422 research outputs found
Coulomb interaction and magnetic catalysis in the quantum Hall effect in graphene
The dynamics of symmetry breaking responsible for lifting the degeneracy of
the Landau levels in the integer quantum Hall effect in graphene is studied in
a low-energy model with the Coulomb interaction. The gap equation for Dirac
quasiparticles is analyzed for both the lowest and higher Landau levels, taking
into account the Landau levels mixing. It is shown that the characteristic
feature of the long-range Coulomb interaction is the decrease of the gap
parameters with increasing the Landau level index ("running" gaps). The
renormalization (running) of the Fermi velocity as a function of is also
studied. The solutions of the gap equation reproduce correctly the
experimentally observed integer quantum Hall plateaus in graphene in strong
magnetic fields.Comment: 22 pages, 5 figures; Final version published in the Proceedings of
the 2010 Nobel Symposium on Graphene and Quantum Matte
Subexponential estimations in Shirshov's height theorem (in English)
In 1993 E. I. Zelmanov asked the following question in Dniester Notebook:
"Suppose that F_{2, m} is a 2-generated associative ring with the identity
x^m=0. Is it true, that the nilpotency degree of F_{2, m} has exponential
growth?" We show that the nilpotency degree of l-generated associative algebra
with the identity x^d=0 is smaller than Psi(d,d,l), where Psi(n,d,l)=2^{18} l
(nd)^{3 log_3 (nd)+13}d^2. We give the definitive answer to E. I. Zelmanov by
this result. It is the consequence of one fact, which is based on combinatorics
of words. Let l, n and d>n be positive integers. Then all the words over
alphabet of cardinality l which length is greater than Psi(n,d,l) are either
n-divided or contain d-th power of subword, where a word W is n-divided, if it
can be represented in the following form W=W_0 W_1...W_n such that W_1 >'
W_2>'...>'W_n. The symbol >' means lexicographical order here. A. I. Shirshov
proved that the set of non n-divided words over alphabet of cardinality l has
bounded height h over the set Y consisting of all the words of degree <n.
Original Shirshov's estimation was just recursive, in 1982 double exponent was
obtained by A.G.Kolotov and in 1993 A.Ya.Belov obtained exponential estimation.
We show, that h<Phi(n,l), where Phi(n,l) = 2^{87} n^{12 log_3 n + 48} l. Our
proof uses Latyshev idea of Dilworth theorem application.Comment: 21 pages, Russian version of the article is located at the link
arXiv:1101.4909; Sbornik: Mathematics, 203:4 (2012), 534 -- 55
Electron screening and excitonic condensation in double-layer graphene systems
We theoretically investigate the possibility of excitonic condensation in a
system of two graphene monolayers separated by an insulator, in which electrons
and holes in the layers are induced by external gates. In contrast to the
recent studies of this system, we take into account the screening of the
interlayer Coulomb interaction by the carriers in the layers, and this
drastically changes the result. Due to a large number of electron species in
the system (two projections of spin, two valleys, and two layers) and to the
suppression of backscattering in graphene, the maximum possible strength of the
screened Coulomb interaction appears to be quite small making the weak-coupling
treatment applicable. We calculate the mean-field transition temperature for a
clean system and demonstrate that its highest possible value
is extremely small
( is the Fermi energy). In addition, any sufficiently short-range
disorder with the scattering time would
suppress the condensate completely. Our findings renders experimental
observation of excitonic condensation in the above setup improbable even at
very low temperatures.Comment: 4+ pages, 3 figure
Bose-Einstein condensation of quasiparticles in graphene
The collective properties of different quasiparticles in various graphene
based structures in high magnetic field have been studied. We predict
Bose-Einstein condensation (BEC) and superfluidity of 2D spatially indirect
magnetoexcitons in two-layer graphene. The superfluid density and the
temperature of the Kosterlitz-Thouless phase transition are shown to be
increasing functions of the excitonic density but decreasing functions of
magnetic field and the interlayer separation. The instability of the ground
state of the interacting 2D indirect magnetoexcitons in a slab of superlattice
with alternating electron and hole graphene layers (GLs) is established. The
stable system of indirect 2D magnetobiexcitons, consisting of pair of indirect
excitons with opposite dipole moments, is considered in graphene superlattice.
The superfluid density and the temperature of the Kosterlitz-Thouless phase
transition for magnetobiexcitons in graphene superlattice are obtained.
Besides, the BEC of excitonic polaritons in GL embedded in a semiconductor
microcavity in high magnetic field is predicted. While superfluid phase in this
magnetoexciton polariton system is absent due to vanishing of
magnetoexciton-magnetoexciton interaction in a single layer in the limit of
high magnetic field, the critical temperature of BEC formation is calculated.
