Perfect one-dimensional chiral states in biased twisted bilayer graphene

Tsim, Bonnie; Nam, Nguyen N. T.; Koshino, Mikito

doi:10.1103/physrevb.101.125409

Cited by 48 publications

(34 citation statements)

References 57 publications

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“…At the interface between the AB and BA regions, and because of the difference in band topology, two EES per spin and valley appear [26,34,35], with opposite propagation direction in opposite valleys, which has been experimentally proven [36][37][38][39][40]. In TBGs the existence of a network of EES encircling the triangular regions with AB and BA stacking has been predicted [41][42][43][44][45][46] and recently experimentally observed [47].…”

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confidence: 85%

Plasmonic Dirac Cone in Twisted Bilayer Graphene

et al. 2020

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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 that appear at the AB-BA interfaces. The CEP form a hexagonal network with a unique energy scale ϵ p ¼ ðe 2 Þ=ðϵ 0 ϵt 0 Þ with t 0 the moiré lattice constant and ϵ 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 ℏω ∼ ϵ p =2 with sound velocity v D ¼ 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.

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confidence: 85%

Plasmonic Dirac Cone in Twisted Bilayer Graphene

et al. 2020

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“…where 𝜏 = [(𝑎/ √ 3) 2 + 𝑑 2 ] 1/2 is the distance between the nearest-neighbor sites. The decay length 𝑟 0 = (𝑎−𝜏)/ln 10 is determined in order to let the second nearest-neighbor hopping 𝑉 (𝑎) be 0.1 times the nearest-neighbor hopping 𝑉 (0) [49]. Note that 𝑉 𝑖 𝑗 𝛼 (𝜏) = 𝑉 (0) 𝑖 𝑗 𝛼 by definition.…”

Section: Slater-koster Tight-binding Modelmentioning

confidence: 99%

Topological edge and corner states and fractional corner charges in blue phosphorene

Tani,

Hitomi,

Kawakami

et al. 2021

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We theoretically study emergent edge and corner states in monolayer blue phosphorus (blue phosphorene) using the first-principles calculation and tight-binding model. We show that the existence of the Wannier orbitals at every bond center yields edge states both in zigzag and armchair nanoribbons. The properties of the edge states can be well described by a simple effective Hamiltonian for uncoupled edge orbitals, where the structural relaxation near the boundary significantly affects the edge band structure. For corner states, we examine two types of corner structures consisting of zigzag and armchair edges, where we find that multiple corner states emerge in the bulk gap as a consequence of hybridization of edge and corner uncoupled orbitals. In the armchair corner, in particular, we demonstrate that corner states appear right at the Fermi energy, which leads to the emergence of fractional corner charge due to filling anomaly. Finally, we discuss the relationship between blue phosphorene and black phosphorene, and show that two systems share the equivalent Wannier orbital positions and similar edge/corner state properties even though their atomic structures are totally different.

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“…The triangular topological network of one-dimensional (1D) states has been predicted by theory [17][18][19][20], and its existence has been attributed to topological phase transitions across the AB/BA domains inside the moiré pattern. This phase transition is caused by the application of a perpendicular electric field, which breaks the inversion symmetry of the AB and BA stacking configurations.…”

Section: Introductionmentioning

confidence: 99%

“…Accounting for spin degeneracy, the total conductance of the one-dimensional boundary states is 4e 2 /h. Additionally, the current along the domain boundaries is valley polarized, i.e., the K and K states counterpropagate [15][16][17][19][20][21][22]. The topological protection ensures that intervalley backscattering is prevented.…”

Section: Introductionmentioning

confidence: 99%

Valley-protected one-dimensional states in small-angle twisted bilayer graphene

et al. 2021

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Theory predicts that the application of an electric field breaks the inversion symmetry of AB and BA stacked domains in twisted bilayer graphene, resulting in the formation of a triangular network of one-dimensional valley-protected helical states. This two-dimensional network of one-dimensional states has been observed in several studies, but direct experimental evidence that the electronic transport in these one-dimensional states is valley protected is still lacking. In this paper, we report the existence of the network in small-angle twisted bilayer graphene at room temperature. Moreover, by analyzing Fourier transforms of atomically resolved scanning tunneling microscopy images of minimally twisted bilayer graphene, we provide convincing experimental evidence that the electronic transport in the counterpropagating one-dimensional states is indeed valley protected.

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Perfect one-dimensional chiral states in biased twisted bilayer graphene

Cited by 48 publications

References 57 publications

Plasmonic Dirac Cone in Twisted Bilayer Graphene

Plasmonic Dirac Cone in Twisted Bilayer Graphene

Topological edge and corner states and fractional corner charges in blue phosphorene

Valley-protected one-dimensional states in small-angle twisted bilayer graphene

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