Observation Of Excitonic n-Strings in a Quasi-One-Dimensional Charge-Transfer Crystal
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ABSTRACT Collective excitations, such as plasmons, rotons, electron-hole liquid, and excitonic molecules, have been extensively studied in condensed matter.I Wannier excitons in inorganic semiconductors are bound by the exchange interactions between two electrons of the exciton, and the bound state of more than two excitons is not possible. We demonstrate here a new type of collective excitations, 2 bound states of multiple charge-transfer (CT) excitons. Coulomb interactions in one dimension are shown to bind a train of several (more than two) CT excitons. Experimental evidence for these new type of elementary excitations is reported in a quasi-one-dimensional CT crystal of anthracene PMDA. High density excitation by femtosecond light pulses generates multi-exciton chains, which we refer to as excitonic n-strings with n = 1, 2, 3, etc., along the stack axis of the crystal. Both the n = 2 excitonic string (biexciton) and the n = 3 string (tri-exciton) are observed. This report provides evidence for an n > 2 exciton chain in this system. 2 The stability of the n-string exciton is supported by our theoretical calculations based on the extended Hubbard Hamiltonian in one dimension. Anthracene pyromellitic-acid-dianhydride (PMDA) is a linear chain molecule consisting of alternately stacked aromatic donor and acceptor molecules. 3,4 Its interesting optical properties arise from a very strong and very sharp optical coupling to the chargetransfer (CT) state. In this paper, we show that the CT exciton can form multi-exciton complexes that are bound, i.e., energetically stable, and we observe their formation in an ultrafast pump-probe experiment. Fig. 1 shows the schematic energy level diagram of the system including the ground (Ig)) state of the donor (D) acceptor (A) chain and the excited states. With optical excitation at 2.271 eV, an electron is transferred from D to A, forming the I1-CT) state consisting of the strongly bound pair D+A-. In this electrostatic picture, the binding energy of the n-exciton string with energy En.er is simply
2n-k
2n,-1
-En n _CT = VI
Sk
k+1
683 Mat. Res. Soc. Symp. Proc. Vol. 328. ©1994 Materials Research Society
(1)
13-CT)
D A D+A- D÷A DWADA
ý2-CT)
DADA DA-D+A-DA
Il-CT)
DADA D+A-DA DA
jg)
DADADADADA
13-CT)
A
2-CT)
li-CT) '
g)
Figure 1: Schematic of the ground state and the n = 1,2, and 3 exciton states in a neutral CT solid, along with the associated photo-induced absorptions a and 13to the 2exciton and 3-exciton, and direct TPA to the 2-exciton (dashed arrows). i.e., the Madelung energy contribution of the fixed ionic chain, with V1 the Coulomb energy of one D+A- pair, and 2e is the CT energy. From Eq. (1), IEf._C-E(l.)-CTI decreases with n, and therefore we expect that exciton n-strings will be experimentally observed as photo-induced absorption (PA) corresponding to excitation of the n exciton to the n+1 exciton. The PA will be energetically below the n = 1 exciton absorption by an amount given by the binding energies. The expected induced absorptions were experimen
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