The essential property of magnetoexcitonic systems based on graphene (in
contrast, e.g., to a quantum well) is stronger influence of magnetic field and
weaker influence of disorder. Observation of the BEC and superfluidity of 2D
quasiparticles in graphene in high magnetic field would be interesting
confirmation of the phenomena we have described.Comment: 13 pages, 5 figure
Neutron lifetime measurements using gravitationally trapped ultracold neutrons
Our experiment using gravitationally trapped ultracold neutrons (UCN) to
measure the neutron lifetime is reviewed. Ultracold neutrons were trapped in a
material bottle covered with perfluoropolyether. The neutron lifetime was
deduced from comparison of UCN losses in the traps with different
surface-to-volume ratios. The precise value of the neutron lifetime is of
fundamental importance to particle physics and cosmology. In this experiment,
the UCN storage time is brought closer to the neutron lifetime than in any
experiments before:the probability of UCN losses from the trap was only 1% of
that for neutron beta decay. The neutron lifetime
obtained,878.5+/-0.7stat+/-0.3sys s, is the most accurate experimental
measurement to date.Comment: 38 pages, 19 figures,changed conten
Excitonic condensation in a double-layer graphene system
The possibility of excitonic condensation in a recently proposed electrically
biased double-layer graphene system is studied theoretically. The main emphasis
is put on obtaining a reliable analytical estimate for the transition
temperature into the excitonic state. As in a double-layer graphene system the
total number of fermionic "flavors" is equal to N=8 due to two projections of
spin, two valleys, and two layers, the large- approximation appears to be
especially suitable for theoretical investigation of the system. On the other
hand, the large number of flavors makes screening of the bare Coulomb
interactions very efficient, which, together with the suppression of
backscattering in graphene, leads to an extremely low energy of the excitonic
condensation. It is shown that the effect of screening on the excitonic pairing
is just as strong in the excitonic state as it is in the normal state. As a
result, the value of the excitonic gap \De is found to be in full agreement
with the previously obtained estimate for the mean-field transition temperature
, the maximum possible value ( is the Fermi energy) of both being in
range for a perfectly clean system. This proves that the energy scale really sets the upper bound for the transition temperature
and invalidates the recently expressed conjecture about the high-temperature
first-order transition into the excitonic state. These findings suggest that,
unfortunately, the excitonic condensation in graphene double-layers can hardly
be realized experimentally.Comment: 21 pages, 5 figures, invited paper to Graphene special issue in
Semiconductor Science and Technolog
Excitonic condensation in a double-layer graphene system
The possibility of excitonic condensation in a recently proposed electrically
biased double-layer graphene system is studied theoretically. The main emphasis
is put on obtaining a reliable analytical estimate for the transition
temperature into the excitonic state. As in a double-layer graphene system the
total number of fermionic "flavors" is equal to N=8 due to two projections of
spin, two valleys, and two layers, the large- approximation appears to be
especially suitable for theoretical investigation of the system. On the other
hand, the large number of flavors makes screening of the bare Coulomb
interactions very efficient, which, together with the suppression of
backscattering in graphene, leads to an extremely low energy of the excitonic
condensation. It is shown that the effect of screening on the excitonic pairing
is just as strong in the excitonic state as it is in the normal state. As a
result, the value of the excitonic gap \De is found to be in full agreement
with the previously obtained estimate for the mean-field transition temperature
, the maximum possible value ( is the Fermi energy) of both being in
range for a perfectly clean system. This proves that the energy scale really sets the upper bound for the transition temperature
and invalidates the recently expressed conjecture about the high-temperature
first-order transition into the excitonic state. These findings suggest that,
unfortunately, the excitonic condensation in graphene double-layers can hardly
be realized experimentally.Comment: 21 pages, 5 figures, invited paper to Graphene special issue in
Semiconductor Science and Technolog
Excitonic condensation in a double-layer graphene system
The possibility of excitonic condensation in a recently proposed electrically
biased double-layer graphene system is studied theoretically. The main emphasis
is put on obtaining a reliable analytical estimate for the transition
temperature into the excitonic state. As in a double-layer graphene system the
total number of fermionic "flavors" is equal to N=8 due to two projections of
spin, two valleys, and two layers, the large- approximation appears to be
especially suitable for theoretical investigation of the system. On the other
hand, the large number of flavors makes screening of the bare Coulomb
interactions very efficient, which, together with the suppression of
backscattering in graphene, leads to an extremely low energy of the excitonic
condensation. It is shown that the effect of screening on the excitonic pairing
is just as strong in the excitonic state as it is in the normal state. As a
result, the value of the excitonic gap \De is found to be in full agreement
with the previously obtained estimate for the mean-field transition temperature
, the maximum possible value ( is the Fermi energy) of both being in
range for a perfectly clean system. This proves that the energy scale really sets the upper bound for the transition temperature
and invalidates the recently expressed conjecture about the high-temperature
first-order transition into the excitonic state. These findings suggest that,
unfortunately, the excitonic condensation in graphene double-layers can hardly
be realized experimentally.Comment: 21 pages, 5 figures, invited paper to Graphene special issue in
Semiconductor Science and Technolog
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