On the radiative width of site shift surface excitons

2 On the radiative width of site shift surface excitons 

The macroscopical surface excitons obtained when retardation is taken into account, i.e. surface polaritons, cannot spontaneously transform into bulk emitted photons. Therefore, surface polaritons are sometimes said to have zero radiation width (it goes without saying that a plane boundary without defects it implies). At the same time the Coulomb surface excitons and polaritons in two-dimensional crystals possess, as was shown in Ch. 4, the radiation width T To(A/27ra)2, where A is the radiation wavelength, a is the lattice constant, and To the radiative width in an isolated molecule. For example, for A=500 nm and a = 0.5 nm the factor (A/2-7Ta)2 2x 104, which leads to enormous increase of the radiative width. For dipole allowed transitions To 5x10 em, so that the value of T 10 cm-1 corresponds to picosecond lifetimes r = 2-kK/T x, 10 12s. 

The effect of a single SSSE transition on the bulk crystal reflection spectrum (top left) calculated for surface barrier hight S = 10, 150, and 200 cm-1. For outermost monolayer S = A/1 + //2). These calculated spectra are qualitatively identically to the measured b-polarized reflection spectra (Fig. 12.6 ) (adopted from (35)). 

For the sake of definiteness we assume that a state of SSSE is localized in the single crystallographic plane z = 0. Let this plane separate media with positive dielectric constants ei(w) (z 0) and 2(10) (z 0), respectively. We ignore an anisotropy in the plane z = 0 and assume that the dipole moment of the transition of the Coulomb 2D exciton is located in the plane z = 0. 

To consider this state when retardation is taken into account, the solutions of Maxwell s equations (12.1) should be obtained in the form (12.3) taking into account the presence of a surface polarization current j = P. Assuming that the x-axis is directed along the direction of the surface exciton wavevector (in this case k2 =0, k = k), we come to the conclusion that in this case the amplitudes of the fields Ex and Hy at z = 0 satisfy the conditions  

---