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...

This article presents our findings on the recursive band gap engineering of chiral fermions in bilayer graphene doubly aligned with hBN. By utilizing two interfering moire′ potentials, we generate a supermoire′ pattern which renormalizes the electronic bands of the pristine bilayer graphene, resulting in higher-order fractal gaps even at very low energies. These Bragg gaps can be mapped using a unique linear combination of periodic areas within the system. To validate our findings, we used electronic transport measurements to identify the position of these gaps as functions of the carrier density and establish their agreement with the predicted carrier densities and corresponding quantum numbers obtained using the continuum model. Our study provides conclusive evidence of quantization of the momentum-space area of quasi-Brillouin zones in a minimally incommensurate lattice. It fills essential gaps in understanding the band structure engineering of Dirac fermions by a doubly periodic superlattice spinor potential.

The planar assembly of twisted bilayer graphene (tBLG) hosts a multitude of interaction-driven phases when the relative rotation is close to the magic angle (θ = 1.1°). This includes correlation-induced ground states that reveal spontaneous symmetry breaking at low temperature, as well as the possibility of non-Fermi liquid (NFL) excitations. However, experimentally, the manifestation of NFL effects in transport properties of twisted bilayer graphene remains ambiguous. Here we report simultaneous measurements of electrical resistivity (ρ) and thermoelectric power (S) in tBLG for several twist angles between θ ≈ 1.0°-1.7°. We observe an emergent violation of the semiclassical Mott relation in the form of excess S close to half-filling for θ≈1.6° that vanishes for ≥ 2°. The excess S (≈2 μV/K at low temperatures T ≈10 K at θ≈1.6°) persists up to ≈ 40 K and is accompanied by metallic T-linear ρ with transport scattering rate (1/τ) of near-Planckian magnitude 1/τ ≈ k_BT/h_bar. Closer to θ_m, the excess S was also observed for fractional band-filling (ν≈ 0.5). The combination of non-trivial electrical transport and violation of Mott relation provides compelling evidence of NFL physics intrinsic to tBLG.