The low-frequency magneto-optical properties of bilayer Bernal graphene are studied by the tight-binding model with the four most important interlayer interactions taken into account. Since the main features of the wave functions are well-depicted, the Landau levels can be divided into two groups based on the characteristics of the wave functions. These Landau levels lead to four categories of absorption peaks in the optical absorption spectra. Such absorption peaks own complex optical selection rules, and these rules can be reasonably explained by the characteristics of the wave functions. In addition, twin-peak structures, regular frequency-dependent absorption rates, and complex field-dependent frequencies are also obtained in this work. The main features of the absorption peaks are very different from those in monolayer graphene and have their origin in the interlayer interactions.

No abstract

A multidimensional transformation design method that allows us to design a cloaking shell of multivariables for matter waves is proposed. As applications, cloaking shells for an elliptical invisible region, a region specified by the radial and angular variables, and an invisible region specified by the polar angle for the Coulomb scattering wave have been designed. It is shown that the mass parameters required for a perfect cloaking of a matter wave in the elliptical coordinate system are constant.

No abstract

The low-frequency magneto-absorption spectra of monolayer and bilayer graphene are evaluated within the gradient approximation. On the basis of Peierls tight-binding model, we can draw the wave function distribution over its sublattices and bring them into the calculation of optical spectra. The optical selection rules and the absorption rate can be accurately determined. The interlayer interactions in bilayers effectively alter the Landau level structures and thus the absorption spectra, such as the field dependence of absorption lines and the appearance of double-peaked absorptions.

The exact Green function of a relativistic Coulomb system is given by the transformation method. The earlier treatments are based on the multiple-valued transformation of Kustaanheimo and Stiefel as well as the perturbation expansions. The method presented in this paper relates the relativistic Coulomb path integral to the simple ones and may apply to a large class of problems.