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Register a new user$textit{Zitterbewegung}$ near new Dirac points in graphene superlattice
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New Dirac points appear when periodic potentials are applied to graphene, and there are many interesting effects near these new Dirac points. Here we investigate the $textit{Zitterbewegung}$ effect of fermions described by a Gaussian wave packet in graphene superlattice near new Dirac points. The $textit{Zitterbewegung}$ near different Dirac points has similar characteristics, while Fermions near new Dirac points have different group velocities in both $x$- and $y$-direction, which causes the different properties of the $textit{Zitterbewegung}$ near new Dirac points. We also investigate the $textit{Zitterbewegung}$ effect influenced by all Dirac points, and get the evolution with changing potential. Our intensive results suggest that graphene superlattice may provide an appropriate system to study $textit{Zitterbewegung}$ effect near new Dirac points experimentally.
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We review different scenarios for the motion and merging of Dirac points in two dimensional crystals. These different types of merging can be classified according to a winding number (a topological Berry phase) attached to each Dirac point. For each scenario, we calculate the Landau level spectrum and show that it can be quantitatively described by a semiclassical quantization rule for the constant energy areas. This quantization depends on how many Dirac points are enclosed by these areas. We also emphasize that different scenarios are characterized by different numbers of topologically protected zero energy Landau levels
The observation of novel physical phenomena such as Hofstadters butterfly, topological currents and unconventional superconductivity in graphene have been enabled by the replacement of SiO$_2$ with hexagonal Boron Nitride (hBN) as a substrate and by the ability to form superlattices in graphene/hBN heterostructures. These devices are commonly made by etching the graphene into a Hall-bar shape with metal contacts. The deposition of metal electrodes, the design and specific configuration of contacts can have profound effects on the electronic properties of the devices possibly even affecting the alignment of graphene/hBN superlattices. In this work we probe the strain configuration of graphene on hBN contacted with two types of metal contacts, two-dimensional (2D) top-contacts and one-dimensional (1D) edge-contacts. We show that top-contacts induce strain in the graphene layer along two opposing leads, leading to a complex strain pattern across the device channel. Edge-contacts, on the contrary, do not show such strain pattern. A finite-elements modelling simulation is used to confirm that the observed strain pattern is generated by the mechanical action of the metal contacts clamped to the graphene. Thermal annealing is shown to reduce the overall doping whilst increasing the overall strain, indicating and increased interaction between graphene and hBN. Surprisingly, we find that the two contacts configurations lead to different twist-angles in graphene/hBN superlattices, which converge to the same value after thermal annealing. This observation confirms the self-locking mechanism of graphene/hBN superlattices also in the presence of strain gradients. Our experiments may have profound implications in the development of future electronic devices based on heterostructures and provide a new mechanism to induce complex strain patterns in 2D materials.
We discuss plasmons of biased twisted bilayer graphene when the Fermi level lies inside the gap. The collective excitations are a network of chiral edge plasmons (CEP) entirely composed of excitations in the topological electronic edge states (EES) that appear at the AB-BA interfaces. The CEP form an hexagonal network with an unique energy scale $epsilon_p=frac{e^2}{epsilon_0epsilon t_0}$ with $t_0$ the moire lattice constant and $epsilon$ the dielectric constant. From the dielectric matrix we obtain the plasmon spectra that has two main characteristics: (i) a diverging density of states at zero energy, and (ii) the presence of a plasmonic Dirac cone at $hbaromegasimepsilon_p/2$ with sound velocity $v_D=0.0075c$, which is formed by zigzag and armchair current oscillations. A network model reveals that the antisymmetry of the plasmon bands implies that CEP scatter at the hexagon vertices maximally in the deflected chiral outgoing directions, with a current ratio of 4/9 into each of the deflected directions and 1/9 into the forward one. We show that scanning near-field microscopy should be able to observe the predicted plasmonic Dirac cone and its broken symmetry phases.
The propagation of Dirac fermions in graphene through a long-period periodic potential would result in a band folding together with the emergence of a series of cloned Dirac points (DPs). In highly aligned graphene/hexagonal boron nitride (G/hBN) heterostructures, the lattice mismatch between the two atomic crystals generates a unique kind of periodic structure known as a moire superlattice. Of particular interests is the emergent phenomena related to the reconstructed band-structure of graphene, such as the Hofstadter butterfly, topological currents, gate dependent pseudospin mixing, and ballistic miniband conduction. However, most studies so far have been limited to the lower-order minibands, e.g. the 1st and 2nd minibands counted from charge neutrality, and consequently the fundamental nature of the reconstructed higher-order miniband spectra still remains largely unknown. Here we report on probing the higher-order minibands of precisely aligned graphene moire superlattices by transport spectroscopy. Using dual electrostatic gating, the edges of these high-order minibands, i.e. the 3rd and 4th minibands, can be reached. Interestingly, we have observed interband Landau level (LL) crossinginducing gap closures in a multiband magneto-transport regime, which originates from band overlap between the 2nd and 3rd minibands. As observed high-order minibands and LL reconstruction qualitatively match our simulated results. Our findings highlight the synergistic effect of minibands in transport, thus presenting a new opportunity for graphene electronic devices.
The electronic structure of a crystalline solid is largely determined by its lattice structure. Recent advances in van der Waals solids, artificial crystals with controlled stacking of two-dimensional (2D) atomic films, have enabled the creation of materials with novel electronic structures. In particular, stacking graphene on hexagonal boron nitride (hBN) introduces moire superlattice that fundamentally modifies graphenes band structure and gives rise to secondary Dirac points (SDPs). Here we find that the formation of a moire superlattice in graphene on hBN yields new, unexpected consequences: a set of tertiary Dirac points (TDPs) emerge, which give rise to additional sets of Landau levels when the sample is subjected to an external magnetic field. Our observations hint at the formation of a hidden Kekule superstructure on top of the moire superlattice under appropriate carrier doping and magnetic fields.
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