25 research outputs found
Note on the Coulomb blockade of a weak tunnel junction with Nyquist noise: Conductance formula for a broad temperature range
We revisit the Coulomb blockade of the tunnel junction with conductance much
smaller than . We study the junction with capacitance , embedded
in an Ohmic electromagnetic environment modelled by a series resistance
which produces the Nyquist noise. In the semiclassical limit the Nyquist noise
charges the junction by a random charge with a Gaussian distribution. Assuming
the Gaussian distribution, we derive analytically the temperature-dependent
junction conductance valid for temperatures and resistances , where and $E_c=e^2/2C \
\text{is}G(T) \propto e^{-E_c/4k_BT}(R_K/\pi R)E_c \ll k_BT \ll E_cR \gg R_Kk_BT \gtrsim (R_K/2\pi R)E_cR \gtrsim R_KRR_K1/4E_c/4$ is due to the
semiclassical Nyquist noise.Comment: to be published in physica status solidi c (2017
Possible persistent current in a ring made of the perfect crystalline insulator
A mesoscopic conducting ring pierced by magnetic flux is known to support the
persistent electron current. Here we propose possibility of the persistent
current in the ring made of the perfect crystalline insulator. We consider a
ring-shaped lattice of one-dimensional "atoms" with a single energy level. We
express the Bloch states in the lattice as a linear combination of atomic
orbitals. The discrete energy level splits into the energy band which serves as
a simple model of the valence band. We show that the insulating ring (with the
valence band fully filled by electrons) supports a nonzero persistent current,
because each atomic orbital overlaps with its own tail when making one loop
around the ring. In the tight-binding limit only the neighboring orbitals
overlap. In that limit the persistent current at full filling becomes zero
which is a standard result.Comment: Conference proceedings. Accepted for publication in Physica
Electron capture in GaAs quantum wells via electron-electron and optic phonon scattering
Electron capture times in a separate confinement quantum well (QW) structure
with finite electron density are calculated for electron-electron (e-e) and
electron-polar optic phonon (e-pop) scattering. We find that the capture time
oscillates as function of the QW width for both processes with the same period,
but with very different amplitudes. For an electron density of 10^11 cm^-2 the
e-e capture time is 10-1000 times larger than the e-pop capture time except for
QW widths near the resonance minima, where it is only 2-3 times larger. With
increasing electron density the e-e capture time decreases and near the
resonance becomes smaller than the e-pop capture time. Our e-e capture time
values are two-to-three orders of magnitude larger than previous results of
Blom et al. [Appl. Phys. Lett. 62, 1490 (1993)]. The role of the e-e capture in
QW lasers is therefore readdressed.Comment: 5 pages, standard LaTeX file + 5 PostScript figures (tarred,
compressed and uuencoded) or by request from [email protected],
accepted to Appl. Phys. Let
Conductance and persistent current in quasi-one-dimensional systems with grain boundaries: Effects of the strongly reflecting and columnar grains
We study mesoscopic transport in the Q1D wires and rings made of a 2D
conductor of width W and length L >> W. Our aim is to compare an impurity-free
conductor with grain boundaries with a grain-free conductor with impurity
disorder. A single grain boundary is modeled as a set of the
2D--function-like barriers positioned equidistantly on a straight line
and disorder is emulated by a large number of such straight lines, intersecting
the conductor with random orientation in random positions. The impurity
disorder is modeled by the 2D -barriers with the randomly chosen
positions and signs. The electron transmission through the wires is calculated
by the scattering-matrix method, and the Landauer conductance is obtained. We
calculate the persistent current in the rings threaded by magnetic flux: We
incorporate into the scattering-matrix method the flux-dependent cyclic
boundary conditions and we introduce a trick allowing to study the persistent
currents in rings of almost realistic size. We mainly focus on the numerical
results for L much larger than the electron mean-free path, when the transport
is diffusive. If the grain boundaries are weakly reflecting, the systems with
grain boundaries show the same (mean) conductance and the same (typical)
persistent current as the systems with impurities, and the results also agree
with the single-particle theories treating disorder as a white-noise-like
potential. If the grain boundaries are strongly reflecting, the typical
persistent currents can be about three times larger than the results of the
white-noise-based theory, thus resembling the experimental results of Jariwala
et al. (PRL 2001). We extend our study to the 3D conductors with columnar
grains. We find that the persistent current exceeds the white-noise-based
result by another one order of magnitude, similarly as in the experiment of
Chandrasekhar et al. (PRL 1991)
Quantum and Boltzmann transport in the quasi-one-dimensional wire with rough edges
We study quantum transport in Q1D wires made of a 2D conductor of width W and
length L>>W. Our aim is to compare an impurity-free wire with rough edges with
a smooth wire with impurity disorder. We calculate the electron transmission
through the wires by the scattering-matrix method, and we find the Landauer
conductance for a large ensemble of disordered wires. We study the
impurity-free wire whose edges have a roughness correlation length comparable
with the Fermi wave length. The mean resistance and inverse mean
conductance 1/ are evaluated in dependence on L. For L -> 0 we observe the
quasi-ballistic dependence 1/ = = 1/N_c + \rho_{qb} L/W, where 1/N_c
is the fundamental contact resistance and \rho_{qb} is the quasi-ballistic
resistivity. As L increases, we observe crossover to the diffusive dependence
1/ = = 1/N^{eff}_c + \rho_{dif} L/W, where \rho_{dif} is the
resistivity and 1/N^{eff}_c is the effective contact resistance corresponding
to the N^{eff}_c open channels. We find the universal results
\rho_{qb}/\rho_{dif} = 0.6N_c and N^{eff}_c = 6 for N_c >> 1. As L exceeds the
localization length \xi, the resistance shows onset of localization while the
conductance shows the diffusive dependence 1/ = 1/N^{eff}_c + \rho_{dif} L/W
up to L = 2\xi and the localization for L > 2\xi only. On the contrary, for the
impurity disorder we find a standard diffusive behavior, namely 1/ =
= 1/N_c + \rho_{dif} L/W for L < \xi. We also derive the wire conductivity from
the semiclassical Boltzmann equation, and we compare the semiclassical electron
mean-free path with the mean free path obtained from the quantum resistivity
\rho_{dif}. They coincide for the impurity disorder, however, for the edge
roughness they strongly differ, i.e., the diffusive transport is not
semiclassical. It becomes semiclassical for the edge roughness with large
correlation length
Coherent "metallic" resistance and medium localisation in a disordered 1D insulator
It is believed, that a disordered one-dimensional (1D) wire with coherent
electronic conduction is an insulator with the mean resistance \simeq
e^{2L/\xi} and resistance dispersion \Delta_{\rho} \simeq e^{L/\xi}, where L is
the wire length and \xi is the electron localisation length. Here we show that
this 1D insulator undergoes at full coherence the crossover to a 1D "metal",
caused by thermal smearing and resonant tunnelling. As a result, \Delta_{\rho}
is smaller than unity and tends to be L/\xi - independent, while grows
with L/\xi first nearly linearly and then polynomially, manifesting the
so-called medium localisation.Comment: 4 pages, 4 figures, RevTeX
Hartree-Fock Simulation of Persistent Current in Rings with Single Scatterer
Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we calculate the persistent current of the interacting electron gas in a one-dimensional ring containing a single δ barrier. Our results agree with correlated models like the Luttinger liquid model and lattice model with nearest-neighbor interaction. The persistent current is a sine-like function of magnetic flux. It decays with the ring length (L) faster than L and eventually like L, where α>0 is universal