Current Spin Density Functional Theory Research Articles

Mathematical modeling of semiconductor quantum dots based on the nonparabolic effective-mass approximation

Within the eective mass and nonparabolic band theory, a general framework of mathematical models and numerical methods is developed for theoretical studies of semiconductor quantum dots. It includes single-electron models and many-electron models of Hartree-Fock, configuration interaction, and current-spin density functional theory approaches. These models result in nonlinear eigenvalue problems from a suitable discretization. Cubic and quintic Jacobi-Davidson methods of block or nonblock version are then presented for calculating the wanted eigenvalues that are clustered in the interior of the spectrum and may have small gaps and degeneracy. These are challenging issues arising from modeling a great variety of semiconductor nanostructures fabricated by advanced technology in semiconductor industry and science. Generic algorithms for many-electron simulations under this framework are also provided. Numerical results obtained within this framework are summarized to three eminent aspects, namely, accuracy of models, physical novelty, and eectivity of nonlinear eigensolvers. Concerning numerical accuracy, important details related to experimental data are also addressed.

Few electron limit of n-type metal oxide semiconductor single electron transistors

We report the electronic transport on n-type silicon single electron transistors (SETs) fabricated in complementary metal oxide semiconductor (CMOS) technology. The n-type metal oxide silicon SETs (n-MOSSETs) are built within a pre-industrial fully depleted silicon on insulator (FDSOI) technology with a silicon thickness down to 10 nm on 200 mm wafers. The nominal channel size of 20 × 20 nm2 is obtained by employing electron beam lithography for active and gate level patterning. The Coulomb blockade stability diagram is precisely resolved at 4.2 K and it exhibits large addition energies of tens of meV. The confinement of the electrons in the quantum dot has been modeled by using a current spin density functional theory (CS-DFT) method. CMOS technology enables massive production of SETs for ultimate nanoelectronic and quantum variable based devices.

Artificial molecular quantum rings under magnetic field influence

The ground states of a few electrons confined in two vertically coupled quantum rings in the presence of an external magnetic field are studied systematically within the current spin-density functional theory. Electron-electron interactions combined with inter-ring tunneling affect the electronic structure and the persistent current. For small values of the external magnetic field, we recover the zero magnetic field molecular quantum ring ground state configurations. Increasing the magnetic field many angular momentum, spin, and isospin transitions are predicted to occur in the ground state. We show that these transitions follow certain rules, which are governed by the parity of the number of electrons, the single-particle picture, Hund’s rules, and many-body effects.

The effect of band nonparabolicity on modeling few-electron ground states of charge-tunable InAs/GaAs quantum dot

Based on the current spin density functional theory and the nonparabolic effective mass approximation, a three-dimensional model is presented to study the few-electron system in InAs/GaAs quantum dot for which the electron spectra have been obtained from the capacitance–voltage (CV) measurements by Miller et al. [Phys. Rev. B 56 (1997) 6764]. The model is an extension of the single-electron model proposed by Filikhin et al. [Solid State Comm. 140 (2006) 483]. Our results can quantitatively well interpret the experimental CV data. It is shown that the energy differences between the parabolic and nonparabolic approximations are comparable with the exchange-correlation energies. Moreover, the nonparabolic effect is shown to be increasingly more significant than that of parabolic case in higher magnetic fields. It is also more pronounced for larger number of electrons.

Optimized effective potential method in current-spin-density-functional theory

Current-spin-density-functional theory (CSDFT) provides a framework to describe interacting many-electron systems in a magnetic field which couples to both spin and orbital degrees of freedom. Unlike in the usual (spin-)density-functional theory, approximations to the exchange-correlation energy based on the model of the uniform electron gas face problems in practical applications. In this work, explicitly orbital-dependent functionals are used and a generalization of the optimized effective potential method to the CSDFT framework is presented. A simplifying approximation to the resulting integral equations for the exchange-correlation potentials is suggested. A detailed analysis of these equations is carried out for the case of open-shell atoms and numerical results are given using the exact-exchange energy functional. For zero external magnetic field, a small systematic lowering of the total energy for current-carrying states is observed due to the inclusion of the current in the Kohn-Sham scheme. For states without current, CSDFT results coincide with those of spin-density-functional theory.

3D simulation of a silicon quantum dot in a magnetic field based on current spin density functional theory

We have developed a code for the simulation of the electrical and magnetic properties of silicon quantum dots in the framework of the TCAD Package NANOTCAD-ViDES. We adopt current spin density functional theory with a local density approximation and with the effective mass approximation. We show that silicon quantum dots exhibit large variations of the total spin as the number of electrons in the dot and the applied magnetic field are varied. Such properties are mainly due to the silicon band structure, and make silicon quantum dots interesting systems for spintronic and quantum computing experiments.

