51 research outputs found
Critical dynamics and effective exponents of magnets with extended impurities
We investigate the asymptotic and effective static and dynamic critical
behavior of (d=3)-dimensional magnets with quenched extended defects,
correlated in dimensions (which can be considered as the
dimensionality of the defects) and randomly distributed in the remaining
dimensions. The field-theoretical renormalization group
perturbative expansions being evaluated naively do not allow for the reliable
numerical data. We apply the Chisholm-Borel resummation technique to restore
convergence of the two-loop expansions and report the numerical values of the
asymptotic critical exponents for the model A dynamics. We discuss different
scenarios for static and dynamic effective critical behavior and give values
for corresponding non-universal exponents.Comment: 12 pages, 6 figure
Theory of Anomalous Quantum Hall Effects in Graphene
Recent successes in manufacturing of atomically thin graphite samples
(graphene) have stimulated intense experimental and theoretical activity. The
key feature of graphene is the massless Dirac type of low-energy electron
excitations. This gives rise to a number of unusual physical properties of this
system distinguishing it from conventional two-dimensional metals. One of the
most remarkable properties of graphene is the anomalous quantum Hall effect. It
is extremely sensitive to the structure of the system; in particular, it
clearly distinguishes single- and double-layer samples. In spite of the
impressive experimental progress, the theory of quantum Hall effect in graphene
has not been established. This theory is a subject of the present paper. We
demonstrate that the Landau level structure by itself is not sufficient to
determine the form of the quantum Hall effect. The Hall quantization is due to
Anderson localization which, in graphene, is very peculiar and depends strongly
on the character of disorder. It is only a special symmetry of disorder that
may give rise to anomalous quantum Hall effects in graphene. We analyze the
symmetries of disordered single- and double-layer graphene in magnetic field
and identify the conditions for anomalous Hall quantization.Comment: 13 pages (article + supplementary material), 5 figure
Effect of Tilted Magnetic Field on the Anomalous H=0 Conducting Phase in High-Mobility Si MOSFETs
The suppression by a magnetic field of the anomalous H=0 conducting phase in
high-mobility silicon MOSFETs is independent of the angle between the field and
the plane of the 2D electron system. In the presence of a parallel field large
enough to fully quench the anomalous conducting phase, the behavior is similar
to that of disordered GaAs/AlGaAs heterostructures: the system is insulating in
zero (perpendicular) field and exhibits reentrant insulator-quantum Hall
effect-insulator transitions as a function of perpendicular field. The results
demonstrate that the suppression of the low-T phase is related only to the
electrons' spin.Comment: 4 pages, including 3 figures. We corrected several typos in the
figures and caption
Critical behavior of two-dimensional cubic and MN models in the five-loop renormalization-group approximation
The critical thermodynamics of the two-dimensional N-vector cubic and MN
models is studied within the field-theoretical renormalization-group (RG)
approach. The beta functions and critical exponents are calculated in the
five-loop approximation and the RG series obtained are resummed using the
Borel-Leroy transformation combined with the generalized Pad\'e approximant and
conformal mapping techniques. For the cubic model, the RG flows for various N
are investigated. For N=2 it is found that the continuous line of fixed points
running from the XY fixed point to the Ising one is well reproduced by the
resummed RG series and an account for the five-loop terms makes the lines of
zeros of both beta functions closer to each another. For the cubic model with
N\geq 3, the five-loop contributions are shown to shift the cubic fixed point,
given by the four-loop approximation, towards the Ising fixed point. This
confirms the idea that the existence of the cubic fixed point in two dimensions
under N>2 is an artifact of the perturbative analysis. For the quenched dilute
O(M) models ( models with N=0) the results are compatible with a stable
pure fixed point for M\geq1. For the MN model with M,N\geq2 all the
non-perturbative results are reproduced. In addition a new stable fixed point
is found for moderate values of M and N.Comment: 26 pages, 3 figure
Anomalous state of a 2DEG in vicinal Si MOSFET in high magnetic fields
We report the observation of an anomalous state of a 2D electron gas near a
vicinal surface of a silicon MOSFET in high magnetic fields. It is
