1,224 research outputs found
Reversible modifications of linear dispersion - graphene between boron nitride monolayers
Electronic properties of the graphene layer sandwiched between two hexagonal
boron nitride sheets have been studied using the first-principles calculations
and the minimal tight-binding model. It is shown that for the ABC-stacked
structure in the absence of external field the bands are linear in the vicinity
of the Dirac points as in the case of single-layer graphene. For certain atomic
configuration, the electric field effect allows opening of a band gap of over
230 meV. We believe that this mechanism of energy gap tuning could
significantly improve the characteristics of graphene-based field-effect
transistors and pave the way for future electronic applications.Comment: 5 pages, v2 with slightly modified introduction and summar
QED2+1 in graphene: symmetries of Dirac equation in 2+1 dimensions
It is well-known that the tight-binding Hamiltonian of graphene describes the
low-energy excitations that appear to be massless chiral Dirac fermions. Thus,
in the continuum limit one can analyze the crystal properties using the
formalism of quantum electrodynamics in 2+1 dimensions (QED2+1) which provides
the opportunity to verify the high energy physics phenomena in the condensed
matter system. We study the symmetry properties of 2+1-dimensional Dirac
equation, both in the non-interacting case and in the case with constant
uniform magnetic field included in the model. The maximal symmetry group of the
massless Dirac equation is considered by putting it in the Jordan block form
and determining the algebra of operators leaving invariant the subspace of
solutions. It is shown that the resulting symmetry operators expressed in terms
of Dirac matrices cannot be described exclusively in terms of gamma matrices
(and their products) entering the corresponding Dirac equation. It is a
consequence of the reducibility of the considered representation in contrast to
the 3+1-dimensional case. Symmetry algebra is demonstrated to be a direct sum
of two gl(2,C) algebras plus an eight-dimensional abelian ideal. Since the
matrix structure which determines the rotational symmetry has all required
properties of the spin algebra, the pseudospin related to the sublattices (M.
Mecklenburg and B. C. Regan, Phys. Rev. Lett. 106, 116803 (2011)) gains the
character of the real angular momentum, although the degrees of freedom
connected with the electron's spin are not included in the model. This seems to
be graphene's analogue of the phenomenon called "spin from isospin" in high
energy physics
Irreducible Representations of an Algebra underlying Hidden Symmetries of a class of Quasi Exactly Solvable Systems of Equations
The set of linear, differential operators preserving the vector space of
couples of polynomials of degrees n and n-2 in one real variable leads to an
abstract associative graded algebra A(2). The irreducible, finite dimensional
representations of this algebra are classified into five infinite discrete sets
and one exceptional case. Their matrix elements are given explicitely. The
results are related to the theory of quasi exactly solvable equations.Comment: 38 pages, late
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