249 research outputs found
Electronic structure of turbostratic graphene
We explore the rotational degree of freedom between graphene layers via the
simple prototype of the graphene twist bilayer, i.e., two layers rotated by
some angle . It is shown that, due to the weak interaction between
graphene layers, many features of this system can be understood by interference
conditions between the quantum states of the two layers, mathematically
expressed as Diophantine problems. Based on this general analysis we
demonstrate that while the Dirac cones from each layer are always effectively
degenerate, the Fermi velocity of the Dirac cones decreases as ; the form we derive for agrees with that found via a
continuum approximation in Phys. Rev. Lett., 99:256802, 2007. From tight
binding calculations for structures with we
find agreement with this formula for . In contrast, for
this formula breaks down and the Dirac bands become
strongly warped as the limit is approached. For an ideal system
of twisted layers the limit as is singular as for the Dirac point is fourfold degenerate, while at one has the
twofold degeneracy of the stacked bilayer. Interestingly, in this limit
the electronic properties are in an essential way determined \emph{globally},
in contrast to the 'nearsightedness' [W. Kohn. Phys. Rev. Lett., 76:3168,
1996.] of electronic structure generally found in condensed matter.Comment: Article as to be published in Phys. Rev B. Main changes: K-point
mapping tables fixed, several changes to presentation
Shockley model description of surface states in topological insulators
We show that the surface states in topological insulators can be understood
based on a well-known Shockley model, a one-dimensional tight-binding model
with two atoms per elementary cell, connected via alternating tunneling
amplitudes. We generalize the one-dimensional model to the three-dimensional
case corresponding to the sequence of layers connected via the amplitudes,
which depend on the in-plane momentum p = (p_x,p_y). The Hamiltonian of the
model is described a (2 x 2) Hamiltonian with the off-diagonal element t(k,p)
depending also on the out-of-plane momentum k. We show that the complex
function t(k,p) defines the properties of the surface states. The surface
states exist for the in-plane momenta p, where the winding number of the
function t(k,p) is non-zero as k is changed from 0 to 2pi. The sign of the
winding number defines the sublattice on which the surface states are
localized. The equation t(k,p)=0 defines a vortex line in the three-dimensional
momentum space. The projection of the vortex line on the two-dimensional
momentum p space encircles the domain where the surface states exist. We
illustrate how our approach works for a well-known TI model on a diamond
lattice. We find that different configurations of the vortex lines are
responsible for the "weak" and "strong" topological insulator phases. The phase
transition occurs when the vortex lines reconnect from spiral to circular form.
We discuss the Shockley model description of Bi_2Se_3 and the applicability of
the continuous approximation for the description of the topological edge
states. We conclude that the tight-binding model gives a better description of
the surface states.Comment: 18 pages, 17 figures; version 3: Sections I-IV revised, Section VII
added, Refs. [33]-[35] added; Corresponds to the published versio
There are No Unfilled Shells in Hartree-Fock Theory
Hartree-Fock theory is supposed to yield a picture of atomic shells which may
or may not be filled according to the atom's position in the periodic table. We
prove that shells are always completely filled in an exact Hartree-Fock
calculation. Our theorem generalizes to any system having a two-body
interaction that, like the Coulomb potential, is repulsive.Comment: 5 pages, VBEHLMLJPS--16/July/9
Response of a cold-electron bolometer on thz radiation from a long yba2cu3o7−δ bicrystal josephson junction
The response of the Cold-Electron Bolometers (CEBs), integrated into a 2-D array of dipole antennas, has been measured by irradiation from YBa2Cu3O7−δ (YBCO) 50 \ub5m long Josephson junction into the THz region at frequencies from 0.1 to 0.8 THz. The possibility of controlling the amplitude-frequency characteristic is demonstrated by the external magnetic field in the traveling wave regime of a long Josephson junction. The YBCO junction has been formed on the bicrystal Zr1−xYxO2 (YSZ) substrate by magnetron sputtering and etching of the film. CEBs have been fabricated using an Al multilayer structure by a self-aligned shadow evaporation technique on Si substrate. Both receiver and oscillator have been located inside the same cryostat at 0.3 K and 2.7 K plates, respectively
Hydrodynamic theory of an electron gas
The generalised hydrodynamic theory of an electron gas, which does not rely
on an assumption of a local equilibrium, is derived as the long-wave limit of a
kinetic equation. Apart from the common hydrodynamics variables the theory
includes the tensor fields of the higher moments of the distribution function.
In contrast to the Bloch hydrodynamics, the theory leads to the correct plasmon
dispersion and in the low frequency limit recovers the Navies-Stocks
hydrodynamics. The linear approximation to the generalised hydrodynamics is
closely related to the theory of highly viscous fluids.Comment: 4 pages, revte
The growth exponent for planar loop-erased random walk
We give a new proof of a result of Kenyon that the growth exponent for
loop-erased random walks in two dimensions is 5/4. The proof uses the
convergence of LERW to Schramm-Loewner evolution with parameter 2, and is valid
for irreducible bounded symmetric random walks on any two-dimensional discrete
lattice.Comment: 62 pages, 7 figures; fixed typos, added reference
Ez-response as a monitor of a Baikal rift fault electrical resistivity: 3D modelling studies
3D numerical studies have shown that the vertical voltage above the Baikal deep-water fault is detectable and that respective transfer functions, Ez-responses, are sensitive to the electrical resistivity changes of the fault, i.e.
these functions appear actually informative with respect to the resistivity «breath» of the fault. It means that if the fault resistivity changed, conventional electromagnetic instruments would be able to detect this fact by measurement
of the vertical electric field, Ez, or the vertical electric voltage just above the fault as well as horizontal magnetic field on the shore. Other electromagnetic field components (Ex, Ey, Hz) do not seem to be sensitive to the resistivity changes in such a thin fault (as wide as 500 m). On the other hand, such changes are thought to
be able to indicate a change of a stress state in the earthquake preparation zone. Besides, the vertical profile at the bottom of Lake Baikal is suitable for electromagnetic monitoring of the fault electrical resistivity changes.
Altogether, the vertical voltage above the deep-water fault might be one of earthquake precursors
Microwave photon detection by an Al Josephson junction
An aluminium Josephson junction (JJ), with a critical current suppressed by a factor of three compared with the maximal value calculated from the gap, is experimentally investigated for application as a threshold detector for microwave photons. We present the preliminary results of measurements of the lifetime of the superconducting state and the probability of switching by a 9 GHz external signal. We found an anomalously large lifetime, not described by the Kramers\u27 theory for the escape time over a barrier under the influence of fluctuations. We explain it by the phase diffusion regime, which is evident from the temperature dependence of the switching current histograms. Therefore, phase diffusion allows for a significant improvement of the noise immunity of a device, radically decreasing the dark count rate, but it will also decrease the single-photon sensitivity of the considered threshold detector. Quantization of the switching probability tilt as a function of the signal attenuation for various bias currents through the JJ is observed, which resembles the differentiation between N and N + 1 photon absorption
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