373 research outputs found
Energy spectrum of graphene multilayers in a parallel magnetic field
We study the orbital effect of a strong magnetic field parallel to the layers
on the energy spectrum of the Bernal-stacked graphene bilayer and multilayers,
including graphite. We consider the minimal model with the electron tunneling
between the nearest sites in the plane and out of the plane. Using the
semiclassical analytical approximation and exact numerical diagonalization, we
find that the energy spectrum consists of two domains. In the low- and
high-energy domains, the semiclassical electron orbits are closed and open, so
the spectra are discrete and continuous, correspondingly. The discrete energy
levels are the analogs of the Landau levels for the parallel magnetic field.
They can be detected experimentally using electron tunneling and optical
spectroscopy. In both domains, the electron wave functions are localized on a
finite number of graphene layers, so the results can be applied to graphene
multilayers of a finite thickness.Comment: 11 pages, 13 figures. Added to v.2: Appendix A, Fig. 13, Refs.
[18-23]. V.3: minor stylistic corrections from the published versio
On the Number of Zeros of Abelian Integrals: A Constructive Solution of the Infinitesimal Hilbert Sixteenth Problem
We prove that the number of limit cycles generated by a small
non-conservative perturbation of a Hamiltonian polynomial vector field on the
plane, is bounded by a double exponential of the degree of the fields. This
solves the long-standing tangential Hilbert 16th problem. The proof uses only
the fact that Abelian integrals of a given degree are horizontal sections of a
regular flat meromorphic connection (Gauss-Manin connection) with a
quasiunipotent monodromy group.Comment: Final revisio
Field-induced spin density wave in (TMTSF)NO
Interlayer magnetoresistance of the Bechgaard salt (TMTSF)NO is
investigated up to 50 teslas under pressures of a few kilobars. This compound,
the Fermi surface of which is quasi two-dimensional at low temperature, is a
semi metal under pressure. Nevertheless, a field-induced spin density wave is
evidenced at 8.5 kbar above 20 T. This state is characterized by a
drastically different spectrum of the quantum oscillations compared to the low
pressure spin density wave state.Comment: to be published in Phys. Rev. B 71 (2005
On the multiplicity of the hyperelliptic integrals
Let be an Abelian integral, where
is a hyperelliptic polynomial of Morse type, a
horizontal family of cycles in the curves , and a polynomial
1-form in the variables and . We provide an upper bound on the
multiplicity of , away from the critical values of . Namely: $ord\
I(t) \leq n-1+\frac{n(n-1)}{2}\deg \omega <\deg H=n+1\delta(t)nHHI(t)\gamma(t)\textbf C^ n\gamma(t)\omegaHI(t)\{H=t\}
\subseteq \textbf C^2\omega\gamma(t)\textbf C^{n+1}ord I(t)\deg \omega$.Comment: 18 page
Sign reversals of the quantum Hall effect and helicoidal magnetic-field-induced spin-density waves in quasi-one-dimensional organic conductors
We study the effect of umklapp scattering on the magnetic-field-induced
spin-density-wave phases, which are experimentally observed in the
quasi-one-dimensional organic conductors of the Bechgaard salts family. Within
the framework of the quantized nesting model, we show that umklapp processes
may naturally explain sign reversals of the quantum Hall effect (QHE) observed
in these conductors. Moreover, umklapp scattering can change the polarization
of the spin-density wave (SDW) from linear (sinusoidal SDW) to circular
(helicoidal SDW). The QHE vanishes in the helicoidal phases, but a
magnetoelectric effect appears. These two characteristic properties may be
utilized to detect the magnetic-field-induced helicoidal SDW phases
experimentally.Comment: 4 pages, latex, 3 figure
Deconfined Fermions but Confined Coherence?
