11 research outputs found
Intrinsic Zeeman Effect in Graphene
The intrinsic Zeeman energy is precisely one half of the cyclotron energy for
electrons in graphene. As a result a Landau-level mixing occurs to create the
energy spectrum comprised of the -fold degenerated zero-energy level and
4-fold degenerated nonzero-energy levels in the -layer graphene, where
for monolayer, bilayer and trilayer, respectively. The degeneracy
manifests itself in the quantum Hall (QH) effect. We study how the degeneracy
is removed by the Coulomb interactions. With respect to the zero-energy level,
an excitonic gap opens by making a BCS-type condensation of electron-hole pairs
at the filling factor . It gives birth to the Ising QH ferromagnet at
for monolayer, for bilayer, and for trilayer graphene from the zero-energy degeneracy. With respect to
the nonzero-energy level, a remarkable consequence is derived that the
effective Coulomb potential depends on spins, since a single energy level
contains up-spin and down-spin electrons belonging to different Landau levels.
The spin-dependent Coulomb interaction leads to the valley polarization at for monolayer,
for bilayer, and for trilayer graphene.Comment: 24 pages, 9 figures, to appear in J. Phys. Soc. Jp
The ground state of the two-leg Hubbard ladder: a density--matrix renormalization group study
We present density-matrix renormalization group results for the ground state
properties of two-leg Hubbard ladders. The half-filled Hubbard ladder is an
insulating spin-gapped system, exhibiting a crossover from a spin-liquid to a
band-insulator as a function of the interchain hopping matrix element. When the
system is doped, there is a parameter range in which the spin gap remains. In
this phase, the doped holes form singlet pairs and the pair-field and the "" density correlations associated with pair density fluctuations decay as
power laws, while the "" charge density wave correlations decay
exponentially. We discuss the behavior of the exponents of the pairing and
density correlations within this spin gapped phase. Additional one-band
Luttinger liquid phases which occur in the large interband hopping regime are
also discussed.Comment: 14 pages, 18 figures, uses Revtex with epsfig to include the figure
Renormalization Group Approach to Low Temperature Properties of a Non-Fermi Liquid Metal
We expand upon on an earlier renormalization group analysis of a non-Fermi
liquid fixed point that plausibly govers the two dimensional electron liquid in
a magnetic field near filling fraction . We give a more complete
description of our somewhat unorthodox renormalization group transformation by
relating both our field-theoretic approach to a direct mode elimination and our
anisotropic scaling to the general problem of incorporating curvature of the
Fermi surface. We derive physical consequences of the fixed point by showing
how they follow from renormalization group equations for finite-size scaling,
where the size may be set by the temperature or by the frequency of interest.
In order fully to exploit this approach, it is necessary to take into account
composite operators, including in some cases dangerous ``irrelevant''
operators. We devote special attention to gauge invariance, both as a formal
requirement and in its positive role providing Ward identities constraining the
renormalization of composite operators. We emphasize that new considerations
arise in describing properties of the physical electrons (as opposed to the
quasiparticles.) We propose an experiment which, if feasible, will allow the
most characteristic feature of our results, that isComment: 42 pages, 5 figures upon request, uses Phyzzx, IASSNS-HEP 94/6
Universal Fluctuation of the Hall Conductance in the Random Magnetic Field
We show that the RMS fluctuation of the antisymmetric part of the Hall
conductance of a planar mesoscopic metal in a random magnetic field with zero
average is universal, of the order of , independent of the amplitude of
the random magnetic field and the diffusion coefficient even in the weak field
limit. This quantity is exactly zero in the case of ordinary scalar disorder.
