Exciton-exciton scattering: Composite boson versus elementary boson

This paper introduces a new quantum object, the ``coboson'', for composite particles, like the excitons, which are made of two fermions. Although commonly dealed with as elementary bosons, these composite bosons -- ``cobosons'' in short -- differ from them due to their composite nature which makes the handling of their many-body effects quite different from the existing treatments valid for elementary bosons. Due to this composite nature, it is not possible to correctly describe the interaction between cobosons as a potential $V$. Consequently, the standard Fermi golden rule, written in terms of $V$, cannot be used to obtain the transition rates between exciton states. Through an unconventional expression for this Fermi golden rule, which is here given in terms of the Hamiltonian only, we here give a detailed calculation of the time evolution of two excitons. We compare the results of this exact approach with the ones obtained by using an effective bosonic exciton Hamiltonian. We show that the relation between the inverse lifetime and the sum of transition rates for elementary bosons differs from the one of composite bosons by a factor of 1/2, whatever the mapping from composite bosons to elementary bosons is. The present paper thus constitutes a strong mathematical proof that, in spite of a widely spread belief, we cannot forget the composite nature of these cobosons, even in the extremely low density limit of just two excitons. This paper also shows the (unexpected) cancellation, in the Born approximation, of the two-exciton transition rate for a finite value of the momentum transfer

Proceedings of the Meeting and the workshop "Algebraic Geometry and Hodge Theory" Vol.I

Meeting:August23-28, 1989, Hokkaido University Workshop:November 28-December 1,1989,Kochi Universit

Proceedings of the Meeting and the workshop "Algebraic Geometru and Hodge Theory" Vol.II

Meeting:Augusy 23-28, Hokkaido Univetsity Workshop:November 28-December 1, 1989, Kochi Universit

Single-crystal growth of underdoped Bi-2223

To investigate the origin of the enhanced Tc ({\approx} 110 K) of the trilayer cuprate superconductor Bi2Sr2Ca2Cu3O10+{\delta} (Bi-2223), its underdoped single crystals are a critical requirement. Here, we demonstrate the first successful in-plane resistivity measurements of heavily underdoped Bi-2223 (zero-resistivity temperatures {\approx} 20~35 K). Detailed crystal growth methods, the annealing process, as well as X-ray diffraction (XRD) and magnetic susceptibility measurement results are also reported.Comment: 4 pages, 4 figures, 27th International Symposium on Superconductivity, ISS 2014, to appear in Physics Procedi