The cuprate superconductors and certain organic conductors exhibit transport
which is qualitatively anisotropic, yet at the same time other properties of
these materials strongly suggest the existence of a Fermi surface and low
energy excitations with substantial free electron character. The former of
these features is very difficult to account for if the material possesses three
dimensional coherence, while the latter is inconsistent with a description
based on a two dimensional fixed point. We therefore present a new proposal for
these materials in which they are categorized by a fixed point at which
transport in one direction is not renormalization group irrelevant, but is
intrinsically incoherent, i.e. the incoherence is present in a pure system, at
zero temperature. The defining property of such a state is that single electron
coherence is confined to lower dimensional subspaces (planes or chains) so that
it is impossible to observe interference effects between histories which
involve electrons moving between these subspaces.Comment: 31 pages, REVTEX, 3 eps figures, epsf.tex macr
Dispersion Instability in Strongly Interacting Electron Liquids
We show that the low-density strongly interacting electron liquid,
interacting via the long-range Coulomb interaction, could develop a dispersion
instability at a critical density associated with the approximate flattening of
the quasiparticle energy dispersion. At the critical density the quasiparticle
effective mass diverges at the Fermi surface, but the signature of this Fermi
surface instability manifests itself away from the Fermi momentum at higher
densities. For densities below the critical density the system is unstable
since the quasiparticle velocity becomes negative. We show that one physical
mechanism underlying the dispersion instability is the emission of soft
plasmons by the quasiparticles. The dispersion instability occurs both in two
and three dimensional electron liquids. We discuss the implications of the
dispersion instability for experiments at low electron densities.Comment: Accepted version for publicatio
Edge electron states for quasi-one-dimensional organic conductors in the magnetic-field-induced spin-density-wave phases
We develop a microscopic picture of the electron states localized at the
edges perpendicular to the chains in the Bechgaard salts in the quantum Hall
regime. In a magnetic-field-induced spin-density-wave state (FISDW)
characterized by an integer N, there exist N branches of chiral gapless edge
excitations. Localization length is much longer and velocity much lower for
these states than for the edge states parallel to the chains. We calculate the
contribution of these states to the specific heat and propose a time-of-flight
experiment to probe the propagating edge modes directly.Comment: 4 pages, 2 figures. V.2: Minor changes to the final version published
in PR
Effect of umklapp scattering on the magnetic-field-induced spin-density waves in quasi-one-dimensional organic conductors
We study the effect of umklapp scattering on the magnetic-field-induced
spin-density-wave (FISDW) phases which are experimentally observed in the
quasi-one-dimensional organic conductors of the Bechgaard salts family. Within
the framework of the quantized nesting model, we show that the transition
temperature is determined by a modified Stoner criterion which includes the
effect of umklapp scattering. We determine the SDW polarization (linear or
circular) by analyzing the Ginzburg-Landau expansion of the free energy. We
also study how umklapp processes modify the quantum Hall effect (QHE) and the
spectrum of the FISDW phases. We find that umklapp scattering stabilizes phases
which exhibit a sign reversal of the QHE, as experimentally observed in the
Bechgaard salts. These ``negative'' phases are characterized by the
simultaneous existence of two SDWs with comparable amplitudes. As the umklapp
scattering strength increases, they may become helicoidal (circularly polarized
SDWs). The QHE vanishes in the helicoidal phases, but a magnetoelectric effect
appears. These two characteristic properties may be utilized to detect the
magnetic-field-induced helicoidal SDW phases experimentally.Comment: Revtex, 27 pages, 9 figure
Collective modes in a system with two spin-density waves: the `Ribault' phase of quasi-one-dimensional organic conductors
We study the long-wavelength collective modes in the magnetic-field-induced
spin-density-wave (FISDW) phases experimentally observed in organic conductors
of the Bechgaard salts family, focusing on phases that exhibit a sign reversal
of the quantum Hall effect (Ribault anomaly). We have recently proposed that
two SDW's coexist in the Ribault phase, as a result of Umklapp processes. When
the latter are strong enough, the two SDW's become circularly polarized
(helicoidal SDW's). In this paper, we study the collective modes which result
from the presence of two SDW's. We find two Goldstone modes, an out-of-phase
sliding mode and an in-phase spin-wave mode, and two gapped modes. The sliding
Goldstone mode carries only a fraction of the total optical spectral weight,
which is determined by the ratio of the amplitude of the two SDW's. In the
helicoidal phase, all the spectral weight is pushed up above the SDW gap. We
also point out similarities with phase modes in two-band or bilayer
superconductors. We expect our conclusions to hold for generic two-SDW systems.Comment: Revised version, 25 pages, RevTex, 7 figure
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