The virial theorem for a system of interacting electrons in a crystal, which is described within the framework of the tight-binding model, is derived. We show that, in the particular case of interacting massless electrons in graphene and other Dirac materials, the conventional virial theorem is violated. Starting from the tight-binding model, we derive the generalized virial theorem for Dirac electron systems, which contains an additional term associated with a momentum cutoff at the bottom of the energy band. Additionally, we derive the generalized virial theorem within the Dirac model using the minimization of the variational energy. The obtained theorem is illustrated by many-body calculations of the ground-state energy of an electron gas in graphene carried out in Hartree-Fock and self-consistent random-phase approximations. Experimental verification of the theorem in the case of graphene is discussed.
A novel type of spaser with the net amplification of surface plasmons (SPs) in a doped graphene nanoribbon is proposed. The plasmons in the THz region can be generated in a doped graphene nanoribbon due to nonradiative excitation by emitters like two level quantum dots located along a graphene nanoribbon. The minimal population inversion per unit area, needed for the net amplification of SPs in a doped graphene nanoribbon, is obtained. The dependence of the minimal population inversion on the surface plasmon wave vector, graphene nanoribbon width, doping, and damping parameters necessary for the amplification of surface plasmons in the armchair graphene nanoribbon is studied.
Helical edge modes of 2D topological insulators are supposed to be protected from time-reversal invariant elastic backscattering. Yet substantial deviations from the perfect conductance are typically observed experimentally down to very low temperatures. To resolve this conundrum we consider the effect of a single magnetic impurity with arbitrary spin on the helical edge transport. We consider the most general structure of the exchange interaction between the impurity and the edge electrons. Moreover, for the first time, we take into the account the local anisotropy for the impurity and show that it strongly affects the backscattering current in a wide range of voltages and temperatures. We show that the sensitivity of the backscattering current to the presence of the local anisotropy is different for half-integer and integer values of the impurity spin. In the latter case the anisotropy can significantly increase the backscattering correction to the current.
Exciton-photon beats known as polariton Rabi oscillations in semiconductor microcavities are usually excited by short pulses of light. We consider a different pumping scheme, assuming a cw pumping of the Rabi oscillator from an exciton reservoir. We account for the initial pulse of light setting the phase, exciton decay due to exciton-phonon and exciton-exciton scattering, photon leakage, and blueshift of the exciton resonance due to interactions. We find nontrivial stationary solutions reminiscent of the Kapitza pendulum, where polaritons are accumulated at the upper branch while the lower branch empties.