Spectral properties of excitons in the bilayer graphene

Abstract

In this paper, we consider the spectral properties of the bilayer graphene with the local excitonic pairing interaction between the electrons and holes. We consider the generalized Hubbard model, which includes both intralayer and interlayer Coulomb interaction parameters. The solution of the excitonic gap parameter is used to calculate the electronic band structure, single-particle spectral functions, the hybridization gap, and the excitonic coherence length in the bilayer graphene. We show that the local interlayer Coulomb interaction is responsible for the semimetal-semiconductor transition in the double layer system, and we calculate the hybridization gap in the band structure above the critical interaction value. The formation of the excitonic band gap is reported as the threshold process and the momentum distribution functions have been calculated numerically. We show that in the weak coupling limit the system is governed by the Bardeen-Cooper-Schrieffer (BCS)-like pairing state. Contrary, in the strong coupling limit the excitonic condensate states appear in the semiconducting phase, by forming the Dirac's pockets in the reciprocal space.PACS numbers: 68.65. Pq, 73.22.Pr, 73.22.Gk, 71.35.Lk, 71.10.Li, 78.67.Wj, 73.30.+y INTRODUCTIONThe electronic band gap of semiconductors and insulators largely determines their optical, transport properties and governs the operation of semiconductor based devices such as p-n junctions, transistors, photodiodes and lasers [1]. Opening up a band gap in the bilayer graphene (BLG), by applying the external electric field and finding a suitable substrate are two challenges for constituting the modern nano-electronic equipment [2,3]. The imposition of external electrical field can tune the bilayer graphene from the semimetal to the semiconducting state [2]. On the other hand, the possibility of formation of the excitonic insulator state and the excitonic condensation in the bilayer graphene structures remains controversial in the modern solid state physics [4][5][6][7][8][9][10][11][12][13][14]. In difference with the quasi two-dimensional (2D) semiconducting systems, where those two states have been observed experimentally and well discussed theoretically [15][16][17][18][19][20][21][22][23][24][25][26][27], the formation of the excitonic condensate states in the BLG system, from the original electron-hole pairing states, is much more obscure because of the complicated nature of the single-particle correlations in these systems [6,8,10,13,14]. The weak correlation diagrammatic mechanism, discussed in the Refs.13, 14, is restricted only to the closed loop expansion in the diagrammatic series, and in this case, only the density fluctuation effects could affect the formation of the excitonic condensate states. Meanwhile, it has been shown [28][29][30] that even the undoped graphene can provide a variety of electron-hole type pairing chiral symmetry breaking * Corresponding author. Tel.: +48 71 3954 284; E-mail address: v.apinyan@int.pan.wroc.pl.orders especially for the strong C...

High energy shift in the optical conductivity spectrum of the bilayer graphene

“…The intralayer Coulomb interaction parameter is fixed at the value U = 2γ 0 = 6 eV, and the interlayer hopping amplitude is γ 1 = 0.128γ 0 = 0.384 eV. In table I, we give the obtained values of the chemical potential [52], the threshold frequency values (the optical gaps) for the real part of the conductivity function, and the Fermi energy in the BLG corresponding to the interlayer interaction parameters, considered in Fig. 2.…”

“…We already showed, in Ref. 52, that the semiconducting (or insulating) state could be reached from the semimetallic limit in the BLG, thus leading to the enhancement of the Bardeen-Cooper-Schrieffer (BCS)-Bose-Einstein-Condensate (BEC) type crossover mechanism in the interacting BLG system. A detailed description of such a transition is given in Ref.…”

“…A detailed description of such a transition is given in Ref. 52. Next, for the product of the Fourier transformed single-particle Green's functions in Eq.…”

Excitonic Tunneling in the AB-bilayer Graphene Josephson Junctions

“…The excitonic gap formation and condensation has been examined also in the bilayer graphene structures [49][50][51][52][53][54][55][56][57]. Namely, the bilayer graphene is very promising for the optoelectronic applications due to its unique gate-controllable band structure properties [58].…”

“…The imposition of the external electrical field can tune the bilayer graphene from the semimetal to the semiconducting state. Nevertheless, the excitonic condensation in the bilayer graphene structures remains controversial in the modern solid-state physics because of the complicated nature of the single-particle correlations in these systems [49][50][51][52][53][54][55][56][57]. It has been shown recently [59] that the critical temperature, which describes the transition from the condensate state to the normal state in graphene double-layer structures, can be very high due to the extremely small effective mass of excitons.…”