場論在凝態系統應用之研究

So far, we have published two papers: B. Rosenstein, H. C. Kao, and M. Lewkowicz, 2017, “Nonlocal electrodynamics in Weyl semimetals,” Phys. Rev. B 95, 085148 (2017). (SCI) J.F. Wang, D.P. Li, H.C. Kao, and B. Rosenstein, “Covariant gaussian approximation in Ginzburg - Landau model,” Annals of Physics, 380, 228-254 (2017). (SCI) The first paper is a collaboration with Prof. Rosenstein and Lewkowicz. In this work, we calculate the charge-charge and current-current correlator of a 3D Weyl semi-metal(WSM). The Coulomb interaction between electrons is unscreened as in a dielectric and hence is long range. We demonstrate that the interaction correction renders the electrodynamics nonlocal on a mesoscopic scale. The longitudinal conductivity and the transverse conductivity are different in the long wave length limit and consequently the standard local Ohm's law description does not apply. This leads to several remarkable effects in optical response. The p-polarized light generates in these materials bulk plasmons as well as the transversal waves. At a specific frequency the two modes coincide, a phenomenon impossible in a local medium. For any frequency there is an Brewster angle where total absorption occurs, turning the WSM opaque. The effect of the surface, including the Fermi arcs, is discussed. The second is a collaboration with Prof. Rosenstein and Ding-Ping Li and his student Jiangfan Wang. It is well-known that naive gaussian approximation is "non-conserving" in the sense that the Ward identities are not obeyed. In particular, the Goldstone bosons become massive in the symmetry broken phase. By using the Covariant gaussian approximation, the Green's functions obey all the Ward identities and describe the fluctuations much better. The results for the order parameter correlator and magnetic penetration depth of the Ginzburg-Landau model of superconductivity are compared with both Monte Carlo simulations and experiments in high Tc cuprates. Since the formulation is quite general, it can be applied to a wide range of systems.