Benny Lassen

Coherent transport through an interacting double quantum dot: Beyond sequential tunneling

Various causes for negative differential conductance in transport through an interacting double quantum dot are investigated. Particular focus is given to the interplay between the renormalization of the energy levels due to the coupling to the leads and the decoherence of the states. The calculations are performed within a basis of many-particle eigenstates and we consider the dynamics given by the von Neumann equation taking into account also processes beyond sequential tunneling. A systematic comparison between the levels of approximation and also with different formalisms is performed. It is found that the current is qualitatively well described by sequential processes as long as the temperature is larger than the level broadening induced by the contacts.

Electron transport through nanosystems driven by Coulomb scattering

Electron transmission through nanosystems is blocked if there are no states connecting the left and the right reservoir. Electron-electron scattering can lift this blockade, and we show that this feature can be conveniently implemented by considering a transport model based on many-particle states. We discuss typical signatures of this phenomenon, such as the presence of a current signal for a finite bias window.

The Ben Daniel-Duke model in general nanowire structures

A simple computationally effective method is developed for solving the Ben Daniel - Duke equations for nanowire semiconductor heterostructures. The method allows eigenstates and associated energy levels of nanowires with varying cross- sectional shape and/ or varying composition to be obtained, and is based on expanding the envelope function eigenstates on local eigenstates of the corresponding cross- sectional problem. In this way, the original partial differential equation problem is reduced to a set of coupled ordinary differential equations ( this set can to a good approximation be limited to a small number of coupled equations). In the first part of the paper, the model equation framework is derived; it can be easily modified to account for a more general set of partial differential equations. In the second part of the paper, three different cases of axisymmetrical nanowire problems are analysed in terms of eigenstates and energy eigenvalues. The cases considered are ( a) conical nanowires, ( b) a nanowire with a step in radius, and ( c) a conical GaAs/ GaAlAs nanowire. Comparison with computationally more expensive finite- element results on a two- dimensional domain is made, and good agreement is found. (Less)

Spurious solutions and boundary conditions in k · p theory

It is well known that the origin of one type of spurious solutions in multiband k(.)p theory is the failure to restrict the Fourier coefficients of the envelope functions to the first Brillouin zone. Often, the set of differential equations obtained is supplemented with interfacial boundary conditions derived by integrating the differential equations across the interface; however, this leads to a mathematically ill-posed problem as the envelope functions cannot simultaneously fulfill these boundary conditions and the requirement that the Fourier coefficients be restricted to the first Brillouin zone. We show, by way of an example, the origin of these spurious solutions and how to remove them.

Effect of strain on optical properties of bent nanowires

In this work we study the deformation of ZnO nanowires under the influence of an applied force at the top of the wire. We show that the Euler‐Bernoulli beam equation can be used even for relatively high forces although a full non linear theory does show quantitative differences, however, not qualitative differences. We furthermore show that strain induces a confinement of the electrons which results in a significant increase in the conduction band energy spacing. It is known that piezoelectric effects are important in ZnO nanowire, however, these are disregarded in this work in order to wholly focus on the effect of strain.

Comparison of Atomistic and Continuum Quantum‐Dot Elastic Models and Implications for Optoelectronic Properties

A comparison between continuum and atomistic valence force field (VFF) strain models is presented for zincblende InGaAs/GaAs spherical quantum dots (QD), showing differences in the off‐diagonal components of the strain tensor, relavant for optoelectronic properties. We also present a comparison with the continuum model between different homogeneous compositions and concentration profiles. It is shown that the biaxial strain component is different from zero inside the QD in the linear concentration case which is known to have an effect on the valence band electrons.

Cylindrical symmetry and spurious solutions in eight band k⋅p theory

Spurious solutions in eight band k⋅p theory for low‐dimensional semiconductor heterostructures is a well‐known problem. In this paper we study two approaches for the removal of spurious solutions, the plane wave cutoff approach [1] and the approach suggested by Foreman [2] where the Kane parameter is changed. We show that in order to use the plane wave cutoff approach for a cylindrical symmetric system Bessel functions has to be used as the expansion basis in the radial direction. Furthermore we compare the two approaches for a InAs/GaAs conical quantum dot.

Exciton states in three-dimensional ring structures a differential-geometric analysis

An effective method for computing excitonic shifts in curved quantum‐wire geometries is presented. As a case example, we consider a GaAs quantum ring with infinite barriers along the cross‐sectional dimensions assumed to be of square shape albeit this assumption can be easily avoided. A simple analytic expression for excitonic shifts is found using first‐order perturbation theory.