characterised by unusual behaviour of the conductivities and
, which can be described as a collapse of the Zeeman spin
splitting accompanied by a large peak in and an anomalous peak in
. It occurs at densities corresponding to the position of the
Fermi level above the onset of the superlattice mini-gap inherent to the
vicinal system. The range of fields and densities where this effect exists has
been determined, and it has been shown that it is suppressed by parallel
magnetic fields
Two-terminal conductance fluctuations in the integer quantum Hall regime
Motivated by recent experiments on the conductance fluctuations in mesoscopic
integr quantum Hall systems, we consider a model in which the Coulomb
interactions are incorporated into the picture of edge-state transport through
a single saddle-point. The occupancies of `classical' localised states in the
two-dimensional electron system change due to the interactions between
electrons when the gate voltage on top of the device is varied. The
electrostatic potential between the localised states and the saddle-point
causes fluctuations of the saddle-point potential and thus fluctuations of the
transmission probability of edge states. This simple model is studied
numerically and compared with the observation.Comment: 6 pages with 3 figures. To be published in Physical Review
Weak quenched disorder and criticality: resummation of asymptotic(?) series
In these lectures, we discuss the influence of weak quenched disorder on the
critical behavior in condensed matter and give a brief review of available
experimental and theoretical results as well as results of MC simulations of
these phenomena. We concentrate on three cases: (i) uncorrelated random-site
disorder, (ii) long-range-correlated random-site disorder, and (iii) random
anisotropy.
Today, the standard analytical description of critical behavior is given by
renormalization group results refined by resummation of the perturbation theory
series. The convergence properties of the series are unknown for most
disordered models. The main object of these lectures is to discuss the
peculiarities of the application of resummation techniques to perturbation
theory series of disordered models.Comment: Lectures given at the Second International Pamporovo Workshop on
Cooperative Phenomena in Condensed Matter (28th July - 7th August 2001,
Pamporovo, Bulgaria). 51 pages, 12 figures, 1 style files include
Quantum and classical localisation, the spin quantum Hall effect and generalisations
We consider network models for localisation problems belonging to symmetry
class C. This symmetry class arises in a description of the dynamics of
quasiparticles for disordered spin-singlet superconductors which have a
Bogoliubov - de Gennes Hamiltonian that is invariant under spin rotations but
not under time-reversal. Our models include but also generalise the one studied
previously in the context of the spin quantum Hall effect. For these systems we
express the disorder-averaged conductance and density of states in terms of
sums over certain classical random walks, which are self-avoiding and have
attractive interactions. A transition between localised and extended phases of
the quantum system maps in this way to a similar transition for the classical
walks. In the case of the spin quantum Hall effect, the classical walks are the
hulls of percolation clusters, and our approach provides an alternative
derivation of a mapping first established by Gruzberg, Read and Ludwig, Phys.
Rev. Lett. 82, 4254 (1999).Comment: 11 pages, 5 figure
The metal-insulator transition in Si:X: Anomalous response to a magnetic field
The zero-temperature magnetoconductivity of just-metallic Si:P scales with
magnetic field, H, and dopant concentration, n, lying on a single universal
curve. We note that Si:P, Si:B, and Si:As all have unusually large magnetic
field crossover exponents near 2, and suggest that this anomalously weak
response to a magnetic field is a common feature of uncompensated doped
semiconductors.Comment: 4 pages (including figures
Phase diagram of localization in a magnetic field
The phase diagram of localization is numerically calculated for a
three-dimensional disordered system in the presence of a magnetic field using
the Peierls substitution. The mobility edge trajectory shifts in the
energy-disorder space when increasing the field. In the band center, localized
states near the phase boundary become delocalized. The obtained field
dependence of the critical disorder is in agreement with a power law behavior
expected from scaling theory. Close to the tail of the band the magnetic field
causes localization of extended states.Comment: 4 pages, RevTeX, 3 PS-figures (4 extra references are included, minor
additions), to appear in Phys. Rev. B as a Brief Repor
- âŠ