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 $e^2/\hbar$. We study the junction with capacitance $C$, embedded in an Ohmic electromagnetic environment modelled by a series resistance $R$ 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 $G(T)$ valid for temperatures $k_BT \gtrsim (R_K/2\pi R)E_c$ and resistances $R \gtrsim R_K$, where $R_K = h/e^2$ and $E_c=e^2/2C \ \text{is}$the single-electron charging energy. Our analytical result shows the leading dependence$G(T) \propto e^{-E_c/4k_BT}$, so far believed to exist only if$(R_K/\pi R)E_c \ll k_BT \ll E_c$and$R \gg R_K$. The validity of our result for$k_BT \gtrsim (R_K/2\pi R)E_c$and$R \gtrsim R_K$is confirmed by a good agreement with the numerical studies which do not assume the semiclassical limit, and by a reasonable agreement with experimental data for$R$as low as$R_K$. Our result also reproduces various asymptotic formulae derived in the past. The factor of$1/4$in the activation energy$E_c/4$ 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-$\delta$-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 $\delta$-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$\text{}^{-1}$ and eventually like L$\text{}^{-α-1}$, where α>0 is universal