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

Abstract

When two planar atomic membranes are placed within the van der Waals distance, the charge and heat transport across the interface are coupled by the rules of momentum conservation and structural commensurability, lead to outstanding thermoelectric properties. Here we show that an effective 'inter-layer phonon drag' determines the Seebeck coefficient (S) across the van der Waals gap formed in twisted bilayer graphene (tBLG). 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• with a renormalized Fermi velocity [4,8], or at specific values of θ, such as θ = 30• ± 8.21• , when the hexagonal crystal structures become commensurate [1]. 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]. In fact, since the in-plane transverse and longitudinal phonons are effectively filtered out from contributing to cross-plane transport because they do not substantially alter the tunneling matrix elements, theoretical calculations predict enhanced cross-plane thermoelectric properties in van der Waals heterojunctions, including high ZT factors at room temperature [12]. However, although the impact of interlayer coherence and electron-phonon interaction on electrical conductance has been studied in detail [1,3], their relevance to the thermal and thermoelectric properties of tBLG remains unexplored.We assembled the tBLG devices with layer-by-layer mechanical transfer method, which is common in van der Waals epitaxy [16][17][18]. Three devices were constructed which show very similar behavior, and we present the results from one of the devices here. The device consists of two graphene layers oriented in a "cross" configuration (inset of Fig. 1a and an optical micrograph in Fig. 1b), and entirely encapsulated within two layers of hexagonal boron nitride (hBN). The carrier mobilities in the upper and lower layers are ≈ 25000 cm 2 V −1 s −1 and ≈ 60000 cm 2 V −1 s −1 , at room tem...

Temperature-dependent layer breathing modes in two-dimensional materials

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2D Materials for Large‐Area Flexible Thermoelectric Devices

“…In spite of these electrical transport investigations in van der Waals heterostructures, the thermoelectric and/or thermal transport measurements have still limited. For example, the Seebeck coefficients have been obtained in twisted bilayer graphene and graphene/BN/graphene heterostructures . The cross‐plane thermoelectric transports have suggested the effects of a unique phonon drag originating from interlayer layer breathing phonon modes .…”

“…For example, the Seebeck coefficients have been obtained in twisted bilayer graphene and graphene/BN/graphene heterostructures. [144,145] The crossplane thermoelectric transports have suggested the effects of a unique phonon drag originating from interlayer layer breathing phonon modes. [145] Thereby, we would like to comment that the inter-layer and stacking effects on heterostructures are interesting subjects toward a high-performance 2D material thermoelectric conversion, and the combined thermoelectric measurements and theoretical calculations will reveal hidden physics behind thermoelectric transports across hetero-stacked layer by layer.…”

Atomistic simulations of phonon behaviors in isotopically doped graphene with Sierpinski carpet fractal structure

“…Graphene, consisting of covalently bonded carbon (C) atoms, is a novel two-dimensional (2D) material with a honeycomb lattice, which has triggered gigantic investigations because of the high charge carrier mobility [1], strong fracture strength [2], and ultrahigh thermal conductivity [3]. Due to the absence of direct bandgap in pristine graphene, the modified graphene structures have been investigated to gain the desired electrical properties, such as unfolded band gap [4], excellent Seebeck coefficient [5][6][7], and adjustable carrier mobility [8]. Moreover, the thermal properties of graphene play a crucial role in the thermal management of nanoelectronic devices to obtain an outstanding electrical performance [9].…”