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Register a new userPseudo chiral anomaly in zigzag graphene ribbons
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Chang-An Li
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As the three-dimensional analogs of graphene, Weyl semimetals display signatures of chiral anomaly which arises from charge pumping between the lowest chiral Landau levels of the Weyl nodes in the presence of parallel electric and magnetic fields. In this work, we study the pseudo chiral anomaly and its transport signatures in graphene ribbon with zigzag edges. Here pseudo refers to the case where the inverse of width of zigzag graphene ribbon plays the same role as magnetic field in three-dimensional Weyl semimetals. The valley chiral bands in zigzag graphene ribbons can be introduced by edge potentials, giving rise to the nonconservation of chiral current, i.e., pseudo chiral anomaly, in the presence of a longitudinal electric field. Further numerical results reveal that pseudo magnetoconductivity of zigzag graphene ribbons is positive and has a nearly quadratic dependence on the pseudofield, which is regarded as the transport signature of pseudo chiral anomaly.
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Low-energy Landau levels of AB-stacked zigzag graphene ribbons in the presence of a uniform perpendicular magnetic field (textbf{B}) are investigated by the Peierls coupling tight-binding model. State energies and associated wave functions are dominated by the textbf{B}-field strength and the $k_z$-dependent interribbon interactions. The occupied valence bands are asymmetric to the unoccupied conduction bands about the Fermi level. Many doubly degenerate Landau levels and singlet curving magnetobands exist along $k_x$ and $k_z$ directions, respectively. Such features are directly reflected in density of states, which exhibits a lot of asymmetric prominent peaks because of 1D curving bands. The $k_z$-dependent interribbon interactions dramatically modify the magnetobands, such as the lift of double degeneracy, the change of state energies, and the production of two groups of curving magnetobands. They also change the characteristics of the wave functions and cause the redistribution of the charge carrier density. The $k_z$-dependent wave functions are further used to predict the selection rule of the optical transition.
Graphene is a monolayer of carbon atoms packed into a hexagon lattice to host two pairs of massless two-dimensional Dirac fermions in the absence of or with negligible spin-orbit coupling. It is known that the existence of non-zero electric polarization in reduced momentum space which is associated with a hidden chiral symmetry will lead to the zero-energy flat band of zigzag nanoribbon. The Adler-Bell-Jackiw chiral anomaly or non-conservation of chiral charges at different valleys can be realized in a confined ribbon of finite width. In the laterally diffusive regime, the finite-size correction to conductivity is always positive and goes inversely with the square of the lateral dimension W, which is different from the finite-size correction inversely with W from boundary modes. This anomalous finite-size conductivity reveals the signature of the chiral anomaly in graphene, and is measurable experimentally.
We construct a phenomenological scattering theory for the triangular network of valley Hall states that arises in twisted bilayer graphene under interlayer bias. Crucially, our network model includes scattering between different valley Hall states within the same valley and spin. We show that in the absence of forward scattering, symmetries reduce the network model to a single parameter that interpolates between a nested Fermi surface and flatbands, which can be understood in terms of one-dimensional chiral zigzag modes and closed triangular orbits, respectively. We demonstrate how unitarity and symmetry constrain the couplings between zigzag modes, which has important implications on the nature of interference oscillations observed in experiments.
We address the electronic structure and magnetic properties of vacancies and voids both in graphene and graphene ribbons. Using a mean field Hubbard model, we study the appearance of magnetic textures associated to removing a single atom (vacancy) and multiple adjacent atoms (voids) as well as the magnetic interactions between them. A simple set of rules, based upon Lieb theorem, link the atomic structure and the spatial arrangement of the defects to the emerging magnetic order. The total spin $S$ of a given defect depends on its sublattice imbalance, but some defects with S=0 can still have local magnetic moments. The sublattice imbalance also determines whether the defects interact ferromagnetically or antiferromagnetically with one another and the range of these magnetic interactions is studied in some simple cases. We find that in semiconducting armchair ribbons and two-dimensional graphene without global sublattice imbalance there is maximum defect density above which local magnetization disappears. Interestingly, the electronic properties of semiconducting graphene ribbons with uncoupled local moments are very similar to those of diluted magnetic semiconductors, presenting giant Zeeman splitting.
The edge states in the integer quantum Hall effect are known to be significantly affected by electrostatic interactions leading to the formation of compressible and incompressible strips at the boundaries of Hall bars. We show here, in a combined experimental and theoretical analysis, that this does not hold for the quantum Hall effect in narrow graphene ribbons. In our graphene Hall bar, which is only 60 nm wide, we observe the quantum Hall effect up to Landau level index k=2 and show within a zero free-parameter model that the spatial extent of the compressible and incompressible strips is of a similar magnitude as the magnetic length. We conclude that in narrow graphene ribbons the single-particle picture is a more appropriate description of the quantum Hall effect and that electrostatic effects are of minor importance.
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