Quantum Transport In Mesoscopic Systems Research Articles

Scattering in Terms of Bohmian Conditional Wave Functions for Scenarios with Non-Commuting Energy and Momentum Operators

Without access to the full quantum state, modeling quantum transport in mesoscopic systems requires dealing with a limited number of degrees of freedom. In this work, we analyze the possibility of modeling the perturbation induced by non-simulated degrees of freedom on the simulated ones as a transition between single-particle pure states. First, we show that Bohmian conditional wave functions (BCWFs) allow for a rigorous discussion of the dynamics of electrons inside open quantum systems in terms of single-particle time-dependent pure states, either under Markovian or non-Markovian conditions. Second, we discuss the practical application of the method for modeling light–matter interaction phenomena in a resonant tunneling device, where a single photon interacts with a single electron. Third, we emphasize the importance of interpreting such a scattering mechanism as a transition between initial and final single-particle BCWF with well-defined central energies (rather than with well-defined central momenta).

Preface to the Special Issue on Quantum Transport in Mesoscopic Systems

Preface to the Special Issue on Quantum Transport in Mesoscopic Systems

Time-dependent thermoelectric transport in mesoscopic systems under a quantum quench

We investigate the transient behavior of the quantum transport in mesoscopic systems under a quantum quench within the Caroli scheme. Using the nonequilibrium Green's function approach, an exact solution of the transient electric current, energy current, and their fluctuations in the presence of both external bias and temperature gradient are presented that goes beyond the wide-band limit. The exact solution of the time-dependent Seebeck coefficient in the linear response regime is also obtained. This formalism is applied to study the transient behavior of a single-level quantum dot with Lorentzian linewidth induced by the temperature gradient. The damped oscillatory behavior is found in the transient electric and energy currents, as well as their fluctuations. The oscillation frequency of electric and energy currents increases with the increasing energy level of quantum dot and the decay rate of oscillation decreases as the bandwidth increases. A significantly enhanced Seebeck coefficient is generated in the transient regime. We find the maximum value of the time-dependent Seebeck coefficient can be enhanced by increasing the energy level of the quantum dot and the reference temperature of leads.

Quantum transport in mesoscopic systems

A short introduction to the quantum transport in mesoscopic systems is given, and various regimes of quantum transport such as diffusive, ballistic, and adiabatic are explained. The effect of interactions and inelastic scattering along with the characteristic coherent effects of mesoscopic systems give interesting new mesoscopic effects, such as CoulombBlockade and Kondo Resonance. The basic physics of these phenomena is explained in simple language. In the end, some current research problems in this field are discussed.

Spin-dependent current noises in transport through coupled quantum dots

Current fluctuations can provide additional insight into quantum transport in mesoscopicsystems. The present work is carried out for the fluctuation properties of transport througha pair of coupled quantum dots which are connected with ferromagnetic electrodes. Basedon an efficient particle-number-resolved master equation approach, we are concernedwith not only fluctuations of the total charge and spin currents, but also of eachindividual spin-dependent component. As a result of competition among the spinpolarization, Coulomb interaction, and dot–dot tunnel coupling, rich behaviorsare found for the self- and mutual-correlation functions of the spin-dependentcurrents.

Full counting statistics for electron number in quantum dots

AbstractMeasurements of the average current and its fluctuations (noise) have been powerful tools to study the quantumtransport in mesoscopic systems. Recently it became possible to measure the probability distribution of current, ‘full counting statistics’ (FCS), by using quantum point‐contact charge‐detectors. Motivated by recent experiments, we developed the FCS theory for the joint probability distribution of the current and the electron number inside quantum dots (QDs).We show that a non‐Gaussian exponential distribution appears when there is no dot state close to the lead chemical potentials. We show that the measurement of the joint probability distribution of current and electron number would reveal nontrivial correlations, which reflect the asymmetry of tunnel barriers.We also show that for increasing strength of tunneling, the quantum fluctuations of charge qualitatively change the probability distribution of the electron number. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Full counting statistics for charge inside a quantum dot

Measurements of the average current and its fluctuation (noise) have been powerful tools to study the quantum transport in mesoscopic systems. Recently it became possible to measure the higher moment of the current probability distribution and moreover, the current distribution itself (‘full counting statistics’ (FCS)) by using quantum point-contact charge-detectors. Motivated by recent experiments, we evaluate the FCS for the probability distribution of electron number inside a quantum dot (QD). We show that a non-Gaussian exponential distribution appears when there is no dot state close to the lead chemical potentials. We propose the measurement of the joint probability distribution of current through the QD and electron number inside the QD, which reveals correlations between the two observables and reflects the asymmetry of tunnel barriers. We also show that for increasing strength of tunneling, the quantum fluctuations qualitatively change the probability distribution of the electron number.

Proximity Effect of the Contacts on Electron Transport in Mesoscopic Devices

The Wigner function formalism is used for studying electron quantum transport in mesoscopic systems. In this work we show that, if the correlation of the electron wave function vanishes outside the region of interest (for example inside the contacts), then transport is affected inside the device. This property is verified analytically. Results show that, for very short devices, tunneling is actually influenced by the distance between the contacts. Modification in the electron density and conductivity have been numerically observed.

Energy and momentum balance equations: An approach to quantum transport in closed circuits

Using the Heisenberg equations of motion, we have derived a set of gauge-invariant quantum-mechanical energy and momentum balance equations governing the transport of charged particles in a closed electric circuit, Because the driving electric field needs not to be uniform along the circuit, the balance equations provide a suitable tool for the investigation of quantum transport in mesoscopic systems. As an example, we investigated the global and local properties of energy dissipation in a quantum wire circuit under the influence of a localized elastic scatterer, modeled by a Dirac-delta potential. In the low-temperature linear-response regime we obtain the Landauer formula for the resistance of the elastic-scattering barrier. The localized electric field originating from this barrier is obtained using a self-consistent solution of the Poisson equation.

Wigner Paths for Quantum Transport

A Monte Carlo algorithm based on the concept of Wigner paths has been developed to study quantum transport in mesoscopic systems in strict analogy with the traditional Monte Carlo simulation used to solve the Boltzmann transport equation. Scatterings with both phonons and impurities can be accounted for. As regards a structure potential profile the effect of the corresponding classical force can be inserted in the dynamics of the free flight, while quantum effects due to rapid potential variations are included as a special scattering mechanism.

Eighth NEC Symposium summary

NEC symposia are world-renowned for bringing together speakers who are at the forefront of fundamental new work in functional materials. The Eighth Symposium on Spin-related Quantum Transport in Mesoscopic Systems was no exception. In this summary, I shall pick out some topics that recurred several times during the Symposium. One such topic — new aspects of the Kondo effect observed in quantum dots — was summarized by Professor Yoshimori.

Diagrammatic method of integration over the unitary group, with applications to quantum transport in mesoscopic systems

A diagrammatic method is presented for averaging over the circular ensemble of random-matrix theory. The method is applied to phase-coherent conduction through a chaotic cavity (a ‘‘quantum dot’’) and through the interface between a normal metal and a superconductor.