Fine structure of excitons inCu2O

Abstract

Three experimental observations on 1s-excitons in Cu2O are not consistent with the picture of the exciton as a simple hydrogenic bound state: the energies of the 1s-excitons deviate from the Rydberg formula, the total exciton mass exceeds the sum of the electron and hole effective masses, and the triplet-state excitons lie above the singlet. Incorporating the band structure of the material, we calculate the corrections to this simple picture arising from the fact that the exciton Bohr radius is comparable to the lattice constant. By means of a self-consistent variational calculation of the total exciton mass as well as the ground-state energy of the singlet and the triplet-state excitons, we find excellent agreement with experiment.

Variational discrete variable representation for excitons on a lattice

“…It could be identified as the lattice constant for realistic band dispersion, but should be considered as an effective model parameter in the present simple treatment, similar to Ref. 4.…”

“…Central-cell corrections become important, which account for the possibility of finding electron and hole in the same unit cell and include non-parabolic dispersions and modifications of the 1/r-Coulomb potential 4 . A prototypical material is the cuprous oxide Cu 2 O, which receives constant attention in the search for an excitonic Bose-Einstein condensate 5,6 .…”

Coherent manipulation of quadrupole biexcitons in cuprous oxide by 2D femtosecond spectroscopy

“…The exciton effective mass m 2 e =m 2 X ¼ 0:14, binding energy Ry 1S ¼ 153 meV and Bohr radius a X ¼ 5.1 A˚are given by the ''central cell correction'' model [1]. They are modified by non-parabolicity of the conduction and valence bands, the coupling of the exciton electron and hole with the longitudinal optical phonons and by the dielectric function dependence on the distance between the electron and hole.…”

“…The relatively large effective mass of the electrons in the conduction band (m e ) and holes in the valence band (m h ) results in a small exciton radius (a X ¼ 5.1 Å ), according to Kavoulakis [1] who considered ''central cell corrections.'' Equal parity of the conduction and valence band states produces dipole-forbidden, quadrupole-allowed 1S exciton which is characterized by a long radiative life-time depending on a dominating dephasing mechanism and varies from ns to ps.…”

Cuprous Oxide (Cu2O): A Unique System Hosting Various Excitonic Matter and Exhibiting Large Third-Order Nonlinear Optical Responses

“…Being a coherent quantum superposition of a quadrupole exciton and a photon, this electron in the lowest conduction band ( 2 Γ + 6 ) and a hole in the highest valence band ( 2 Γ + 7 ), and shows a hydrogenic Rydberg series in the optical absorption spectrum [Hayashi & Katsuki (1952)]. Including so-called central cell corrections [Kavoulakis et al (1997)], a spectroscopic fit to the observed Rydberg series reveals a tightly bound 1s excitonic state with a binding energy of 153 meV, corresponding to Bohr radius of 0.7 nm. The measured translational mass of the exciton is about 2.7m e ,wherem e is the electron mass ].…”