Topological edge plasmons in graphene's viscous Hall fluid
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Abstract The nontrivial topological origin and pseudospinorial character of electron wavefunctions make edge states possess unusual electronic properties. Twenty years ago, the tight‐binding model calculation predicted that zigzag termination of 2D sheets of carbon atoms have peculiar edge states, which show potential application in spintronics and modern information technologies. Although scanning probe microscopy is employed to capture this phenomenon, the experimental demonstration of its optical response remains challenging. Here, the propagating graphene plasmon provides an edge‐selective polaritonic probe to directly detect and control the electronic edge state at ambient condition. Compared with armchair, the edge‐band structure in the bandgap gives rise to additional optical absorption and strongly absorbed rim at zigzag edge. Furthermore, the optical conductivity is reconstructed and the anisotropic plasmon damping in graphene systems is revealed. The reported approach paves the way for detecting edge‐specific phenomena in other van der Waals materials and topological insulators.
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This study examines the edge modes of chiral Berry plasmons propagating along zigzag or armchair edges of a graphene nanoribbon under a finite Berry flux and Fermi pressure. A two-dimensional quantum hydrodynamic model is used to derive analytical expressions of the dispersion relation and transverse confinement length. Direction-dependent edge modes exist in armchair nanoribbons under antisymmetric or symmetric boundary conditions. A confined mode appears in the zigzag nanoribbon under hard-wall boundary conditions. The transverse confinement length of edge plasmons in the nanoribbon can be an order of magnitude shorter than that in the semi-infinite structure.
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The concept of valley physics, as inspired by the recent development in valleytronic materials, has been extended to acoustic crystals for manipulation of air-borne sound. Many valleytronic materials follow the model of a gapped graphene. Yet the previously demonstrated valley acoustic crystal adopted a mirror-symmetry-breaking mechanism, lacking a direct counterpart in condensed matter systems. In this paper, we investigate a two-dimensional (2D) periodic acoustic resonator system with inversion symmetry breaking, as an analogue of a gapped graphene monolayer. It demonstrates the quantum valley Hall topological phase for sound waves. Similar to a gapped graphene, gapless topological valley edge states can be found at a zigzag domain wall separating different domains with opposite valley Chern numbers, while an armchair domain wall hosts no gapless edge states. Our study offers a route to simulate novel valley phenomena predicted in gapped graphene and other 2D materials with classical acoustic waves.
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We study surface plasmons localized on interfaces between topologically trivial and topologically non-trivial time reversal invariant materials in three dimensions. For the interface between a metal and a topological insulator the magnetic polarization of the surface plasmon is rotated out of the plane of the interface; this effect should be experimentally observable by exciting the surface plasmon with polarized light. More interestingly, we argue that the same effect also is realized on the interface between vacuum and a doped topological insulator with non-vanishing bulk carrier density.
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The quantum Hall effect is studied in the topological insulator ${\mathrm{BiSbTeSe}}_{2}$. By employing top- and back-gate electric fields at high magnetic field, the Landau levels of the Dirac cones in the top and bottom topological surface states can be tuned independently. When one surface is tuned to the electron-doped side of the Dirac cone and the other surface to the hole-doped side, the quantum Hall edge channels are counter-propagating. The opposite edge mode direction, combined with the opposite helicities of top and bottom surfaces, allows for scattering between these counter-propagating edge modes. The total Hall conductance is expected to be integer valued only when the scattering is strong. For weaker interaction, a noninteger quantum Hall effect is expected and indications for this effect are measured.
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We study the integer and fractional quantum Hall effect on a honeycomb lattice at half-filling (graphene) in the presence of disorder and electron-electron interactions. We show that the interactions between the delocalized chiral edge states (generated by the magnetic field) and Anderson-localized surface states (created by the presence of zig-zag edges) lead to edge reconstruction. As a consequence, the point contact tunneling on a graphene edge has a nonuniversal tunneling exponent, and the Hall conductivity is not perfectly quantized in units of ${e}^{2}∕h$. We argue that the magnetotransport properties of graphene depend strongly on the strength of electron-electron interactions, the amount of disorder, and the details of the edges.
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