Electron-electron interactions in decoupled graphene layers

Rosario E. V. Profumo, Marco Polini, Reza Asgari, Rosario Fazio, and A. H. MacDonald

Phys. Rev. B 82, 085443 – Published 26 August 2010

Abstract

Multilayer graphene on the carbon face of silicon carbide is an intriguing electronic system which typically consists of a stack of ten or more layers. Rotational stacking faults in this system dramatically reduce interlayer coherence. In this paper we report on the influence of interlayer interactions, which remain strong even when coherence is negligible, on the Fermi-liquid properties of charged graphene layers. We find that interlayer interactions increase the magnitudes of correlation energies and decrease quasiparticle velocities, even when remote-layer carrier densities are small, and that they lessen the influence of exchange and correlation on the distribution of carriers across layers.

Received 26 April 2010

DOI:https://doi.org/10.1103/PhysRevB.82.085443

Authors & Affiliations

Rosario E. V. Profumo¹, Marco Polini^2,*, Reza Asgari^3,†, Rosario Fazio⁴, and A. H. MacDonald⁵

¹NEST, Istituto Nanoscienze-CNR and Dipartimento di Fisica, Università di Pisa, I-56127 Pisa, Italy
²NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56126 Pisa, Italy
³School of Physics, Institute for Research in Fundamental Sciences, IPM, Tehran 19395-5531, Iran
⁴NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa, Italy
⁵Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA

^*m.polini@sns.it
^†asgari@ipm.ir

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Vol. 82, Iss. 8 — 15 August 2010

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Figure 1
(Color online) A stack of $ℓ = 1, \dots, N$ graphene layers is placed between top and bottom dielectrics. The layers are coupled solely by interlayer Coulomb interactions (red wiggly lines). The dielectric constant in the region above the $ℓ th$ layer is labeled by $ϵ_{ℓ}$ while the one of the substrate is labeled by $ϵ_{N + 1}$ . The separation between the $(ℓ + 1) th$ and the $ℓ th$ layer is labeled by $d_{ℓ + 1, ℓ}$ .Reuse & Permissions
Figure 2
(Color online) Quasiparticle velocities in double-layer graphene on SiC [ $ϵ_{1} = ϵ_{2} = 1.0$ and $ϵ_{3} = 6.6$ (SiC dielectric constant)]. The data shown in this figure have been obtained by setting $d = 3.35 Å$ and $α_{ee} = 2.2$ . Panel (a): quasiparticle velocity $v_{1}^{⋆}$ in the top layer (in units of the bare velocity $v$ ) as a function of the density $n_{1}$ in that layer (in units of $10^{12} {cm}^{- 2}$ ), for different values of the density $n_{2}$ in the opposite layer. Panel (b): quasiparticle velocity $v_{2}^{⋆}$ in the bottom layer (in units of the bare velocity $v$ ) as a function of the density $n_{2}$ in that layer (in units of $10^{12} {cm}^{- 2}$ ), for different values of the density $n_{1}$ in the opposite layer. Circles label data for the quasiparticle velocity in single-layer graphene (Ref. 35) on SiC.Reuse & Permissions
Figure 3
(Color online) Interaction energies in double-layer graphene on SiC, measured from the reference undoped system. All parameters are the same as in Fig. 2. Panel (a): the exchange energy $δ ε_{x}$ in units of the Fermi energy $ε_{F}$ as a function of $n$ (in units of $10^{12} {cm}^{- 2}$ ) and for different values of $ζ$ . Panel (b): same as in the top panel but for the RPA correlation energy $δ ε_{c}^{RPA}$ . Crosses label the RPA correlation energy for $ζ = 1$ if the interlayer interaction $V_{12}$ is set to zero. Circles label the exchange and RPA correlation energies in single-layer graphene (Ref. 30) on SiC. Note that the correlation energy obtained neglecting interlayer interactions (crosses) is practically equal to the single-layer graphene result (circles).Reuse & Permissions
Figure 4
(Color online) Electrochemical equilibrium for double-layer graphene on SiC in the absence of top and bottom gates $(E_{1} = E_{4} = 0)$ . All parameters are the same as in Figs. 2, 3. The distance between buffer and bottom layers is equal to $3.35 Å$ . Panel (a): equilibrium density in the top layer, $n_{1}^{⋆}$ (in units of $10^{12} {cm}^{- 2}$ ), as a function of the chemical potential $ϕ$ (in eV) in the buffer layer. Here we have reported results obtained (i) neglecting intralayer and interlayer e-e interactions (circles), (ii) including e-e interactions at the exchange-only level (squares), and (iii) including both exchange and correlations (triangles). Panel (b): same as in panel (a) but for the bottom layer. Note how $n_{2}^{⋆} > n_{1}^{⋆}$ .Reuse & Permissions

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