Surface Exciton States Research Articles

Theory of Surface Excitons in Molecular Crystals

A theory of surface excitons in molecular crystals is presented using the localized perturbation method. Conditions for the existence of surface excitons and the criterion to determine whether surface exciton states lie above or below bulk exciton states are given in terms of the enviromental shift term and the exciton transfer term within the nearest neighbour approximation. It is shown that localization energies of surface excitons are not sensitive to the crystal thickness. Densities of states for bulk and surface exciton states are calculated. The Davydov splitting of surface excitons is also evaluated.

On the calculation of surface exciton energies in molecular crystals

In this paper a general theory is established for surface exciton states in a molecular crystal. Starting from the bulk exciton formalism the pertubation caused by the surface is taken into account by introducing a perturbation matrix. Symmetry properties of the “surface exciton bands” are derived.

Surface, subsurface, and bulk exciton transitions of crystalline anthracene

The polarized reflection spectrum of the first singlet transition of crystalline anthracene at 2 °K is reported for light at near normal angles of incidence on the (001) face. The effect on the spectra of condensing small amounts of gases, transparent in the 400 nm region, has been studied and found to be a useful technique for differentiating surface from bulk exciton transitions. The optical properties of the bulk crystal have been calculated by a Kramers–Kronig transformation of the reflectivity data. The complex refractive index so obtained was used to calculate the effect of surface transitions on the bulk reflection spectrum using equations given by a microscopic theory of surface and bulk exciton states. The agreement between the calculated and experimental spectra is excellent. Model calculations show that the two-dimensional sums of excited state van der Waals interactions are of sufficient range to create a series of excitons localized on surface planes. It is also demonstrated that the reflectivity formulas of thin film optics and the microscopic surface exciton theory are equivalent. The reflection spectra of crystals coated with frozen deposits of air show the presence of a satellite minimum that upon further absorption of gas first grow more prominent at the expense of the original minimum and then are replaced by a single minimum with an even larger red shift. These observations appear to correspond to nucleation, growth, and coalescence of islands of the adsorbed molecules. The higher vibronic transitions are not effected by frozen gas films, except for one peak in the a spectrum that disappears. This peak is located at the position expected of the a-polarized factor group component of the surface state and as such provides new evidence for this assignment. A partial analysis of some of the higher vibronic transitions is presented based on the concepts of single-particle transitions embedded in bands of two-particle states.

Effect of solidified gas layers on the reflection spectra of anthracene crystals

Measurements are reported for the b-polarized reflection spectrum of anthracene crystals off the (001) face coated with solidified layers of some permanent gases. In the wavelength range 4020 to 3800 Å spanning the 0-0 vibronic transition to the first electronic state there are several narrow minima attributed to surface transitions. The minimum I at 3954 Å is shifted 11 Å to longer wavelengths by solidified air, whilst the rest of the spectrum exhibits little or no change. This red-shift, expecied for transitions to surface exciton states, is new evidence for the assignment of minimum I as such. In addition a new minimum at ca. 3985 Å has been observed on the long wavelength edge of the 0-0 b reflection band, very close to minimum II at 3984 Å.

Surface and bulk exciton transitions in the reflection spectrum of tetracene crystals

The reflection spectrum of the 0–0 component of the first singlet transition of tetracene crystal has been measured for temperatures ranging from 300 to 1.7 °K. A discontinuous change in the Davydov splitting occurs near 186 °K signifying the occurrence of a phase transition. At the lowest temperatures two anomalous reflectivity minima are observed inside the b-polarized stopping band that are very similar to structure in the corresponding reflection band of anthracene crystal. The reflectivity minima are tentatively assigned to transitions to surface exciton states lying approximately 5 cm−1 and 160 cm−1 above the b-polarized exciton transition at 5349 Å. The other structure within the reflection band is interpreted as a coupling of the polariton to vibrational modes of intra- and intermolecular origins.

Exciton surface states in molecular crystals

A new Hamiltonian partition method, used previously for cooperative excitations in molecular crystals, has been adopted for the treatment of surface exciton states in molecular crystals. The formation of surface excitons depends on the relative magnitude of the exciton transfer integrals, J terms, as compared to the environmental shift integrals, D terms. This was established for a sample calculation on a simple cubic molecular crystal. It was found that when the absolute value of the nearest neighbor D term exceeds the corresponding J term two localized states emerge for each value of a two dimensional wavevector. The two localized states are degenerate in the limit of an infinitely thick crystal. The localization of the surface states increases with an increase in the magnitude of the D term.

Theory of electromagnetic waves in a crystal with excitons

Light waves are considered the frequencies of which are close to or fall in a region of exciton absorption in a crystal. A relationship is obtained between polarization dipole moment of the crystal and electric field intensity; this relationship is not one of direct proportionality, as is usually assumed, but is expressed by a differential equation. For this reason the Maxwell equations are of a higher order and their solutions are more complex than the well-known ones which follow from the simple phenomenological theory. It is shown that a number of waves exists in the crystal all of which have the same frequency, polarization and direction but different refractive indices. This effect is different from double refraction and occurs also in isotropically polarizable (cubic) crystals. Existence of purely longitudinal electric waves in the crystal is proved. Surface exciton states, the analogues of surface electron states, are discussed.