A model for semiconductor quantum dot molecule based on the current spin density functional theory

Based on the current spin density functional theory, a theoretical model of three vertically aligned semiconductor quantum dots is proposed and numerically studied. This quantum dot molecule (QDM) model is treated with realistic hard-wall confinement potential and external magnetic field in three-dimensional setting. Using the effective-mass approximation with band nonparabolicity, the many-body Hamiltonian results in a cubic eigenvalue problem from a finite difference discretization. A self-consistent algorithm for solving the Schrödinger–Poisson system by using the Jacobi–Davidson method and GMRES is given to illustrate the Kohn–Sham orbitals and energies of six electrons in the molecule with some magnetic fields. It is shown that the six electrons residing in the central dot at zero magnetic field can be changed to such that each dot contains two electrons with some feasible magnetic field. The Förster–Dexter resonant energy transfer may therefore be generated by two individual QDMs. This may motivate a new paradigm of Fermionic qubits for quantum computing in solid-state systems.

Testing of two-dimensional local approximations in the current-spin and spin-density-functional theories

We study a model quantum dot system in an external magnetic field by using both spin-density-functional theory and current-spin density-functional theory. The theories are used with local approximations for the spin-density and vorticity. The reliabilities of different parametrizations for the exchange-correlation functionals are tested by comparing the ensuing energetics with quantum Monte Carlo results. The limit where the vorticity dependence should be used in the exchange-correlation functionals is discussed.

Current-spin density-functional theory of the electronic and magnetic properties of quantum dots and quantum rings

A systematic investigation of the electronic states and magnetism in quantum dots and quantum rings within current-spin density-functional theory (CSDFT) has been performed. CSDFT allows for studying the combined effects of confinement, Coulomb interaction, spin polarization, and magnetic field for a realistic dot or ring system. The dot and ring systems are considered to be three dimensional and the screening due to the gate electrodes is included. The chemical potential, addition energy, and spontaneous magnetization for a quantum dot and a quantum ring in zero magnetic field have been calculated as a function of electron number. A number of spin-polarized ground states in both the quantum dot and the quantum ring, which generally obey Hund's rule, are found. The chemical potential, spin magnetization, orbital angular momentum, and persistent current in the quantum systems under a magnetic field have also been calculated. With increasing magnetic field, a rich variety of transitions between the ground states with different orbital angular momentum and spin configuration are predicted. The calculated addition energy spectrum of the quantum dot reproduces the observed spectrum very well, especially, the charging energy, exchange energy, and shell structure. The features in the calculated chemical potential versus magnetic-field spectra of the quantum dot, which reflect the many-electron state transitions, agree well with those observed in the experiments, indicating that CSDFT is a useful tool for studying the correlated electrons in quantum dots and quantum rings.

Two vertically coupled quantum dots in a magnetic field

We studied the ground state of two vertically coupled quantum dots as a function of the interdot distance in the presence of a perpendicular magnetic field. The theoretical approach is based on the current spin density functional theory. Increasing the interdot distance leads to the population of antibonding levels, resulting in molecule-type phases. However, for increasing magnetic field strengths, we find that electrons hop back from antibonding to bonding levels, which is a consequence of electron interactions. The maximum density droplet is much less stable than in a single quantum dot.

Current-spin-density-functional study of persistent currents in quantum rings

We present a numerical study of persistent currents in quantum rings using current spin density functional theory (CSDFT). This formalism allows for a systematic study of the joint effects of both spin, interactions and impurities for realistic systems. It is illustrated that CSDFT is suitable for describing the physical effects related to Aharonov-Bohm phases by comparing energy spectra of impurity-free rings to existing exact diagonalization and experimental results. Further, we examine the effects of a symmetry-breaking impurity potential on the density and current characteristics of the system and propose that narrowing the confining potential at fixed impurity potential will suppress the persistent current in a characteristic way.

Magnetic interaction between coupled quantum dots

We study the magnetic coupling in artificial molecules composed of two and four laterally coupled quantum dots. The electronic ground-state configurations of such systems are determined by applying current spin density functional theory which allows to include effects of magnetic fields. While the ground-state of a two-dot molecule with strong enough inter-dot coupling tends to be antiferromagnetic with respect to the spins of the single dot components, we find that a square lattice of four dots has a ferromagnetic ground state.

Shell structure and exchange-related spin effects for quantum dots in a magnetic field

Ground-state calculations based on current spin density-functional theory for circular parabolic quantum dots are presented which reveal interesting spin effects in dependence on an external magnetic field: Hund's first rule (well-known from atomic physics for zero magnetic field) is related to the level occupancy near the Fermi energy and determines the spin configuration of the ground state in finite magnetic field. Consequently, the addition spectrum of the quantum dot exhibits a specific non-monotonous dependence on magnetic field, which is visible in recent quantum transport experiments.