Phonon-Mediated Interlayer Conductance in Twisted Graphene Bilayers

Abstract

Conduction between graphene layers is suppressed by momentum conservation whenever the layer stacking has a rotation. Here we show that phonon scattering plays a crucial role in facilitating interlayer conduction. The resulting dependence on orientation is radically different than previously expected, and far more favorable for device applications. At low temperatures, we predict diodelike current-voltage characteristics due to a phonon bottleneck. Simple scaling relationships give a good description of the conductance as a function of temperature, doping, rotation angle, and bias voltage, reflecting the dominant role of the interlayer beating phonon mode.Graphene has generated broad excitement both for fundamental science and for its potential applications in technology [1]. Attention has turned increasingly to bilayer and few layer graphene [2], because of their scientific richness and their promise in technological applications involving band-gap opening by an external electric field, high current-carrying capacity, and electro-optical coupling [3][4][5][6][7][8][9][10][11][12]. Interlayer conductance is crucial in almost all such applications. However, most fabrication methods lead to "twisted" layer stacking, with a random angle of rotation between layers. As a result, momentum conservation in certain respects "decouples" the layers [13][14][15][16][17][18][19]. Strictly speaking, the layers do couple, as evidenced by velocity renormalization [20][21][22][23][24]. But the states near the Dirac point in one layer largely decouple from those near the rotated Dirac point in the other layer [17][18][19]25], suppressing interlayer current [19].Understanding the interlayer conduction has proven surprisingly subtle and difficult. Calculations of the interlayer conductance to date have required some phenomenological lifetime broadening, with the conductance depending on this broadening [19]. In the limit of small carrier scattering the incoherent transport picture will fail, and it becomes problematic to even define an interlayer conductance independent of the external contacts [19]. With a realistic scattering lifetime the conductance is well defined, but it's calculated value is extraordinarily sensitive to even small details of the matrix-element modeling [19,25]. Finite conductance is predicted even for twisted stacking [19] due to Umklapp electronic coupling [18], but the coupling decays exponentially with the size of the rotational supercell [17][18][19]25]. (Here "supercell" denotes the primitive cell of the Bravais lattice of the commensurate rotated bilayer.) This would pose a serious obstacle to many device applications, where some reliable lower bound on the interlayer conductivity is essential. Experimentally, some interlayer transport is observed [26,27], but the mechanism remains unclear. Extrinsic scattering mechanisms could also relax momentum conservation, especially for defect-rich substrates.Here we show that essentially all of the conceptual and computational problems of twisted bilayers are res...

Seebeck Coefficient of a Single van der Waals Junction in Twisted Bilayer Graphene

“…2e, and allows us to estimate the Ω ph which sets The observed magnitude of Ω ph ∼ 150 − 200 K, suggests that the low-energy ZO /ZA 2 layer breathing phonon modes [6,22] in tBLG, which determines the interlayer electrical conductance [2,3] are also primarily responsible for thermoelectric transport across the van der Waals gap. However, to cross-verify this quantitatively, we assume the phenomenological phonon dispersion of the out-of-plane breathing modes [2], Ω ph =…”

“…The cross-plane thermovoltage which is nonmonotonic in both temperature and density, is generated through scattering of electrons by the out-of-plane layer breathing (ZO /ZA2) phonon modes and differs dramatically from the expected LandauerButtiker formalism in conventional tunnel junctions. The Tunability of cross-plane seebeck effect in van der Waals junctions may be valuable in creating a new genre of versatile thermoelectric systems with layered solidsIn spite of subnanometer separation of the van der Waals gap (∼ 0.5 nm), the coupling of the two graphene layers in twisted bilayer graphene (tBLG) varies strongly with temperature (T ), and the twist or misorientation angle θ between the hexagonal lattices of participating graphene layers [1][2][3][4][5][6][7][8][9]. At T Θ BG , where Θ BG is the Bloch-Grüneisen temperature, the layers are coherently coupled either for θ 10…”

“…• (and away from the 'magic' angles), the layers are essentially decoupled at low T , but get effectively re-coupled at higher T (> Θ BG ), when the interlayer phonons drive cross-plane electrical transport through strong electron-phonon scattering [2,3]. These phonons are also expected to determine thermal and thermoelectric transport across the interface [10][11][12][13][14][15].…”

Homoepitaxial tunnel barriers with functionalized graphene-on-graphene for charge and spin transport

“…Although single-layer graphene itself has been shown to function as a tunnel barrier in a heterostructure 5,6,20,21 , it does not effectively serve as a tunnel barrier on another layer of graphene because there is always some electrical interaction between the two layers, regardless of the stacking orientation 22,23 , except in a large magnetic field 24 . One can markedly alter graphene's physical properties with chemical functionalization 25 .…”

Layered Two-Dimensional Heterostructures and Their Tunneling Characteristics

“…[1,32,110] Concerning possible misorientation within the graphene bilayers themselves, this is known experimentally not to occur for the devices of Fallahazad et al [33] An additional source of misorientation in the device would be that between the graphene bilayers and the h-BN layers of the tunnel barrier. We have not investigated this e ect in detail, although referring to prior work for twisted BLG, [145,146] it appears that such an e ect would give rise to a reduced transmission current through the entire heterostructure. Indeed, for the case of tunneling between MLG layers separated by h-BN, computed tunnel currents agree in detail with experiment, except that the theory is a factor of 10 3 to 10 4 too large.…”