Bose-Einstein condensation and superfluidity of magnetoexcitons in bilayer graphene

Abstract

We propose experiments to observe Bose-Einstein condensation (BEC) and superfluidity of quasitwo-dimensional (2D) spatially indirect magnetoexcitons in bilayer graphene. The magnetic field B is assumed strong. The energy spectrum of collective excitations, the sound spectrum as well as the effective magnetic mass of magnetoexcitons are presented in the strong magnetic field regime. The superfluid density nS and the temperature of the Kosterlitz-Thouless phase transition Tc are shown to be increasing functions of the excitonic density n but decreasing functions of B and the interlayer separation D. Numerical results are presented from these calculations.PACS numbers: 71.35.Ji, 71.35.Lk, Indirect excitons in coupled quantum wells (CQWs) in the presence or absence of a magnetic field B have been the subject of recent experimental investigations [1,2,3,4]. These systems are of particular interest because of the possibility of Bose-Einstein condensation (BEC) and the superfluidity of indirect excitons formed from electron-hole pairs. These may result in persistent electrical currents in each QW or coherent optical properties and Josephson junction phenomena [5,6,7,8,9]. In high magnetic fields, two-dimensional (2D) excitons survive in a substantially wider temperature range, as the exciton binding energies increase with magnetic field [10,11,12,13,14,15,16].In this Letter we propose a new physical realization of magnetoexcitonic BEC and superfluidity in bilayer graphene with spatially separated electrons and holes in high magnetic field. Recent technological advances have allowed the production of graphene, which is a 2D honeycomb lattice of carbon atoms that form the basic planar structure in graphite [17,18] Graphene has been attracting a great deal of experimental and theoretical attention because of unusual properties in its bandstructure [19,20,21,22]. It is a gapless semiconductor with massless electrons and holes which have been described as Dirac-fermions [23]. Since there is no gap between the conduction and valence bands in graphene without magnetic field, the screening effects result in the absence of excitons in graphene in the absence of magnetic field. A strong magnetic field produces a gap since the energy spectrum becomes discrete formed by Landau levels. The gap reduces screening and leads to the formation of magnetoexcitons.We consider two parallel graphene layers separated by an insulating slab of SiO 2 . The electrons in one layer and holes in the other can be controlled as in the experiments with CQWs[1, 2, 3, 4] by laser pumping (far infrared in graphene). The spatial separation of electrons and holes in different graphene layers can be achieved by applying an external electric field. Furthermore, the spatially separated electrons and holes can be created by varying the chemical potential by using a bias voltage between two graphene layers or between two gates located near the corresponding graphene sheets. Indirect magnetoexcitons are bound states of spatially separated electrons and holes in a...

High-temperature superfluidity of the two-component Bose gas in a transition metal dichalcogenide bilayer

“…47, the exchange interactions in a spatially separated electron-hole system in a bilayer are suppressed due to the low tunneling probability coming from the shielding of the dipole-dipole interaction by the insulating barrier. Hence, at large interlayer separations the exchange phenomena, caused by the distinction between excitons and bosons, can be neglected for the electron-hole bilayers [73]. Two dipolar excitons in a dilute bilayer system interact according to the dipole-dipole potential U (R) = ke 2 D 2 / ǫ d R 3 , where R is the distance between excitonic dipoles.…”

“…Two dipolar excitons in a dilute bilayer system interact according to the dipole-dipole potential U (R) = ke 2 D 2 / ǫ d R 3 , where R is the distance between excitonic dipoles. The probability of tunneling though the barrier of the dipole-dipole interaction can be described by the transmission coefficient T [73]:…”

Bose–Einstein condensation of quasiparticles in graphene

“…[21]). In strong magnetic fields at D ≫ r B the exciton magnetic mass is m B (D) = ǫD 3 /(e 2 r 4 B ) for the QWs [21] and m B (D) = ǫD 3 /(4e 2 r 4 B ) for the GLs [52]. We study the magnetoexciton-magnetoexciton scattering applying the theory of weakly-interacting 2D Bose-gas [16,19].…”

Exciton states in narrow-gap carbon nanotubes

“…Electronelectron interactions plays an important role Dirac materials [18] and it has been predicted that graphene may undergo a metalinsulator transition [19,20,21]. Therefore knowledge of the two body problem is an important step in the understanding of excitonic systems such as Bose-Einstein condensation [22,23,24] and Superfluidity [25,26]. However, a common consensus has not been met regarding the formation of coupled pairs in intrinsic graphene.…”