Dynamical correlation functions and the related physical effects in three-dimensional Weyl/Dirac semimetals

We present a unified derivation of the dynamical correlation functions including density-density, density-current and current-current, of three-dimensional Weyl/Dirac semimetals by use of the Passarino-Veltman reduction scheme at zero temperature. The generalized Kramers-Kronig relations with arbitrary order of subtraction are established to verify these correlation functions. Our results lead to the exact chiral magnetic conductivity and directly recover the previous ones in several limits. We also investigate the magnetic susceptibilities, the orbital magnetization and briefly discuss the impact of electron interactions on these physical quantities within the random phase approximation. Our work could provide a starting point for the investigation of the nonlocal transport and optical properties due to the higher-order spatial dispersion in three-dimensional Weyl/Dirac semimetals.Comment: 21 pages, 3+1 figures, 1 table. Accepted in PR

RKKY interaction in three-dimensional electron gases with linear spin-orbit coupling

We theoretically study the impacts of linear spin-orbit coupling (SOC) on the Ruderman-Kittel-Kasuya-Yosida interaction between magnetic impurities in two kinds of three-dimensional noncentrosymmetric systems. It has been found that linear SOCs lead to the Dzyaloshinskii-Moriya interaction and the Ising interaction, in addition to the conventional Heisenberg interaction. These interactions possess distinct range functions from three dimensional electron gases and Dirac/Weyl semimetals. In the weak SOC limit, the Heisenberg interaction dominates over the other two interactions in a moderately large region of parameters. Sufficiently strong Rashba SOC makes the Dzyaloshinskii-Moriya interaction or the Ising interaction dominate over the Heisenberg interaction in some regions. The change in topology of the Fermi surface leads to some quantitative changes in periods of oscillations of range functions. The anisotropy of Ruderman-Kittel-Kasuya-Yosida interaction in bismuth tellurohalides family BiTe$X$ ($X$ = Br, Cl, and I) originates from both the specific form of Rashba SOC and the anisotropic effective mass. Our work provides some insights into understanding observed spin textures and the application of these materials in spintronics.Comment: 11 pages, 4 figures, Final Version in PR

Effective Graph-Based Content--Based Image Retrieval Systems for Large-Scale and Small-Scale Image Databases

This dissertation proposes two novel manifold graph-based ranking systems for Content-Based Image Retrieval (CBIR). The two proposed systems exploit the synergism between relevance feedback-based transductive short-term learning and semantic feature-based long-term learning to improve retrieval performance. Proposed systems first apply the active learning mechanism to construct users\u27 relevance feedback log and extract high-level semantic features for each image. These systems then create manifold graphs by incorporating both the low-level visual similarity and the high-level semantic similarity to achieve more meaningful structures for the image space. Finally, asymmetric relevance vectors are created to propagate relevance scores of labeled images to unlabeled images via manifold graphs. The extensive experimental results demonstrate two proposed systems outperform the other state-of-the-art CBIR systems in the context of both correct and erroneous users\u27 feedback