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We explore a network of electronic quantum valley Hall (QVH) states in the moire crystal of minimally twisted bilayer graphene. In our transport measurements we observe Fabry-Perot and Aharanov-Bohm oscillations which are robust in magnetic fields ranging from 0 to 8T, in strong contrast to more conventional 2D systems where trajectories in the bulk are bent by the Lorentz force. This persistence in magnetic field and the linear spacing in density indicate that charge carriers in the bulk flow in topologically protected, one dimensional channels. With this work we demonstrate coherent electronic transport in a lattice of topologically protected states.
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Topological insulators realized in materials with strong spin-orbit interactions challenged the long-held view that electronic materials are classified as either conductors or insulators. The emergence of controlled, two-dimensional moire patterns has opened new vistas in the topological materials landscape. Here we report on evidence, obtained by combining thermodynamic measurements, local and non-local transport measurements, and theoretical calculations, that robust topologically non-trivial, valley Chern insulators occur at charge neutrality in twisted double-bilayer graphene (TDBG). These time reversal-conserving valley Chern insulators are enabled by valley-number conservation, a symmetry that emerges from the moire pattern. The thermodynamic gap extracted from chemical potential measurements proves that TDBG is a bulk insulator under transverse electric field, while transport measurements confirm the existence of conducting edge states. A Landauer-Buttiker analysis of measurements on multi-terminal samples allows us to quantitatively assess edge state scattering and demonstrate that it does not destroy the edge states, leaving the bulk-boundary correspondence largely intact.
We numerically investigate the electronic transport properties between two mesoscopic graphene disks with a twist by employing the density functional theory coupled with non-equilibrium Greens function technique. By attaching two graphene leads to upper and lower graphene layers separately, we explore systematically the dependence of electronic transport on the twist angle, Fermi energy, system size, layer stacking order and twist axis. When choose different twist axes for either AA- or AB-stacked bilayer graphene, we find that the dependence of conductance on twist angle displays qualitatively distinction, i.e., the systems with top axis exhibit finite conductance oscillating as a function of the twist angle, while the ones with hollow axis exhibit nearly vanishing conductance for different twist angles or Fermi energies near the charge neutrality point. These findings suggest that the choice of twist axis can effectively tune the interlayer conductance, making it a crucial factor in designing of nanodevices with the twisted van der Waals multilayers.
We study conductance across a twisted bilayer graphene coupled to single-layer graphene leads in two setups: a flake of graphene on top of an infinite graphene ribbon and two overlapping semi-infinite graphene ribbons. We find conductance strongly depends on the angle between the two graphene layers and identify three qualitatively different regimes. For large angles ($theta gtrsim 10^{circ}$) there are strong commensurability effects for incommensurate angles the low energy conductance approaches that of two disconnected layers, while sharp conductance features correlate with commensurate angles with small unit cells. For intermediate angles ($3^{circ}lesssim theta lesssim 10^{circ}$), we find a one-to-one correspondence between certain conductance features and the twist-dependent Van Hove singularities arising at low energies, suggesting conductance measurements can be used to determine the twist angle. For small twist angles ($1^{circ}lesssimthetalesssim 3^{circ}$), commensurate effects seem to be washed out and the conductance becomes a smooth function of the angle. In this regime, conductance can be used to probe the narrow bands, with vanishing conductance regions corresponding to spectral gaps in the density of states, in agreement with recent experimental findings.
Active control of heat flow is of both fundamental and applied interest in thermal management and energy conversion. Here, we present a fluctuational electrodynamic study of thermal radiation between twisted bilayer graphene (TBLG), motivated by its unusual and highly tunable plasmonic properties. We show that near-field heat flow can vary by more than 10-fold over only a few degrees of twist, and identify special angles leading to heat flow extrema. These special angles are dictated by the Drude weight in the intraband optical conductivity of TBLG, and are roughly linear with the chemical potential. Further, we observe multiband thermal transport due to the increasing role of interband transitions as the twist angle decreases, in analogy to monolayer graphene in a magnetic field. Our findings are understood via the surface plasmons in TBLG, and highlight its potential for manipulating radiative heat flow.
Higher-order topological insulators are newly proposed topological phases of matter, whose bulk topology manifests as localized modes at two- or higher-dimensional lower boundaries. In this work, we propose the twisted bilayer graphenes with large angles as higher-order topological insulators, hosting topological corner charges. At large commensurate angles, the intervalley scattering opens up the bulk gap and the corner states occur at half filling. Based on both first-principles calculations and analytic analysis, we show the striking results that the emergence of the corner states do not depend on the choice of the specific angles as long as the underlying symmetries are intact. Our results show that the twisted bilayer graphene can serve as a robust candidate material of two-dimensional higher-order topological insulator.
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