A variety of disordered systems are studied in the group with different aims, perspectives and methods of solution, ranging from model Hamiltonians to realistic ab initio simulations. Some of the relevant topics un- der current study are summarized below.
Transport properties of organic semiconductors and devices
Crystalline organic semiconductors have been puzzling the scientific community for the last 50 years, and de- spite decades of active investigation there is still no well-established theory of charge transport. These materials exhibit a ‘‘bandlike’’ mobility characterized by a power-law decrease with temperature, but with absolute values close to the Mott-Ioffe-Regel limit, corresponding to mean free paths that are comparable or even lower than the intermolecular spacing. In this situation, neither the conventional bandlike description of wide-band inorganic semiconductors, nor the opposite localized picture where carriers hop classically from molecule to molecule apply.
In order to understand the transport mechanism of organic semiconductors and devices we have been developing an original scenario, termed “transient localization”, which identifies the thermal vibrations of the molecular lattice as the key factor limiting the carrier mobility. Molecular vibrations, that are seen by the electrons as a strong source of disorder, makes these systems prone to Anderson localization while at the same time allowing for a diffusive transport behavior. The duality embodied in the transient localization scenario has allowed us to give a natural explanation for several features experimentally observed in organic semiconductors such as the low values of the mobility, its power-law temperature dependence, its strong sensitivity to the electrostatic environment and to extrinsic sources of disorder, as well as the existence of a previously unexplained localization peak in the optical conductivity.
[Minder et al, Adv. Mater. 2014]
Models in statistical mechanics.
Potts models are generalizations of the famous Ising model, which have been introduced to modelize experi- mental situations not described by the original Ising model. These soon became also very interesting from the point of view of model studies. We have investigated the properties of the disordered Potts model in the particular case of an arbitrary large number of states, which makes exact calculations possible.
In high energy physics a model has been introduced which could be an effective model of the lattice quantum chromodynamics. In the so-called quenched approximation this model can be seen as a disordered particular lattice statistical mechanics model. We have shown using extensive Monte-Carlo simulations that this quenched approximation is not valid, and therefore a much more complicated model needs to be considered.
Experiments of sorption of helium in porous media have been performed at the Institut NEEL. These experiments include optical measurements and provide valuable information about the correlations in the fluid, in ad- dition to the usual thermodynamical measurements. We have developed a phenomenological model, in the spirit of percolation models, aimed at reproducing these experimental results. The goal is to disentangle the various contributions to the vaporization or liquefaction phenomena.
Phase diagram of the disordered Potts model on a hierarchical lattice, in polar logarithmic coordinates. The two parameters are temperature and disorder. These results suggest that in proximity of the ti-critical point, the phase diagram is self-similar.