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We propose to control of an electron-hole superfluid in semiconductor coupled quantum wells and double layers of two-dimensional (2D) material by an external periodic field. This can either be created by the gates periodically located and attached to the quantum wells or double layers of 2D material or by the Moir\'e pattern of two twisted layers. The dependence of the electron-hole pairing order parameter on the temperature, the charge carrier density, and the gate parameters is obtained by minimization of the mean-field free energy. The second order phase transition between superfluid and electron-hole plasma, controlled by the external periodic gate field, is analyzed for different parameters., Comment: 10 pages, 4 figures

We consider excitons in a two-dimensional periodic potential and study the linear response of the excitonic superfluid to an electromagnetic wave at low and high densities. It turns out that the static structure factor for small wavevectors is very sensitive to a change of density and temperature. It is a consequence of the fact that thermal fluctuations play a crucial role at small wavevectors, since exchanging the order of the two limits, zero temperature and vanishing wavevector, leads to different results for the structure factor. This effect could be used for high accuracy measurements in the superfluid exciton phase, which might be realized by a gated electron-hole gas. The transition of the exciton system from the superfluid state to a non-superfluid state and its manifestation by light scattering are discussed., Comment: 9 pages, 5 figures

An exciton gas on a lattice is analyzed in terms of a convergent hopping expansion. For a given chemical potential our calculation provides a sufficient condition for the hopping rate to obtain an exponential decay of the exciton correlation function. This result indicates the existence of a Mott phase in which strong fluctuations destroy the long range correlations in the exciton gas at any temperature, either by thermal or by quantum fluctuations., Comment: 5 pages, 1 figure

We study the propagation of a Bose-Einstein condensate (BEC) of long-lifetime exciton polaritons in a high-quality microcavity with an embedded semiconductor quantum well or a graphene layer using the Gross-Pitaevskii equation. It is shown that in these heterostructures the BEC of the long-lifetime polaritons can propagate over the distance up to 0.5 mm. The obtained results are consistent with the recent experimental observations for GaAs/AlGaAs microcavity. It is demonstrated that the BEC density in a polariton trace in a microcavity with embedded graphene at large distances from the excitation spot is higher for the microcavity with higher dielectric constant. It is also predicted that the propagation of a polariton BEC in a microcavity with graphene is dynamically tunable by changing the gap energy, that makes it potentially useful for applications in integrated optical circuits., Comment: 8 pages, 7 figures

A study of the formation of excitons as a problem of two Dirac particles in a gapped graphene layer and in two gapped graphene layers separated by a dielectric is presented. In the low energy limit the separation of the center-of-mass and relative motions is obtained. Analytical solutions for the wave function and energy dispersion for both cases when electron and hole interact via a Coulomb potential are found. It is shown that the energy spectrum and the effective exciton mass are functions of the energy gaps as well as interlayer separation in case of two layer gapped graphene., Comment: 12 pages, 7 figures. arXiv admin note: substantial text overlap with arXiv:1110.6744

The nonlinear dynamics of a Bose-Einstein condensate (BEC) of dipolar excitons trapped in an external confining potential in coupled quantum wells is analysed. It is demonstrated that under typical experimental conditions the dipolar excitons BEC can be described by a generalized Gross-Pitaevskii equation with the local interaction between the excitons, which depends on the exciton distribution function. It is shown that, if the system is pumped at sufficiently high frequencies, a steady turbulent state can be formed., Comment: 4 pages, 4 figures

This paper is currently withdrawn and is being revised by the authors., Comment: This paper is presently being revised by the authors

The second order response functions and susceptibilities of finite temperature Bose-Einstein Condensates (BEC) in a one dimensional harmonic trap driven by an external field that couples to the particle density are calculated by solving the time-dependent Hartree-Fock-Bogoliubov (TDHFB) equations. These provide additional insight into BEC dynamics, beyond the linear response regime. The results also apply to electron liquids in the Fractional Quantum Hall Effect (FQHE) regime which can be mapped onto an effective boson system coupled to a Chern-Simons gauge field., Comment: 11 figures. Submitted to Phys. Rev. A

Superfluidity of spatially separated electrons and holes and unbalanced two-layer electron system in high magnetic field is considered. The temperature of the Kosterlitz-Thouless transition to a superfluid state is obtained as a function of magnetic field and interlayer separation. The equation of state for magnetoexciton system in quasi-classical regime is analyzed. The transition from excitonic phase to electron-hole phase is considered. Possible experimental manifestations of the predicted effects are briefly discussed., Comment: 21 pages, 3 Postscript figures