Proximity Effect in Graphene–Topological-Insulator Heterostructures

Abstract

We formulate a continuum model to study the low-energy electronic structure of heterostructures formed by graphene on a strong three-dimensional topological insulator (TI) for the case of both commensurate and incommensurate stacking. The incommensurability can be due to a twist angle between graphene and the TI surface or a lattice mismatch between the two systems. We find that the proximity of the TI induces in graphene a strong enhancement of the spin-orbit coupling that can be tuned via the twist angle.The surfaces of strong three-dimensional (3D) topological insulators (TIs) [1] and graphene [2,3] have very similar low-energy electronic structures: the conduction and valence bands touch at isolated points, the Dirac points (DPs), and around these points the fermionic excitations are well described as massless two-dimensional (2D) chiral Dirac fermions for which the phase of a twostate quantum degree of freedom is locked with the momentum direction. However, there are also qualitative differences: (i) in graphene the chirality is associated with the sublattice degree of freedom whereas in a TI surface (TIS) it is associated with the electron spin; (ii) in graphene the number of DPs is even whereas in a TIS it is odd ; (iii) in TIs the electron-phonon scattering is much stronger than that in graphene. Therefore, the transport properties of graphene [4] and TIs are different in significant aspects: in graphene, because the intrinsic spin-orbit (SO) coupling is negligible [5][6][7][8], no quantum spin Hall effect is expected, contrary to the case in a TI; graphene has the highest room-temperature mobility, whereas TIs have very low mobilities. These facts, together with the recent experimental progress [9], motivated us to study graphene-TI heterostructures, in which the proximity to a TI is expected to enhance the SO coupling of graphene and create a novel 2D system with nontrivial spin textures and high, room-temperature, electron mobility. This approach to enhance the SO coupling in graphene appears to be more practical than previously proposed approaches [10] that rely on doping graphene with heavy adatoms.In this work, we study the low-energy electronic structure of heterostructures formed by one sheet of graphene placed on the conducting surface of a 3D TI. Our results show that not only can the proximity of a TIS enhance the SO coupling in graphene and bilayer graphene (BLG), but also that this enhancement can be controlled via the relative rotation, the twist angle, between the graphene lattice and the TI's lattice. The presence of a relative rotation, in general, induces an incommensurate stacking of the graphene and the substrate [11] [12-36]. As a consequence we develop and present a theory that is able to take into account the incommensurability between graphene and the TIS. This cannot be achieved via standard approaches, such as density functional theory [37], and tight-binding models, due to the computational cost of these approaches for incommensurate structures. A continuous model, on the other...

Electronic Coupling between Graphene and Topological Insulator Induced Anomalous Magnetotransport Properties

“…Owing to the high carrier mobility and unique spin textures, TIs and graphene are promising for high speed electronics and spintronics [16]. Recent theories [8][9][10][11] have predicted the hybridization of graphene and TIs can create nontrivial spin textures in graphene, even leading to quantum spin Hall states [1]. Generally, the rigorous √3 × √3 supercell of graphene stacked with TI is adopted in the calculations [8][9][10][11].…”

“…1b These observations can be understood in the framework of the graphene-TI proximity effect that was theoretically predicted via band calculations in Refs. [8][9][10][11]. Under the magnetic field perpendicular to the graphene plane, the unevenly spaced energy spectrum is expressed as = ( )√2 ℏ 2 | | , where ℏ is reduced Planck's constant, the Fermi velocity is ~10 6 ⁄ , and the LL index N is positive for electrons and negative for holes [12,13].…”

“…With increasing temperature, the decrease of can be attributed to the nonlinear energy bands induced by the proximity effect (Fig. 4b,c), because more carriers can be thermally excited to the multiple bands near the charge neutrality point [10,11]. Interestingly, the hybrid graphene exhibits metallic behaviors, as a small magnetic field such as -1 T is applied.…”

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/ 31Graphene and surface states of topological insulators (TIs) can be described by two-dimensional (2D) massless Dirac Hamiltonian at the low energy excitations, which can be further modulated by adatom adsorption or interfacing with other functional materials [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. Owing to the high carrier mobility and unique spin textures, TIs and graphene are promising for high speed electronics and spintronics [16].

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“…3b,c. In the classical regime, the two-carrier model can be used to describe a zero-gap conductor with the same mobility for electrons and holes, giving Predicted by theoretical models [8][9][10][11], graphene can inherit spin-orbital textures from TI surface states near the Dirac point due to the proximity effect. Accordingly, we summarize the reforming band structures of graphene hybridized with TI surface in Fig.…”