Screening effect for excitonic spectrum of Coulomb coupling between two Dirac particles

The properties of screening effect for energy spectrum of excitons in monolayer transition metal dichalcogenides are investigated using a multiband model. The excitonic hamiltonian in the product base of the Dirac single-particle is used. The corresponding energy eigenvalue system of the first order ODE (radial equations) was solved using the finite difference method. This enables to determine the energy eigenvalues of the discrete excitonic spectrum and the wave functions. We compare the results for the energy spectrum and the corresponding eigen-functions forms for WS 2 and WSe 2 computed for two different potentials: pure Coulomb and screened Coulomb (Keldysh potential). It is demonstrated that excitonic energy levels for unscreened potential lie dipper, and the corresponding eigen-functions’ forms differ from those obtained for screened one.

Semiclassical approach for excitonic spectrum of Coulomb coupling between two Dirac particles

The properties of the energy spectrum of excitons in monolayer transition metal dichalcogenides are investigated using a multiband model. In the multiband model, we use the excitonic Hamiltonian in the product base of the Dirac single-particle states at the conduction and valence band edges. Following the separation of variables, we decouple the corresponding energy eigenvalue system of the first-order ODE radial equations rigorously and solve the resulting second-order ODE self-consistently, using the finite difference method, thus we determine the energy eigenvalues of the discrete excitonic spectrum and the corresponding wave functions. We also developed a WKB approach to solve the same spectral problem in semiclassical approximation for the resulting ODE. We compare the results for the energy spectrum and the corresponding eigen-function forms for WS 2 and WSe 2 obtained by means of both methods. We also compare our results for the energy spectrum with other theoretical works for excitons, and with available experimental data.

Temperature-Dependent s± ↔ s++ Transitions in the Multiband Model for Fe-Based Superconductors with Impurities

We study the dependence of the superconducting gaps on both the disorder and the temperature within the two-band model for iron-based materials. In the clean limit, the system is in the s± state with sign-changing gaps. Scattering by nonmagnetic impurities leads to the change of the sign of the smaller gap, resulting in a transition from the s± to the s++ state with the sign-preserving gaps. We show here that the transition is temperature-dependent. Thus, there is a line of s±→s++ transition in the temperature–disorder phase diagram. There is a narrow range of impurity scattering rates, where the disorder-induced s±→s++ transition occurs at low temperatures, but then the low-temperature s++ state transforms back to the s± state at higher temperatures. With increasing impurity scattering rate, the temperature of such s++→s± transition shifts to the critical temperature Tc, and only the s++ state is left for higher amounts of disorder.