Delocalization of tightly bound excitons in disordered systems

The localization length of a low energy tightly bound electron-hole pair (excitons) is calculated by exact diagonalization for small interacting disordered systems. The exciton localization length (which corresponds to the thermal electronic conductance) is strongly enhanced by electron-electron interactions, while the localization length (pertaining to the charge conductance) is only slightly enhanced. This shows that the two particle delocalization mechanism widely discussed for the electron pair case is more efficient close to the Fermi energy for an electron-hole pair. The relevance to experiment is also discussed. PACS numbers: 71.55.Jv,72.15.Rh,71.30.+h Typeset using REVTEX 1 Interacting electrons in random potentials are in the center of recent studies in mesoscopic systems because of their relevance to many different phenomena such as the Coulomb gap [1], persistent currents [2], the two-dimensional (2D) MIT (metal-insulator transition) [3], and delocalization of two particle states [2,4–6]. Although the subject of two particle state delocalization due to electron-electron (e-e) interaction has been the center of many recent studies [2], most of those studies concentrate on the situation of two particles in an empty band of a one-dimensional (1D) system. This is an idealized situation which is not very relevant to experimental systems. A more relevant situation, i.e. two excited electrons above the Fermi sea, was considered in Refs. [6,7]. In Ref. [7] it was shown that two electrons close to the Fermi energy show no enhancement in 1D systems. Nevertheless, it has been emphasized that the situation may be more favorable for higher dimensions [6], for which, up to now, only the empty band case was studied [8]. Recently it has been pointed out [9] that when the effect of the Coulomb gap is taken into account the two electron delocalization scenario becomes less likely. In this letter we consider a different type of two particle delocalization, namely the delocalization of a tightly bound electron-hole pair (strongly bound excitons). This exciton is analogous to the classical compact electron-hole pair excitations discussed in Ref. [1], which can transfer energy across the system but not charge. This is different from most previous discussion of two particle delocalization which were concerned with the charge conductance of the system. Thus, delocalization of the electron-hole will manifest itself in the enhancement of the heat conductance of the disordered system, an effect which can be measured in the laboratory. Indeed, the relevance of the two particle delocalization scenario to electron-hole pairs has been noted by Imry [6]. In Ref. [9] it was suggested that not only is the two particle localization length enhancement relevant to an electron-hole pair, it is also much more effective than for the two electron case, because of the Coulomb enhancement of the exciton density. This scenario will be verified in this letter by explicit calculation of the localization length. Moreover, the existence of delocalized excitons may have interesting consequences for low temperature hopping conductance, which will be discussed in more 2 details after presenting the evidence for the exciton localization length enhancement. Our study is based on the following interacting many-particle tight-binding Hamiltonian: