Strong electron tunneling through a small metallic grain

Electron tunneling through mesoscopic metallic grains can be treated perturbatively only under the conduction that the tunnel junction conductances are sufficiently small. If that is not the case, fluctuations of the grain charge become strong. As a result (i) the contributions of all—including high energy—charge states become important, and (ii) the excited charge states become broadened and essentially overlap. At the same time, the grain charge remains discrete and the system conductance e-periodically depends on the gate charge. We develop a non-perturbative approach which accounts for all these features and calculate the temperature-dependent conductance of the system in the strong tunneling regime at different values of the gate charge. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 953–958 (25 June 1996) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Effects of geometrical symmetry on the vortex in mesoscopic superconductors

We first systematically study the multivortex states in mesoscopic superconductors via self-consistent Bogoliubov-de Gennes equations. Our work focuses on how the geometrical symmetry affects the penetration and arrangement of vortices in mesoscopic superconductors and find that the key parameter determining the entrance of the vortex is the current density at the hot spots on the edge of sample. Through determining the spatial distribution of hot spots, the geometrical symmetry of the superconducting sample influences the nucleation and entrance of vortices. Our results propose one possible experimental approach to control and manipulate the quantum states of mesoscopic superconductors with their topological geometries, and they can be easily generalized to the confined superfluids and Bose-Einstein condensates.     

Quantum Interference Effects for the Electronic Fluctuations in Quantum Dots

For the main quantum interference term of coherent electronic transport, we study the effect of temperature, perpendicular and/or parallel magnetic fields, spin-orbit coupling and tunneling rates in both metallic grains and mesoscopic heterostructures. We show that the Zeeman effects determines a crucial way to characterize the quantum interference phenomena of the noise for anisotropic systems (mesoscopic heterostructures), qualitatively distinct from those observed in isotropic structures (metallic grains).     

Well-defined quasiparticles in interacting metallic grains

We analyze spectral functions of mesoscopic systems with large dimensionless conductance, which can be described by a universal Hamiltonian. We show that an important class of spectral functions are dominated by one single state only, which implies the existence of well-defined (i.e., infinite-lifetime) quasiparticles. Furthermore, the dominance of a single state enables us to calculate zero-temperature spectral functions with high accuracy using the density-matrix renormalization group. We illustrate the use of this method by calculating the tunneling density of states of metallic grains, of which we discuss the crossover from the few-electron to the bulk regime.     

Persistent current in an almost staggered Harper model

In this paper we study the persistent current (PC) of a staggered Harper model, close to the half-filling. The Harper model is different than other one dimensional disordered systems which are always localized, since it is a quasi-periodic system with correlated disorder resulting in the fact that it can be in the metallic regime. Nevertheless, the PC for a wide range of parameters of the Harper model does not show typical metallic behavior, although the system is in the metallic regime. This is a result of the nature of the central band states, which are a hybridization of Gaussian states localized in superlattice points. When the superlattice is not commensurate with the system length, the PC behaves as an insulator. Thus even in the metallic regime a typical finite Harper model may exhibit a PC expected from an insulator.     

Long-range coherence and mesoscopic transport in N–S metallic structures

We review the mesoscopic transport in a diffusive proximity superconductor made of a normal metal (N) in metallic contact with a superconductor (S). The Andreev reflection of electrons on the N–S interface is responsible for the diffusion of electron pairs in N. Superconducting-like properties are induced in the normal metal. In particular, the conductivity of the N metal is locally enhanced by the proximity effect. A re-entrance of the metallic conductance occurs when all the energies involved (e.g. temperature and voltage) are small. The relevant characteristic energy is the Thouless energy which is divided by the diffusion time for an electron travelling throughout the sample. In loop-shaped devices, a 1 / T temperature-dependent oscillation of the magnetoresistance arises with a large amplitude from the long-range coherence of low-energy pairs.     

Giant oscillations of energy levels in mesoscopic superconductors

The interplay of geometrical and Andreev quantization in mesoscopic superconductors leads to giant mesoscopic oscillations of energy levels as functions of the Fermi momentum and/or sample size. Quantization rules are formulated for closed quasiparticle trajectories in the presence of normal scattering at the sample boundaries. Two generic examples of mesoscopic systems are studied: (i) one-dimensional Andreev states in a quantum box and (ii) a single vortex in a mesoscopic cylinder.     

Persistent currents in a mesoscopic ring with a side connected quantum dot

We study the persistent current circulating along a mesoscopic ring with a dot side-coupled to it when threaded by a magnetic field. A cluster including the dot and its vicinity is diagonalized and embedded into the rest of the system. The result is numerically exact. We show that in the Kondo regime, the current can be a smooth or a strongly dependent function of the gate potential according to the structure of occupation of the highest energetic electrons of the system.     

Dephasing effects in nonlinear δ-models: A phenomenological approach

We introduce a technique of simulating the destruction of mesoscopic conductance fluctuations phenomenologically within the nonlinear -formalism. A similar approach has already been applied within diagrammatic models. Dephasing is generated by adding a second random potential to the Hamilton operator which differs from the potential describing the metallic disorder only in its statistical properties. For that reason, the approach cannot serve to describe physical effects relying on dynamic aspects of dephasing interactions (e.g. the destruction of weak localization effects). The technique is introduced within the framework of a scattering-theoretical model of mesoscopic systems.     

Fast quantum gates for neutral atoms

We propose several schemes for implementing a fast two-qubit quantum gate for neutral atoms with the gate operation time much faster than the time scales associated with the external motion of the atoms in the trapping potential. In our example, the large interaction energy required to perform fast gate operations is provided by the dipole-dipole interaction of atoms excited to low-lying Rydberg states in constant electric fields. A detailed analysis of imperfections of the gate operation is given.     

Local density of states of vortex state in mesoscopic superconductors

We study local density of states (LDOS) of vortex state in mesoscopic square superconductors with Bogoliubov-de Gennes (BdG) equation. We develop one effective numerical method based on the finite element method to self-consistently solve the BdG equation. The LDOS for various vortex states is obtained. Our results about the single vortex show that the LDOS has the particle-hole asymmetry and the results for one- and two-vortex state agree very well with the experimental observation. Besides, we predict the LDOS of multi-vortex states, which is crucial for the further STM/STS experimental study of vortex state in mesoscopic superconducting system.     

Polynomial-time simulation of pairing models on a quantum computer

We propose a polynomial-time algorithm for simulation of the class of pairing Hamiltonians, e.g., the BCS Hamiltonian, on an NMR quantum computer. The algorithm adiabatically finds the low-lying spectrum in the vicinity of the gap between the ground and the first excited states and provides a test of the applicability of the BCS Hamiltonian to mesoscopic superconducting systems, such as ultrasmall metallic grains.     

Absorbing/emitting phonons with one dimensional MOSFETs

We consider nanowires in the field effect transistor device configuration. Modeling each nanowire as a one dimensional lattice with random site potentials, we study the heat exchanges between the nanowire electrons and the substrate phonons, when electron transport is due to phonon-assisted hops between localized states. Shifting the nanowire conduction band with a metallic gate induces different behaviors. When the Fermi potential is located near the band center, a bias voltage gives rise to small local heat exchanges which fluctuate randomly along the nanowire. When it is located near one of the band edges, the bias voltage yields heat currents which flow mainly from the substrate towards the nanowire near one boundary of the nanowire, and in the opposite direction near the other boundary. This opens interesting perspectives for heat management at submicron scales: arrays of parallel gated nanowires could be used for a field control of phonon emission/absorption.     

Reprint of : Absorbing/Emitting Phonons with one dimensional MOSFETs

We consider nanowires in the field effect transistor device configuration. Modeling each nanowire as a one dimensional lattice with random site potentials, we study the heat exchanges between the nanowire electrons and the substrate phonons, when electron transport is due to phonon-assisted hops between localized states. Shifting the nanowire conduction band with a metallic gate induces different behaviors. When the Fermi potential is located near the band center, a bias voltage gives rise to small local heat exchanges which fluctuate randomly along the nanowire. When it is located near one of the band edges, the bias voltage yields heat currents which flow mainly from the substrate towards the nanowire near one boundary of the nanowire, and in the opposite direction near the other boundary. This opens interesting perspectives for heat management at submicron scales: arrays of parallel gated nanowires could be used for a field control of phonon emission/absorption.     

De Gennes parameter limit for the occurrence of a single vortex in a square mesoscopic superconductor

The time dependent Ginzburg–Landau equations (TDGLE) are used to study the properties of a mesoscopic superconducting square surrounded by different metallic materials. The properties of the metallic environment are taken into account by De Gennes boundary conditions, via the extrapolation length b. The external magnetic field is applied perpendicularly to the square surface. The TDGLE are used upon taking the magnetic field and the order parameter invariant along z-direction. It is determined the b-limit for the occurrence of a single vortex in a mesoscopic square of area d², d varies discretely from 4ξ(0) to 10ξ(0). We can show a logarithmical dependence of the sample size as a function on b parameter.     

Mesoscopic entangled coherent states implemented with a circuit quantum electrodynamics system

We show a scheme to generate entangled coherent states in a circuit quantum electrodynamics system, which consists of a nanomechanical resonator, a superconducting Cooper-pair box (CPB), and a superconducting transmission line resonator. In the system, the CPB plays the role of a nonlinear medium and can be conveniently controlled by a gate voltage including direct-current and alternating-current components. The scheme provides a powerful tool for preparing the multipartite mesoscopic entangled coherent states.     

Structure of quantum disordered wave functions: weak localization, far tails, and mesoscopic transport

We report on the comprehensive numerical study of the fluctuation and correlation properties of wave functions in three-dimensional mesoscopic diffusive conductors. Several large sets of nanoscale samples with finite metallic conductance, modeled by an Anderson model with different strengths of diagonal box disorder, have been generated in order to investigate both small and large deviations (as well as the connection between them) of the distribution function of eigenstate amplitudes from the universal prediction of random matrix theory. We find that small, weak localization-type, deviations contain both diffusive contributions (determined by the bulk and boundary conditions dependent terms) and ballistic ones which are generated by electron dynamics below the length scale set by the mean free path ℓ. By relating the extracted parameters of the functional form of nonperturbative deviations (“far tails”) to the exactly calculated transport properties of mesoscopic conductors, we compare our findings based on the full solution of the Schr?dinger equation to different approximative analytical treatments. We find that statistics in the far tail can be explained by the exp-log-cube asymptotics (convincingly refuting the log-normal alternative), but with parameters whose dependence on ℓ is linear and, therefore, expected to be dominated by ballistic effects. It is demonstrated that both small deviations and far tails depend explicitly on the sample size--the remaining puzzle then is the evolution of the far tail parameters with the size of the conductor since short-scale physics is supposedly insensitive to the sample boundaries. Received 19 August 2002 Published online 19 November 2002     

Optical control of the mobility of a MODFET with a layer of self-assembled quantum dots

We report an experimental study of GaAs/Al_0.33Ga_0.67As modulation doped field effect (MODFET) transistors, in which an InAs layer of self-assembled quantum dots is placed in one of the Al_0.33Ga_0.67As barrier layers close to the two-dimensional electron gas (2DEG). We find the source–drain resistance is bistable with the two states controlled by illumination and applied gate bias. Brief illumination induces a large, persistent drop in the resistance, which can be recovered by applying a positive gate bias. Magneto-transport measurements show that while illumination causes only a relatively small change in the 2DEG density, it can greatly enhance its mobility. We suggest this is because the 2DEG mobility is limited by percolation of the electrons through the rough electrostatic potential induced by the charged dots. Illumination reduces the negative charge trapped in the dots, thus smoothing the conduction band potential, which produces a large increase in the mobility.     

Gate‐controlled metal–insulator transition in the LaAlO3/SrTiO3 system with sub‐critical LaAlO3 thickness

We studied the electrical conduction in the LaAlO₃/SrTiO₃ (LAO/STO) interface electron system with a sub‐critical LAO layer thickness of ～3.5 unit cells (uc). It was found that the true dividing point between metallic and insulating behaviour without gating lies near the LAO thickness of 3.5 uc. Our marginally metallic 3.5 uc sample showed a sharp transition to insulating state at temperatures which strongly depended on the applied negative back‐gate voltage. The superior gate‐controllability of the sample was attributed to its sheet carrier density which was an order of magnitude lower than those of conducting LAO/STO samples with 4 uc or more of LAO layers. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Charge densities and charge noise in mesoscopic conductors

We introduce a hierarchy of density of states to characterize the charge distribution in a mesoscopic conductor. At the bottom of this hierarchy are the partial density of states which represent the contribution to the local density of states if both the incident and the out-going scattering channel is prescribed. The partial density of states play a prominent role in measurements with a scanning tunneling microscope on multiprobe conductors in the presence of current flow. The partial density of states determine the degree of dephasing generated by a weakly coupled voltage probe. In addition the partial density of states determine the frequency-dependent response of mesoscopic conductors in the presence of slowly oscillating voltages applied to the contacts of the sample. The partial density of states permit the formulation of a Friedel sum rule which can be applied locally. We introduce the off-diagonal elements of the partial density of states matrix to describe charge fluctuation processes. This generalization leads to a local Wigner-Smith life-time matrix.