Phase diagram of microcavity exciton-polariton condensates

In this work, we study the exciton-polariton condensate phase transition in a microcavity matter-light system in which electron-hole Coulomb interaction and matter-light coupling effects are treated on an equal footing. In the framework of the unrestricted Hartree-Fock approximation applying the two-dimensional exciton-polariton model, we derive the self-consistent equations determining simultaneously the excitonic and the photonic condenstate order parameters. In the thermal equilibrium limit, we find a condensed state of the exciton-polariton systems and phase diagrams are then constructed. At a given low temperature, the condensate by its nature shows a crossover from an excitonic to a polaritonic and finally photonic condensed state as the excitation density increases at large detuning. Without the detuning, the excitonic condensed state disappears whereas the polaritonic or photonic phases dominate. The crossover is also found by lowering the Coulomb interaction at a finite matter-light coupling. Lowering the Coulomb interaction or increasing the temperature, the excitonic Mott transition occurs, at which the exciton-polariton condensates dissociate to free electron-hole/photon. Depending on temperature and excitation density, the phase transition of the exciton-polariton condensates is also addressed in signatures of photoluminescence mapping to the photonic momentum distribution.Comment: 7 pages, 6 figure

Coulomb interaction effects in graphene bilayers: electron-hole pairing and plasmaron formation

We report a theoretical study of the many-body effects of electron-electron interaction on the ground-state and spectral properties of double-layer graphene. Using a projector-based renormalization method we show that if a finite voltage difference is applied between the graphene layers electron-hole pairs can be formed and---at very low temperatures---an excitonic instability might emerge in a double-layer graphene structure. The single-particle spectral function near the Fermi surface exhibits a prominent quasiparticle peak, different from neutral (undoped) graphene bilayers. Away from the Fermi surface, we find that the charge carriers strongly interact with plasmons, thereby giving rise to a broad plasmaron peak in the angle-resolved photoemission spectrum.Comment: 11 pages, 5 figures, final (substantially revised) versio

Reducibility of nilpotent commuting varieties

Let $\N_n$ be the set of nilpotent $n$ by $n$ matrices over an algebraically closed field $k$. For each $r\ge 2$, let $C_r(\N_n)$ be the variety consisting of all pairwise commuting $r$-tuples of nilpotent matrices. It is well-kown that $C_2(\N_n)$ is irreducible for every $n$. We study in this note the reducibility of $C_r(\N_n)$ for various values of $n$ and $r$. In particular it will be shown that the reducibility of $C_r(\mathfrak{gl}_n)$, the variety of commuting $r$-tuples of $n$ by $n$ matrices, implies that of $C_r(\N_n)$ under certain condition. Then we prove that $C_r(\N_n)$ is reducible for all $n, r\ge 4$. The ingredients of this result are also useful for getting a new lower bound of the dimensions of $C_r(\N_n)$ and $C_r(\mathfrak{gl}_n)$. Finally, we investigate values of $n$ for which the variety $C_3(\N_n)$ of nilpotent commuting triples is reducible.Comment: 8 page

Doping change and distortion effect on double-exchange ferromagnetism

Doping change and distortion effect on the double-exchange ferromagnetism are studied within a simplified double-exchange model. The presence of distortion is modelled by introducing the Falicov-Kimball interaction between itinerant electrons and classical variables. By employing the dynamical mean-field theory the charge and spin susceptibility are exactly calculated. It is found that there is a competition between the double-exchange induced ferromagnetism and disorder-order transition. At low temperature various long-range order phases such as charge ordered and segregated phases coexist with ferromagnetism depending on doping and distortion. A rich phase diagram is obtained.Comment: 8 pages, 8 figure