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Register a new userEdge states in Graphene: from gapped flat band to gapless chiral modes
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We study edge-states in graphene systems where a bulk energy gap is opened by inversion symmetry breaking. We find that the edge-bands dispersion can be controlled by potentials applied on the boundary with unit cell length scale. Under certain boundary potentials, gapless edge-states with valley-dependent velocity are found, exactly analogous to the spin-dependent gapless chiral edge-states in quantum spin Hall systems. The connection of the edge-states to bulk topological properties is revealed.
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A central question in the field of graphene-related research is how graphene behaves when it is patterned at the nanometer scale with different edge geometries. Perhaps the most fundamental shape relevant to this question is the graphene nanoribbon (GNR), a narrow strip of graphene that can have different chirality depending on the angle at which it is cut. Such GNRs have been predicted to exhibit a wide range of behaviour (depending on their chirality and width) that includes tunable energy gaps and the presence of unique one-dimensional (1D) edge states with unusual magnetic structure. Most GNRs explored experimentally up to now have been characterized via electrical conductivity, leaving the critical relationship between electronic structure and local atomic geometry unclear (especially at edges). Here we present a sub-nm-resolved scanning tunnelling microscopy (STM) and spectroscopy (STS) study of GNRs that allows us to examine how GNR electronic structure depends on the chirality of atomically well-defined GNR edges. The GNRs used here were chemically synthesized via carbon nanotube (CNT) unzipping methods that allow flexible variation of GNR width, length, chirality, and substrate. Our STS measurements reveal the presence of 1D GNR edge states whose spatial characteristics closely match theoretical expectations for GNRs of similar width and chirality. We observe width-dependent splitting in the GNR edge state energy bands, providing compelling evidence of their magnetic nature. These results confirm the novel electronic behaviour predicted for GNRs with atomically clean edges, and thus open the door to a whole new area of applications exploiting the unique magnetoelectronic properties of chiral GNRs.
Photo-induced edge states in low dimensional materials have attracted considerable attention due to the tunability of topological properties and dispersion. Specifically, graphene nanoribbons have been predicted to host chiral edge modes upon irradiation with circularly polarized light. Here, we present numerical calculations of time-resolved angle resolved photoemission spectroscopy (trARPES) and time-resolved resonant inelastic x-ray scattering (trRIXS) of a graphene nanoribbon. We characterize pump-probe spectroscopic signatures of photo-induced edge states, illustrate the origin of distinct spectral features that arise from Floquet topological edge modes, and investigate the roles of incoming photon energies and finite core-hole lifetime in RIXS. With momentum, energy, and time resolution, pump-probe spectroscopies can play an important role in understanding the behavior of photo-induced topological states of matter.
Precise control over the size and shape of graphene nanostructures allows engineering spin-polarized edge and topological states, representing a novel source of non-conventional $pi$-magnetism with promising applications in quantum spintronics. A prerequisite for their emergence is the existence of robust gapped phases, which are difficult to find in extended graphene systems: only armchair graphene nanoribbons (GNRs) show a band gap that, however, closes for any other GNR orientation. Here we show that semi-metallic chiral GNRs (chGNRs) narrowed down to nanometer widths undergoes a topological phase transition, becoming first topological insulators, and transforming then into trivial band insulators for the narrowest chGNRs. We fabricated atomically precise chGNRs of different chirality and size by on surface synthesis using predesigned molecular precursors. Combining scanning tunnelling microscopy (STM) measurements and theory simulations, we follow the evolution of topological properties and bulk band gap depending on the width, length, and chirality of chGNRs. The first emerging gapped phases are topological, protected by a chiral interaction pattern between edges. For narrower ribbons, the symmetry of the interaction pattern changes, and the topological gap closes and re-opens again as a trivial band insulator. Our findings represent a new platform for producing topologically protected spin states and demonstrates the potential of connecting chiral edge and defect structure with band engineering.
We address the problem of hybridization between topological surface states and a non-topological flat bulk band. Our model, being a mixture of three-dimensional Bernevig-Hughes-Zhang and two-dimensional pseudospin-1 Hamiltonian, allows explicit treatment of the topological surface state evolution by continuously changing the hybridization between the inverted bands and an additional parasitic flat band in the bulk. We show that the hybridization with a flat band lying below the edge of conduction band converts the initial Dirac-like surface states into a branch below and one above the flat band. Our results univocally demonstrate that the upper branch of the topological surface states is formed by Dyakonov-Khaetskii surface states known for HgTe since the 1980s. Additionally we explore an evolution of the surface states and the arising of Fermi arcs in Dirac semimetals when the flat band crosses the conduction band.
We theoretically study electronic properties of a graphene sheet on xy plane in a spatially nonuniform magnetic field, $B = B_0 hat{z}$ in one domain and $B = B_1 hat{z}$ in the other domain, in the quantum Hall regime and in the low-energy limit. We find that the magnetic edge states of the Dirac fermions, formed along the boundary between the two domains, have features strongly dependent on whether $B_0$ is parallel or antiparallel to $B_1$. In the parallel case, when the Zeeman spin splitting can be ignored, the magnetic edge states originating from the $n=0$ Landau levels of the two domains have dispersionless energy levels, contrary to those from the $n e 0$ levels. Here, $n$ is the graphene Landau-level index. They become dispersive as the Zeeman splitting becomes finite or as an electrostatic step potential is additionally applied. In the antiparallel case, the $n=0$ magnetic edge states split into electron-like and hole-like current-carrying states. The energy gap between the electron-like and hole-like states can be created by the Zeeman splitting or by the step potential. These features are attributed to the fact that the pseudo-spin of the magnetic edge states couples to the direction of the magnetic field. We propose an Aharonov-Bohm interferometry setup in a graphene ribbon for experimental study of the magnetic edge states.
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