925 research outputs found
Luttinger Liquid at the Edge of a Graphene Vacuum
We demonstrate that an undoped two-dimensional carbon plane (graphene) whose
bulk is in the integer quantum Hall regime supports a non-chiral Luttinger
liquid at an armchair edge. This behavior arises due to the unusual dispersion
of the non-interacting edges states, causing a crossing of bands with different
valley and spin indices at the edge. We demonstrate that this stabilizes a
domain wall structure with a spontaneously ordered phase degree of freedom.
This coherent domain wall supports gapless charged excitations, and has a power
law tunneling with a non-integral exponent. In proximity to a bulk lead,
the edge may undergo a quantum phase transition between the Luttinger liquid
phase and a metallic state when the edge confinement is sufficiently strong
relative to the interaction energy scale.Comment: 4 pages, 3 figure
Electronic States of Wires and Slabs of Topological Insulators: Quantum Hall Effects and Edge Transport
We develop a simple model of surface states for topological insulators,
developing matching relations for states on surfaces of different orientations.
The model allows one to write simple Dirac Hamiltonians for each surface, and
to determine how perturbations that couple to electron spin impact them. We
then study two specific realizations of such systems: quantum wires of
rectangular cross-section and a rectangular slab in a magnetic field. In the
former case we find a gap at zero energy due to the finite size of the system.
This can be removed by application of exchange fields on the top and bottom
surfaces, which lead to gapless chiral states appearing on the lateral
surfaces. In the presence of a magnetic field, we examine how Landau level
states on surfaces perpendicular to the field join onto confined states of the
lateral surfaces. We show that an imbalance in the number of states propagating
in each direction on the lateral surface is sufficient to stabilize a quantized
Hall effect if there are processes that equilibrate the distribution of current
among these channels.Comment: 14 pages, 9 figures include
Effective Magnetic Fields in Graphene Superlattices
We demonstrate that the electronic spectrum of graphene in a one-dimensional
periodic potential will develop a Landau level spectrum when the potential
magnitude varies slowly in space. The effect is related to extra Dirac points
generated by the potential whose positions are sensitive to its magnitude. We
develop an effective theory that exploits a chiral symmetry in the Dirac
Hamiltonian description with a superlattice potential, to show that the low
energy theory contains an effective magnetic field. Numerical diagonalization
of the Dirac equation confirms the presence of Landau levels. Possible
consequences for transport are discussed.Comment: 4 pages (+ 2 pages of supplementary material), 3 figure
Lattice-Spin Mechanism in Colossal Magnetoresistant Manganites
We present a single-orbital double-exchange model, coupled with cooperative
phonons (the so called breathing-modes of the oxygen octahedra in manganites).
The model is studied with Monte Carlo simulations. For a finite range of doping
and coupling constants, a first-order Metal-Insulator phase transition is
found, that coincides with the Paramagnetic-Ferromagnetic phase transition. The
insulating state is due to the self-trapping of every carrier within an oxygen
octahedron distortion.Comment: 4 pages, 5 figures, ReVTeX macro, accepted for publication in PR
Transport in superlattices on single layer graphene
We study transport in undoped graphene in the presence of a superlattice
potential both within a simple continuum model and using numerical
tight-binding calculations. The continuum model demonstrates that the
conductivity of the system is primarily impacted by the velocity anisotropy
that the Dirac points of graphene develop due to the potential. For
one-dimensional superlattice potentials, new Dirac points may be generated, and
the resulting conductivities can be approximately described by the anisotropic
conductivities associated with each Dirac point. Tight-binding calculations
demonstrate that this simple model is quantitatively correct for a single Dirac
point, and that it works qualitatively when there are multiple Dirac points.
Remarkably, for a two dimensional potential which may be very strong but
introduces no anisotropy in the Dirac point, the conductivity of the system
remains essentially the same as when no external potential is present.Comment: 8 pages, 7 figures, submitted to Phys. Rev.
Electronic States of Graphene Nanoribbons
We study the electronic states of narrow graphene ribbons (``nanoribbons'')
with zigzag and armchair edges. The finite width of these systems breaks the
spectrum into an infinite set of bands, which we demonstrate can be
quantitatively understood using the Dirac equation with appropriate boundary
conditions. For the zigzag nanoribbon we demonstrate that the boundary
condition allows a particle- and a hole-like band with evanescent wavefunctions
confined to the surfaces, which continuously turn into the well-known zero
energy surface states as the width gets large. For armchair edges, we show that
the boundary condition leads to admixing of valley states, and the band
structure is metallic when the width of the sample in lattice constant units is
divisible by 3, and insulating otherwise. A comparison of the wavefunctions and
energies from tight-binding calculations and solutions of the Dirac equations
yields quantitative agreement for all but the narrowest ribbons.Comment: 5 pages, 6 figure
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