Graphene: Topological Properties, Chiral Symmetry and Their Manipulation

Hatsugai, Yasuhiro; Aoki, Hideo

doi:10.1007/978-3-319-02633-6_7

Cited by 8 publications

(24 citation statements)

References 88 publications

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“…Graphene lattice is two-dimensional, unlike that of polyacetylene. Chiral symmetry then leads to a phenomenon called “fermion doubling” [27] (K and K’ valleys exist). It implies that a GNR with the shortest width has two domain-wall states, in contrast to polyacetylene (for other values of the width the number of zero modes is an even integer [13]).…”

Section: Solitons In Insulating Gnrmentioning

confidence: 99%

Soliton Fractional Charges in Graphene Nanoribbon and Polyacetylene: Similarities and Differences

Yang

2019

Nanomaterials

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An introductory overview of current research developments regarding solitons and fractional boundary charges in graphene nanoribbons is presented. Graphene nanoribbons and polyacetylene have chiral symmetry and share numerous similar properties, e.g., the bulk-edge correspondence between the Zak phase and the existence of edge states, along with the presence of chiral boundary states, which are important for charge fractionalization. In polyacetylene, a fermion mass potential in the Dirac equation produces an excitation gap, and a twist in this scalar potential produces a zero-energy chiral soliton. Similarly, in a gapful armchair graphene nanoribbon, a distortion in the chiral gauge field can produce soliton states. In polyacetylene, a soliton is bound to a domain wall connecting two different dimerized phases. In graphene nanoribbons, a domain-wall soliton connects two topological zigzag edges with different chiralities. However, such a soliton does not display spin-charge separation. The existence of a soliton in finite-length polyacetylene can induce formation of fractional charges on the opposite ends. In contrast, for gapful graphene nanoribbons, the antiferromagnetic coupling between the opposite zigzag edges induces integer boundary charges. The presence of disorder in graphene nanoribbons partly mitigates antiferromagnetic coupling effect. Hence, the average edge charge of gap states with energies within a small interval is e / 2 , with significant charge fluctuations. However, midgap states exhibit a well-defined charge fractionalization between the opposite zigzag edges in the weak-disorder regime. Numerous occupied soliton states in a disorder-free and doped zigzag graphene nanoribbon form a solitonic phase.

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Section: Solitons In Insulating Gnrmentioning

confidence: 99%

Soliton Fractional Charges in Graphene Nanoribbon and Polyacetylene: Similarities and Differences

Yang

2019

Nanomaterials

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“…where −∆ c is the upper bound of the lower Hubbard band given in Eq. (35). Note that this quantity becomes…”

Section: Single-particle Excitation Spectrummentioning

confidence: 97%

Emergence of massless Dirac quasiparticles in correlated hydrogenated graphene with broken sublattice symmetry

et al. 2016

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Using the variational cluster approximation (VCA) and the cluster perturbation theory, we study the finite temperature phase diagram of a half-depleted periodic Anderson model on the honeycomb lattice at half filling for a model of graphone, i.e., single-side hydrogenated graphene. The ground state of this model is found to be ferromagnetic (FM) semi-metal. The origin of this FM state is attributed to the instability of a flat band located at the Fermi energy in the noninteracting limit and is smoothly connected to the Lieb-Mattis type ferromagnetism. The spin wave dispersion in the FM state is linear in momentum at zero temperature but becomes quadratic at finite temperatures, implying that the FM state is fragile against thermal fluctuations. Indeed, our VCA calculations find that the paramagnetic (PM) state dominates the finite temperature phase diagram. More surprisingly, we find that massless Dirac quasiparticles with the linear energy dispersion emerge at the Fermi energy upon introducing the electron correlation U at the impurity sites in the PM phase. The Dirac Fermi velocity is found to be highly correlated to the quasiparticle weight of the emergent massless Dirac quasiparticles at the Fermi energy and monotonically increases with U . These unexpected massless Dirac quasiparticles are also examined with the Hubbard-I approximation and the origin is discussed in terms of the spectral weight redistribution involving a large energy scale of U . Considering an effective quasiparticle Hamiltonian which reproduces the single-particle excitations obtained by the Hubbard-I approximation, we argue that the massless Dirac quasiparticles are protected by the electron correlation. Our finding is therefore the first example of the emergence of massless Dirac quasiparticles due to dynamical electron correlations without breaking any spatial symmetry. The experimental implications of our results for graphone as well as a graphene sheet on transition metal substrates are also briefly discussed.

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“…For the two-dimensional massless Dirac fermions as in graphene [2][3][4], it has been shown that the symmetry protects the zero-mode Landau levels, which gives rise to a criticality of the quantum Hall transition at the chargeneutrality point [5][6][7][8]. The chiral symmetry has then been extended to encompass more general cases, namely tilted Dirac fermions such as observed in an organic compound α-(BEDT-TTF) 2 I 3 [9][10][11][12][13][14][15], where the robustness of the zero modes is retained for tilted massless as well as massive Dirac fermions [16,17].…”

Section: Introductionmentioning

confidence: 99%

Lattice realization of the generalized chiral symmetry in two dimensions

2016

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While it has been pointed out that the chiral symmetry, which is important for the Dirac fermions in graphene, can be generalized to tilted Dirac fermions as in organic metals, such a generalized symmetry was so far defined only for a continuous low-energy Hamiltonian. Here we show that the generalized chiral symmetry can be rigorously defined for lattice fermions as well. A key concept is a continuous "algebraic deformation" of Hamiltonians, which generates lattice models with the generalized chiral symmetry from those with the conventional chiral symmetry. This enables us to explicitly express zero modes of the deformed Hamiltonian in terms of that of the original Hamiltonian. Another virtue is that the deformation can be extended to non-uniform systems, such as fermion-vortex systems and disordered systems. Application to fermion vortices in a deformed system shows how the zero modes for the conventional Dirac fermions with vortices can be extended to the tilted case.

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Graphene: Topological Properties, Chiral Symmetry and Their Manipulation

Cited by 8 publications

References 88 publications

Soliton Fractional Charges in Graphene Nanoribbon and Polyacetylene: Similarities and Differences

Soliton Fractional Charges in Graphene Nanoribbon and Polyacetylene: Similarities and Differences

Emergence of massless Dirac quasiparticles in correlated hydrogenated graphene with broken sublattice symmetry

Lattice realization of the generalized chiral symmetry in two dimensions

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