D. J. Priour Jr. | Searcharxiv

arXiv2009

Localization in one-dimensional incommensurate lattices beyond the Aubry-André model

Localization properties of particles in one-dimensional incommensurate lattices without interaction are investigated with models beyond the tight-binding Aubry-André (AA) model. Based on a tight-binding t_1 - t_2 model with finite next-nearest-neighbor hopping t_2, we find the localization properties qualitatively different from those of the AA model, signaled by the appearance of mobility edges. We then further go beyond the tight-binding assumption and directly study the system based on the more fundamental single-particle Schrödinger equation. With this approach, we also observe the presence of mobility edges and localization properties dependent on incommensuration.

quant-ph↗

arXiv2006

Magnetic Percolation and the Phase Diagram of the Disordered RKKY model

We consider ferromagnetism in spatially randomly located magnetic moments, as in a diluted magnetic semiconductor, coupled via the carrier-mediated indirect exchange RKKY interaction. We obtain via Monte Carlo the magnetic phase diagram as a function of the impurity moment density $n_{i}$ and the relative carrier concentration $n_{c}/n_{i}$. As evidenced by the diverging correlation length and magnetic susceptibility, the boundary between ferromagnetic (FM) and non-ferromagnetic (NF) phases constitutes a line of zero temperature critical points which can be viewed as a magnetic percolation transition. In the dilute limit, we find that bulk ferromagnetism vanishes for $n_{c}/n_{i}>.1$. We also incorporate the local antiferromagnetic direct superexchange interaction between nearest neighbor impurities, and examine the impact of a damping factor in the RKKY range function.

cond-mat.mtrl-sci↗