Excitonic Mechanism of Local Phase Transformations by Optical Pumping

Abstract

Transformations of cooperative electronic states by impacts of optical pumping and/or electrostatic doping is a new mainstream in physics of correlated systems. Here we present a semi-phenomenological modeling of spatio-temporal effects in a system where the light absorption goes through a channel creating the excitons—intra-molecular ones or bound electron–hole pairs—and finally the condensate of optical excitons feeds and stimulates phase transformations. Interacting with a near-critical order parameter and deformations, the excitons are subject to self-trapping. That locally enhances their density which can surpass a critical value to trigger the phase transformation, even if the mean density is below the required threshold. The model can be used e.g. as a simplified version of optically induced neutral-ionic transitions in organic chain compounds.

Appendix

The critical pumping n _c1=|ψ _c1|² can be found as a point where the following conditions are fulfilled:

$$\begin{aligned} &{W ( \eta, \psi ) = W ( \eta, \psi )\quad \mathrm{i}.\mathrm{e}.}\\ &{\frac{a}{2} \eta^{2} - \frac{b}{3} \eta^{3} + \frac{c}{4} \eta^{4} -\mathrm{g}\eta | \psi |^{2} =0,} \end{aligned}$$

$$\begin{aligned} &{\frac{\partial W}{\partial \eta} =a\eta- b \eta^{2} +c \eta^{3} - \mathrm{g} |\psi |^{2} =0,}\\ &{\frac{\partial^{2} W}{\partial \eta^{2}} =a- 2b\eta+3c \eta^{2} < 0} \end{aligned}$$

The critical value n _c2 for the absolute instability of the phase 1 is reached when the barrier merges the minimum corresponding the phase 1: η ₁=η _b =η _c2 at ∂W/∂η=0 and ∂ ² W/∂η ²=0. We find the position and the threshold pumping as

$$\begin{aligned} &{\eta_{c2} = \frac{b- \sqrt{b^{2} -3ac}}{3c},}\\ &{n_{c2} = \frac{9 abc +2 ( b^{2} - 3 ac ) ( \sqrt{b^{2} - 3 ac} - b ) - 2 b^{3}}{27 gc^{2}}} \end{aligned}$$

Choosing a=1, b=6, c=8.2, g=2, we obtain for the strong excitons’ repulsion (k=1): η _d =0.161, n _d ≈0.0186, and for the weak one (k=0.1): η _d =0.163, n _d =0.0181. For the second threshold, independently of k and g: η _c2=0.107, n _c2=0.0242.