Excitons in metals

From the theoretical point of view, there are two ways in which free carriers can affect exciton formation. 

The explanation of this peak is as follows. Suppose that the number of conduction electrons is small, so that the Coulomb field is not screened out and that a hole in the X-ray level creates an exciton level below the bottom of the conduction band. The levels are shown in Fig. 2.13. Then an exciton absorption line should be possible. But the sudden change in field will produce excitations of electrons at the Fermi level, so that the exciton line is broadened as shown in Fig. 2.14(a). Also, we do not expect a sharp increase in absorption when the electron jumps to the Fermi level, leaving the exciton level A in Fig. 2.13 unoccupied, because of the very large Auger broadening due to transitions from the Fermi level into this unoccupied state. 

As the number of electrons in the conduction band increases, the situation goes over continuously to that described by Nozieres and De Dominids and illustrated in Fig. 2.14(b). The peak is obtained as follows. At the moment in time when the transition occurs, the wave functions Xf) of all the other conduction electrons have to change to new functions which screen the positive charge left in the inner level. So the transition probability must be multiplied by the product 

This in general gives a logarithmic divergence, as shown by Nozieres and De Dominicis, so the transition probability is infinite. The exciton state, if one exists, is of course filled, and this model provides one description of the way the hole is screened (see Friedel 1952a, b). 

The question of whether the carriers screen the hole and so prevent the formation of any exciton level has not been discussed recently (see Cauchois and Mott 1949). Gearly this is a qualitative rather than an exact question, for the 

---

Sugawara Y, Keif TA, Baumberg JJ, Abdelsalam ME, Bartlett PN (2006) Strong coupling between localized plasmons and organic excitons in metal nanovoids. Phys Rev Lett 97 266808... 

Deslippe, J., Spataru, C. D., Prendergast, D., 8c Louie, S. G. (2007). Bound excitons in metallic single-walled carbon nanotubes. Nano Letters, 7, 1626-1630. 

---