287 research outputs found
Asymmetric higher-harmonic SQUID as a Josephson diode
We theoretically investigate asymmetric two-junction SQUIDs with different
current-phase relations in the two Josephson junctions, involving higher
Josephson harmonics. Our main focus is on the "minimal model" with one junction
in the SQUID loop possessing the sinusoidal current-phase relation and the
other one featuring additional second harmonic. The current-voltage
characteristic (CVC) turns out to be asymmetric, . The
asymmetry is due to the presence of the second harmonic and depends on the
magnetic flux through the interferometer loop, vanishing only at special values
of the flux such as integer or half-integer in the units of the flux quantum.
The system thus demonstrates the flux-tunable Josephson diode effect (JDE), the
simplest manifestations of which is the direction dependence of the critical
current. We analyze asymmetry of the overall shape both in the absence
and in the presence of external ac irradiation. In the voltage-source case of
external signal, the CVC demonstrates the Shapiro spikes. The integer spikes
are asymmetric (manifestation of the JDE) while the half-integer spikes remain
symmetric. In the current-source case, the CVC demonstrates the Shapiro steps.
The JDE manifests itself in asymmetry of the overall CVC shape, including
integer and half-integer steps.Comment: 18 pages, 5 figures. Version 2: extended introduction, added
references. Final version as published in PR
Classical properties of low-dimensional conductors: Giant capacitance and non-Ohmic potential drop
Electrical field arising around an inhomogeneous conductor when an electrical
current passes through it is not screened, as distinct from 3D conductors, in
low-dimensional conductors. As a result, the electrical field depends on the
global distribution of the conductivity sigma(x) rather than on the local value
of it, inhomogeneities of sigma(x) produce giant capacitances C(omega) that
show frequency dependence at relatively low omega, and electrical fields
develop in vast regions around the inhomogeneities of sigma(x). A theory of
these phenomena is presented for 2D conductors.Comment: 5 pages, two-column REVTeX, to be published in Physical Review
Letter
The valence band energy spectrum of HgTe quantum wells with inverted band structures
The energy spectrum of the valence band in HgTe/CdHgTe quantum
wells with a width ~nm has been studied experimentally by
magnetotransport effects and theoretically in framework -bands -method.
Comparison of the Hall density with the density found from period of the
Shubnikov-de Haas (SdH) oscillations clearly shows that the degeneracy of
states of the top of the valence band is equal to 2 at the hole density ~cm. Such degeneracy does not agree with the
calculations of the spectrum performed within the framework of the -bands
-method for symmetric quantum wells. These calculations show that the top
of the valence band consists of four spin-degenerate extremes located at (valleys) which gives the total degeneracy . It is shown that taking
into account the "mixing of states" at the interfaces leads to the removal of
the spin degeneracy that reduces the degeneracy to . Accounting for any
additional asymmetry, for example, due to the difference in the mixing
parameters at the interfaces, the different broadening of the boundaries of the
well, etc, leads to reduction of the valleys degeneracy, making . It is
noteworthy that for our case two-fold degeneracy occurs due to degeneracy of
two single-spin valleys. The hole effective mass () determined from
analysis of the temperature dependence of the amplitude of the SdH oscillations
show that is equal to and weakly increases with the
hole density. Such a value of and its dependence on the hole density are
in a good agreement with the calculated effective mass.Comment: 8 pages, 11 figure
Why nonlocal recursion operators produce local symmetries: new results and applications
It is well known that integrable hierarchies in (1+1) dimensions are local
while the recursion operators that generate them usually contain nonlocal
terms. We resolve this apparent discrepancy by providing simple and universal
sufficient conditions for a (nonlocal) recursion operator in (1+1) dimensions
to generate a hierarchy of local symmetries. These conditions are satisfied by
virtually all known today recursion operators and are much easier to verify
than those found in earlier work.
We also give explicit formulas for the nonlocal parts of higher recursion
operators, Poisson and symplectic structures of integrable systems in (1+1)
dimensions.
Using these two results we prove, under some natural assumptions, the
Maltsev--Novikov conjecture stating that higher Hamiltonian, symplectic and
recursion operators of integrable systems in (1+1) dimensions are weakly
nonlocal, i.e., the coefficients of these operators are local and these
operators contain at most one integration operator in each term.Comment: 10 pages, LaTeX 2e, final versio
Representations of sl(2,?) in category O and master symmetries
We show that the indecomposable sl(2,?)-modules in the Bernstein-Gelfand-Gelfand category O naturally arise for homogeneous integrable nonlinear evolution systems. We then develop a new approach called the O scheme to construct master symmetries for such integrable systems. This method naturally allows computing the hierarchy of time-dependent symmetries. We finally illustrate the method using both classical and new examples. We compare our approach to the known existing methods used to construct master symmetries. For new integrable equations such as a Benjamin-Ono-type equation, a new integrable Davey-Stewartson-type equation, and two different versions of (2+1)-dimensional generalized Volterra chains, we generate their conserved densities using their master symmetries
Energy spectrum of valence band in HgTe quantum wells on the way from a two to the three dimensional topological insulator
The magnetic field, temperature dependence and the Hall effect have been
measured in order to determine the energy spectrum of the valence band in HgTe
quantum wells with the width (20-200)nm. The comparison of hole densities
determined from the period Shubnikov-de Haas oscillations and the Hall effect
shows that states at the top of valence band are double degenerate in teh entry
quantum wells width the width range. The cyclotron mass determined from
temperature dependence of SdH oscillations increases monotonically from
(0.2-0.3) mass of the free electron, with increasing hole density from 2e11 to
6e11 cm^-2. The determined dependence has been compared to theoretical one
calculate within the four band kp model. The experimental dependence was found
to be strongly inconsistent with this predictions. It has been shown that the
inclusion of additional factors (electric field, strain) does not remove the
contradiction between experiment and theory. Consequently it is doubtful that
the mentioned kp calculations adequately describe the valence band for any
width of quantum well.Comment: 7 pages 8 figure
Renormalization of the conduction band spectrum in HgTe quantum wells by electron-electron interaction
The energy spectrum of the conduction band in HgTe/CdHgTe quantum
wells of a width nm has been experimentally studied in a wide
range of electron density. For this purpose, the electron density dependence of
the effective mass was measured by two methods: by analyzing the temperature
dependence of the Shubnikov-de Haas oscillations and by means of the quantum
capacitance measurements. There was shown that the effective mass obtained for
the structures with , where nm is a critical width of
quantum well corresponding to the Dirac-like energy spectrum, is close to the
calculated values over the whole electron density range; with increasing width,
at nm, the experimental effective mass becomes noticeably less than
the calculated ones. This difference increases with the electron density
decrease, i.e., with lowering the Fermi energy; the maximal difference between
the theory and experiment is achieved at nm, where the ratio
between the calculated and experimental masses reaches the value of two and
begins to decrease with a further increase. We assume that observed
behavior of the electron effective mass results from the spectrum
renormalization due to electron-electron interaction.Comment: 8 pages, 10 figure
Gravity in a stabilized brane world model in five-dimensional Brans-Dicke theory
Linearized equations of motion for gravitational and scalar fields are found
and solved in a stabilized brane world model in five-dimensional Brans-Dicke
theory. The physical degrees of freedom are isolated, the mass spectrum of
Kaluza-Klein excitations is found and the coupling constants of these
excitations to matter on the negative tension brane are calculated.Comment: 12 pages, LaTe
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