Giant current fluctuations in an overheated single electron transistor

Interplay of cotunneling and single-electron tunneling in a thermally isolated single-electron transistor (SET) leads to peculiar overheating effects. In particular, there is an interesting crossover interval where the competition between cotunneling and single-electron tunneling changes to the dominance of the latter. In this interval, the current exhibits anomalous sensitivity to the effective electron temperature of the transistor island and its fluctuations. We present a detailed study of the current and temperature fluctuations at this interesting point. The methods implemented allow for a complete characterization of the distribution of the fluctuating quantities, well beyond the Gaussian approximation. We reveal and explore the parameter range where, for sufficiently small transistor islands, the current fluctuations become gigantic. In this regime, the optimal value of the current, its expectation value, and its standard deviation differ from each other by parametrically large factors. This situation is unique for transport in nanostructures and for electron transport in general. The origin of this spectacular effect is the exponential sensitivity of the current to the fluctuating effective temperature.Comment: 10 pages, 11 figure

Universality of the Kondo Effect in a Quantum Dot out of Equilibrium

We study the Kondo effect in a quantum dot driven out of equilibrium by an external ac field. The Kondo effect can be probed by measuring the dc current induced by an auxiliary dc bias $V_{dc}$ applied across the dot. In the absence of ac perturbation, the corresponding differential conductance $G(V_{dc})$ is known to exhibit a sharp peak at $V_{dc}=0$, which is the manifestation of the Kondo effect. In the equilibrium, there exists only one energy scale, the Kondo temperature $T_K$, which controls all the low-energy physics of the system; $G$ is some universal function of $eV_{dc}/T_K$. We demonstrate that the dot out of equilibrium is also characterized by a universal behavior: conductance $G$ depends on the ac field only through two dimensionless parameters, which are the frequency $\omega$ and the amplitude of the ac perturbation, both divided by $T_K$. We find analytically the large- and small-frequency asymptotes of the universal dependence of $G$ on these parameters. The obtained results allow us to predict the behavior of the conductance in the crossover regime $\hbar\omega\sim T_K$.Comment: 18 pages, 5 figure

A sufficient condition for a discrete spectrum of the Kirchhoff plate with an infinite peak

Sufficient conditions for a discrete spectrum of the biharmonic equation in a two-dimensional peak-shaped domain are established. Different boundary conditions from Kirchhoff's plate theory are imposed on the boundary and the results depend both on the type of boundary conditions and the sharpness exponent of the peak.Comment: 12 pages, 1 figure, submitted to Math. Mech. Compl. Sy

Effects of two dimensional plasmons on the tunneling density of states

We show that gapless plasmons lead to a universal $(\delta\nu(\epsilon)/\nu\propto |\epsilon|/E_F)$ correction to the tunneling density of states of a clean two dimensional Coulomb interacting electron gas. We also discuss a counterpart of this effect in the "composite fermion metal" which forms in the presence of a quantizing perpendicular magnetic field corresponding to the half-filled Landau level. We argue that the latter phenomenon might be relevant for deviations from a simple scaling observed by A.Chang et al in the tunneling $I-V$ characteristics of Quantum Hall liquids.Comment: 12 pages, Latex, NORDITA repor

Superconducting Spin Qubits

We propose and theoretically investigate spin superconducting qubits. Spin superconducting qubit consists of a single spin confined in a Josephson junction. We show that owing to spin-orbit interaction, superconducting difference across the junction can polarize this spin. We demonstrate that this enables single qubit operations and more complicated quantum gates, where spins of different qubits interact via a mutual inductance of superconducting loop where the junctions are embedded. Recent experimental realizations of Josephson junctions made of semiconductor quantum dots in contact with superconducting leads have shown that the number of electrons in the quantum dot can be tuned by a gate voltage. Spin superconducting qubit is realized when the number of electrons is odd. We discuss the qubit properties at phenomenological level. We present a microscopic theory that enables us to make accurate estimations of the qubit parameters by evaluating the spin-dependent Josephson energy in the framework of fourth-order perturbation theory.Comment: 11 pages, 8 figure

Andreev reflection eigenvalue density in mesoscopic conductors

The energy-dependent Andreev reflection eigenvalues determine the transport properties of normal-superconducting systems. We evaluate the eigenvalue density to get an insight into formation of resonant electron-hole transport channels. The circuit-theory-like method developed can be applied to any generic mesoscopic conductor or combinations thereof. We present the results for experimentally relevant cases of a diffusive wire and a double tunnel junction.Comment: 5 pages, 3 figure