Cooper pairing of electrons and holes in graphene bilayer: Correlation effects

Cooper pairing of spatially separated electrons and holes in graphene bilayer is studied beyond the mean-field approximation. Suppression of the screening at large distances, caused by appearance of the gap, is considered self-consistently. A mutual positive feedback between appearance of the gap and enlargement of the interaction leads to a sharp transition to correlated state with greatly increased gap above some critical value of the coupling strength. At coupling strength below the critical, this correlation effect increases the gap approximately by a factor of two. The maximal coupling strength achievable in experiments is close to the critical value. This indicated importance of correlation effects in closely-spaced graphene bilayers at weak substrate dielectric screening. Another effect beyond mean-field approximation considered is an influence of vertex corrections on the pairing, which is shown to be very weak.Comment: 6 pages, 5 figures; some references were adde

On the minimal number of critical points of functions on h-cobordisms

Let (W,M,M'), dim W > 5, be a non-trivial h-cobordism (i.e., the Whitehead torsion of (W,V) is non-zero). We prove that every smooth function f: W --> [0,1], f(M)=0, f(M')=1 has at least 2 critical points. This estimate is sharp: W possesses a function as above with precisely two critical points.Comment: 7 pages, Late

Quantum phase transition in a two-dimensional system of dipoles

The ground-state phase diagram of a two-dimensional Bose system with dipole-dipole interactions is studied by means of quantum Monte Carlo technique. Our calculation predicts a quantum phase transition from gas to solid phase when the density increases. In the gas phase the condensate fraction is calculated as a function of the density. Using Feynman approximation, the collective excitation branch is studied and appearance of a roton minimum is observed. Results of the static structure factor at both sides of the gas-solid phase are also presented. The Lindeman ratio at the transition point comes to be $\gamma = 0.230(6)$. The condensate fraction in the gas phase is estimated as a function of the density.Comment: 4 figures v.3 One citation added, updated Fig.4. Minor changes following referee's and editor's comment

Bose-Einstein condensation of trapped polaritons in 2D electron-hole systems in a high magnetic field

The Bose-Einstein condensation (BEC) of magnetoexcitonic polaritons in two-dimensional (2D) electron-hole system embedded in a semiconductor microcavity in a high magnetic field $B$ is predicted. There are two physical realizations of 2D electron-hole system under consideration: a graphene layer and quantum well (QW). A 2D gas of magnetoexcitonic polaritons is considered in a planar harmonic potential trap. Two possible physical realizations of this trapping potential are assumed: inhomogeneous local stress or harmonic electric field potential applied to excitons and a parabolic shape of the semiconductor cavity causing the trapping of microcavity photons. The effective Hamiltonian of the ideal gas of cavity polaritons in a QW and graphene in a high magnetic field and the BEC temperature as functions of magnetic field are obtained. It is shown that the effective polariton mass $M_{\rm eff}$ increases with magnetic field as $B^{1/2}$. The BEC critical temperature $T_{c}^{(0)}$ decreases as $B^{-1/4}$ and increases with the spring constant of the parabolic trap. The Rabi splitting related to the creation of a magnetoexciton in a high magnetic field in graphene and QW is obtained. It is shown that Rabi splitting in graphene can be controlled by the external magnetic field since it is proportional to $B^{-1/4}$, while in a QW the Rabi splitting does not depend on the magnetic field when it is strong.Comment: 16 pages, 6 figures. accepted in Physical Review

Finite groups and Lie rings with an automorphism of order 2n2^n

Suppose that a finite group $G$ admits an automorphism $\varphi$ of order $2^n$ such that the fixed-point subgroup $C_G(\varphi ^{2^{n-1}})$ of the involution $\varphi ^{2^{n-1}}$ is nilpotent of class $c$. Let $m=|C_G(\varphi)|$ be the number of fixed points of $\varphi$. It is proved that $G$ has a characteristic soluble subgroup of derived length bounded in terms of $n,c$ whose index is bounded in terms of $m,n,c$. A similar result is also proved for Lie rings.Comment: minor corrections and addition