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Glassy properties of Anderson localization

par Gabriel LeMarié - 20 juin 2019

Disorder is often present in condensed matter, in the form of impurities in crystalline solids, or in the random structural arrangement of glasses. It can have dramatic consequences, such as preventing transport or inducing extremely slow relaxations to equilibrium (infinitely slow flow of glasses). In the quantum regime, where the wave nature of particles can not be neglected, Anderson localization arises from the effects of interference in the presence of disorder. It is a key mechanism of non-ergodicity, that is to say, the emergence of a very strong spatial inhomogeneity, in disordered quantum systems. Its most remarkable effects are, for example, the insulating nature of disordered materials. Anderson localization has been observed in many experimental situations, with classical waves or matter waves. Glassy physics is another paradigm of non-ergodic behaviors in disordered classical systems. A simple model, but with extremely rich physics, is the spin glass : a disordered magnet, where the magnetic moments of the constituent atoms (the spins) are not aligned in a regular way. The study of these glasses has led to important theoretical advances and has found many applications in biology or in optimization.

Few analogies have been established between Anderson localization and glassy physics : finite temperature transport (electron glass) or localization in some types of random graphs. In an article published in Physical Review Letters, a physicist from the Laboratory of Theoretical Physics (LPT, CNRS / University Toulouse Paul Sabatier) shows that quantum transport at zero temperature (perfectly coherent unlike the case of electron glass) in two-dimension follows characteristic properties of spin glasses in the localized regime. The results of numerical simulations show that Anderson localization confines the quantum transport along paths pinned by disorder, just as a river necessarily flows in a valley carved between two mountains. These paths are frozen in a configuration that does not move gradually when the system is perturbed, but sometimes perform an avalanche, that is to say jump suddenly in a very different configuration. The glassy property of chaos characterizes the extreme fragility of these glassy configurations : an infinitesimal perturbation, for example a slight change of energy, induces a complete reorganization of the paths taken by the transport. Finally, these glassy properties are crucially dependent on the effects of quantum interference. Anderson localization opens up a new playground for the study of quantum glassy physics, which could be explored experimentally in many systems, from condensed matter to cold atoms.

Figure : In strongly disordered two-dimensional samples, Anderson localization confines quantum transport along directed paths. These paths, for a given sample, are pinned by the disorder in a configuration that does not move when the energy E_F varies, except at certain E_F values where it performs an avalanche to a very different configuration. Thus, in the right panel representing the final position of these paths as a function of E_F, pinning is associated with plateaus while the avalanches correspond to sudden jumps. Pinning and avalanches are two characteristic properties of glassy physics. © LPT (CNRS / University Toulouse Paul Sabatier)

Reference : Glassy properties of Anderson localization : pinning, avalanches, and chaos. Gabriel Lemarié, Physical Review Letters 122, 030401 (2019).

Read the article on ArXiv and HAL open archive databases.

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Contact :Gabriel Lemarié