We propose an experiment to measure this surprising effect, and also discuss
its implications on the localization physics of this system. Our result applies
to some other systems with broken time-reversal ({\bf T}) symmetry.Comment: 4 pages, Revtex 3.0; added the paragraph regarding applicability to
other systems with broken T-invariance, misc. minor change
Observation of Electron-Hole Puddles in Graphene Using a Scanning Single Electron Transistor
The electronic density of states of graphene is equivalent to that of
relativistic electrons. In the absence of disorder or external doping the Fermi
energy lies at the Dirac point where the density of states vanishes. Although
transport measurements at high carrier densities indicate rather high
mobilities, many questions pertaining to disorder remain unanswered. In
particular, it has been argued theoretically, that when the average carrier
density is zero, the inescapable presence of disorder will lead to electron and
hole puddles with equal probability. In this work, we use a scanning single
electron transistor to image the carrier density landscape of graphene in the
vicinity of the neutrality point. Our results clearly show the electron-hole
puddles expected theoretically. In addition, our measurement technique enables
to determine locally the density of states in graphene. In contrast to
previously studied massive two dimensional electron systems, the kinetic
contribution to the density of states accounts quantitatively for the measured
signal. Our results suggests that exchange and correlation effects are either
weak or have canceling contributions.Comment: 13 pages, 5 figure
QED3 theory of underdoped high temperature superconductors
Low-energy theory of d-wave quasiparticles coupled to fluctuating vortex
loops that describes the loss of phase coherence in a two dimensional d-wave
superconductor at T=0 is derived. The theory has the form of 2+1 dimensional
quantum electrodynamics (QED3), and is proposed as an effective description of
the T=0 superconductor-insulator transition in underdoped cuprates. The
coupling constant ("charge") in this theory is proportional to the dual order
parameter of the XY model, which is assumed to be describing the quantum
fluctuations of the phase of the superconducting order parameter. The principal
result is that the destruction of phase coherence in d-wave superconductors
typically, and immediately, leads to antiferromagnetism. The transition can be
understood in terms of the spontaneous breaking of an approximate "chiral"
SU(2) symmetry, which may be discerned at low enough energies in the standard
d-wave superconductor. The mechanism of the symmetry breaking is analogous to
the dynamical mass generation in the QED3, with the "mass" here being
proportional to staggered magnetization. Other insulating phases that break
chiral symmetry include the translationally invariant "d+ip" and "d+is"
insulators, and various one dimensional charge-density and spin-density waves.
The theory offers an explanation for the rounded d-wave-like dispersion seen in
ARPES experiments on Ca2CuO2Cl2 (F. Ronning et. al., Science 282, 2067 (1998)).Comment: Revtex, 20 pages, 5 figures; this is a much extended follow-up to the
Phys. Rev. Lett. vol.88, 047006 (2002) (cond-mat/0110188); improved
presentation, many additional explanations, comments, and references added,
sec. IV rewritten. Final version, to appear in Phys. Rev.
Effects of disorder on two strongly correlated coupled chains
We study the effects of disorder on a system of two coupled chain of strongly
correlated fermions (ladder system), using renormalization group. The stability
of the phases of the pure system is investigated as a function of interactions
both for fermions with spin and spinless fermions. For spinless fermions the
repulsive side is strongly localized whereas the system with attractive
interactions is stable with respect to disorder, at variance with the single
chain case. For fermions with spins, the repulsive side is also localized, and
in particular the d-wave superconducting phase found for the pure system is
totally destroyed by an arbitrarily small amount of disorder. On the other hand
the attractive side is again remarkably stable with respect to localization. We
have also computed the charge stiffness, the localization length and the
temperature dependence of the conductivity for the various phases. In the range
of parameter where d-wave superconductivity would occur for the pure system the
conductivity is found to decrease monotonically with temperature, even at high
temperature, and we discuss this surprising result. For a model with one site
repulsion and nearest neighbor attraction, the most stable phase is an orbital
antiferromagnet . Although this phase has no divergent superconducting
fluctuation it can have a divergent conductivity at low temperature. We argue
based on our results that the superconductivity observed in some two chain
compounds cannot be a simple stabilization of the d-wave phase found for a pure
single ladder. Applications to quantum wires are discussed.Comment: 47 pages, ReVTeX , 8 eps figures submitted to PR