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Register a new userElectronic structure calculations of twisted multi-layer graphene superlattices
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Quantum confinement endows two-dimensional (2D) layered materials with exceptional physics and novel properties compared to their bulk counterparts. Although certain two- and few-layer configurations of graphene have been realized and studied, a systematic investigation of the properties of arbitrarily layered graphene assemblies is still lacking. We introduce theoretical concepts and methods for the processing of materials information, and as a case study, apply them to investigate the electronic structure of multi-layer graphene-based assemblies in a high-throughput fashion. We provide a critical discussion of patterns and trends in tight binding band structures and we identify specific layered assemblies using low-dispersion electronic bands as indicators of potentially interesting physics like strongly correlated behavior. A combination of data-driven models for visualization and prediction is used to intelligently explore the materials space. This work more generally aims to increase confidence in the combined use of physics-based and data-driven modeling for the systematic refinement of knowledge about 2D layered materials, with implications for the development of novel quantum devices.
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We have used scanning tunneling microscopy and spectroscopy to resolve the spatial variation of the density of states of twisted graphene layers on top of a highly oriented pyrolytic graphite substrate. Owing to the twist a moire pattern develops with a periodicity that is substantially larger than the periodicity of a single layer graphene. The twisted graphene layer has electronic properties that are distinctly different from that of a single layer graphene due to the nonzero interlayer coupling. For small twist angles (about 1-3.5 degree) the integrated differential conductivity spectrum exhibits two well-defined Van Hove singularities. Spatial maps of the differential conductivity that are recorded at energies near the Fermi level exhibit a honeycomb structure that is comprised of two inequivalent hexagonal sub-lattices. For energies |E-E_F|>0.3 eV the hexagonal structure in the differential conductivity maps vanishes. We have performed tight-binding calculations of the twisted graphene system using the propagation method, in which a third graphene layer is added to mimic the substrate. This third layer lowers the symmetry and explains the development of the two hexagonal sub-lattices in the moire pattern. Our experimental results are in excellent agreement with the tight-binding calculations.
We theoretically investigate electron transport through corrugated graphene ribbons and show how the ribbon curvature leads to an electronic superlattice with a period set by the corrugation wave length. Transport through the ribbon depends sensitively on the superlattice band structure which, in turn, strongly depends on the geometry of the deformed sheet. In particular, we find that for ribbon widths where the transverse level separation is comparable to the the band edge energy, a strong current switching occurs as function of an applied backgate voltage. Thus, artificially corrugated graphene sheets or ribbons can be used for the study of Dirac fermions in periodic potentials. Furthermore, this provides an additional design paradigm for graphene-based electronics.
We report a combined nano-photocurrent and infrared nanoscopy study of twisted bilayer graphene (TBG) enabling access to the local electronic phenomena at length scales as short as 20 nm. We show that the photocurrent changes sign at carrier densities tracking the local superlattice density of states of TBG. We use this property to identify domains of varying local twist angle by local photo-thermoelectric effect. Consistent with the photocurrent study, infrared nano-imaging experiments reveal optical conductivity features dominated by twist-angle dependent interband transitions. Our results provide a fast and robust method for mapping the electronic structure of TBG and suggest that similar methods can be broadly applied to probe electronic inhomogeneities of moire superlattices in other van der Waals heterostructures.
We study the electronic properties of twisted bilayers graphene in the tight-binding approximation. The interlayer hopping amplitude is modeled by a function, which depends not only on the distance between two carbon atoms, but also on the positions of neighboring atoms as well. Using the Lanczos algorithm for the numerical evaluation of eigenvalues of large sparse matrices, we calculate the bilayer single-electron spectrum for commensurate twist angles in the range $1^{circ}lesssimthetalesssim30^{circ}$. We show that at certain angles $theta$ greater than $theta_{c}approx1.89^{circ}$ the electronic spectrum acquires a finite gap, whose value could be as large as $80$ meV. However, in an infinitely large and perfectly clean sample the gap as a function of $theta$ behaves non-monotonously, demonstrating exponentially-large jumps for very small variations of $theta$. This sensitivity to the angle makes it impossible to predict the gap value for a given sample, since in experiment $theta$ is always known with certain error. To establish the connection with experiments, we demonstrate that for a system of finite size $tilde L$ the gap becomes a smooth function of the twist angle. If the sample is infinite, but disorder is present, we expect that the electron mean-free path plays the same role as $tilde L$. In the regime of small angles $theta<theta_c$, the system is a metal with a well-defined Fermi surface which is reduced to Fermi points for some values of $theta$. The density of states in the metallic phase varies smoothly with $theta$.
Twisted bi-layer graphene (tBLG) has recently attracted interest due to the peculiar electrical properties that arise from its random rotational configurations. Our experiments on CVD-grown graphene from Cu foil and transferred onto Si substrates, with an oxide layer of 100 nm, reveal naturally-produced bi-layer graphene patches which present different colorations when shined with white light. In particular yellow-, pink- and blue- colored areas are evidenced. Combining optical microscopy, Raman spectroscopy and transmission electron microscopy we have been able to assign these colorations to ranges of rotational angles between the two graphene layers. Optical contrast simulations have been carried out, proving that the observation of the different colorations is due to the angle-dependent electronic properties of tBLG combined with the reflection that results from the layered structure tBLG / 100 nm-thick SiO2 / Si. Our results could lead the way to an easy selective identification of bi-layer graphene merely through the observation on an optical microscope.
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