8,212 research outputs found
Generalized transfer matrix theory on electronic transport through graphene waveguide
In the effective mass approximation, electronic property in graphene can be
characterized by the relativistic Dirac equation. Within such a continuum model
we investigate the electronic transport through graphene waveguides formed by
connecting multiple segments of armchair-edged graphene nanoribbons of
different widths. By using appropriate wavefunction connection conditions at
the junction interfaces, we generalize the conventional transfer matrix
approach to formulate the linear conductance of the graphene waveguide in terms
of the structure parameters and the incident electron energy. In comparison
with the tight-binding calculation, we find that the generalized transfer
matrix method works well in calculating the conductance spectrum of a graphene
waveguide even with a complicated structure and relatively large size. The
calculated conductance spectrum indicates that the graphene waveguide exhibits
a well-defined insulating band around the Dirac point, even though all the
constituent ribbon segments are gapless. We attribute the occurrence of the
insulating band to the antiresonance effect which is intimately associated with
the edge states localized at the shoulder regions of the junctions.
Furthermore, such an insulating band can be sensitively shifted by a gate
voltage, which suggests a device application of the graphene waveguide as an
electric nanoswitch.Comment: 11 pages, 5 figure
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Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
We introduce the notion of algebraic higher symmetry, which generalizes
higher symmetry and is beyond higher group. We show that an algebraic higher
symmetry in a bosonic system in -dimensional space is characterized and
classified by a local fusion -category. We find another way to describe
algebraic higher symmetry by restricting to symmetric sub Hilbert space where
symmetry transformations all become trivial. In this case, algebraic higher
symmetry can be fully characterized by a non-invertible gravitational anomaly
(i.e. an topological order in one higher dimension). Thus we also refer to
non-invertible gravitational anomaly as categorical symmetry to stress its
connection to symmetry. This provides a holographic and entanglement view of
symmetries. For a system with a categorical symmetry, its gapped state must
spontaneously break part (not all) of the symmetry, and the state with the full
symmetry must be gapless. Using such a holographic point of view, we obtain (1)
the gauging of the algebraic higher symmetry; (2) the classification of
anomalies for an algebraic higher symmetry; (3) the equivalence between classes
of systems, with different (potentially anomalous) algebraic higher symmetries
or different sets of low energy excitations, as long as they have the same
categorical symmetry; (4) the classification of gapped liquid phases for
bosonic/fermionic systems with a categorical symmetry, as gapped boundaries of
a topological order in one higher dimension (that corresponds to the
categorical symmetry). This classification includes symmetry protected trivial
(SPT) orders and symmetry enriched topological (SET) orders with an algebraic
higher symmetry.Comment: 61 pages, 31 figure
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