes in quasi-one-dimensional semiconductors

Relative stability of excitonic complexes in quasi-one-dimensional semiconductors
Igor Bondarev
Math & Physics Department, North Carolina Central University, Durham, North Carolina, United States
ibondarev@nccu.edu
The (asymptotically exact) Landau-Herring approach [1,2] that was first implemented earlier in Ref.[3] to evaluate the biexciton binding energy in small-diameter carbon nanotubes (CNs), is now used to derive a universal asymptotic relationship between the lowest energy trion (charged exciton), biexciton and exciton binding energies in quasi-one-dimensional (1D) semiconductors. The model operates in terms of the under-barrier tunneling current between equivalent configurations of the system in the configuration space. It allows one to interpret theoretically and thus to understand some important relative stability peculiarities of neutral and charged exciton complexes in quasi-1D systems, such as why in semiconducting quantum wires the positive trion binding energy is less than the biexciton binding energy [4,5], whereas in CNs the binding energy of the trion (negative or positive) is greater than that of the biexciton [6-8]. For CNs with diameters ~1 nm, the model predicts the trion binding energy greater than that of the biexciton by a factor ~1.4 decreasing with the diameter, in reasonable agreement with the latest non-linear spectroscopy measurements of Refs.[7,8] [1.46 for the (6,5) CN and 1.42 for the (9,7) CN, respectively]. This research is supported by the US Department of Energy (DE-SC0007117). References: [1] L.D. Landau and E.M. Lifshitz, Quantum Mechanics (Pergamon, Oxford, 1991). [2] C. Herring, Rev. Mod. Phys. 34, 631 (1962). [3] I.V. Bondarev, Phys. Rev. B 83, 153409 (2011). [4] B. Szafran, et al., Phys. Rev. B 71, 235305 (2005). [5] H. Zhang, M. Shen, and J.-J. Liu, J. Appl. Phys. 103, 043705 (2008). [6] R. Matsunaga, K. Matsuda, and Y. Kanemitsu, Phys. Rev. Lett. 106, 037404 (2011). [7] B. Yuma, et al., Phys. Rev. B 87, 205412 (2013). [8] L. Colombier, et al., Phys. Rev. Lett. 109, 197402 (2013).