Exciton In Quantum Dots Under Magnetic Filed

Quantum dots are semiconductor nanostructure exhibiting three-dimensionalconfinement effect on carriers, which makes the carrier’s wave function length scalecomparable to the De Broglie wavelength. The electronic properties in quantum dots aresimilar to those of atoms, for example, their characteristic discrete energy spectra andcontrollable physical parameters. Thus single quantum dot can be regarded as an artificialatom. Corresponding to the analogy between a quantum dot and an artificial atom, a pair ofvertically or laterally coupled quantum dots is called an artificial molecule. Coupled quantumdots can be fabricated by a lot of techniques. It has been proved by the experiment thatself-assemble method is well suited to fabricate the coupled quantum dots possessingparticular high qualities. Systems of the coupled quantum dots are interesting because of theirpotential applications in not only quantum devices designing but also the currently active fieldof quantum information processing. They have been proposed in order to realize solid-statequantum gates involving two quantum bits that can be represented by either electron spinstates or exciton states. Moreover, many people investigate the possibility of an application ofquantum dots in solid-state quantum computation because it is easy to scale up for usingquantum dots as quantum bits. The quantum entanglement of qubits plays an important role inquantum communication and quantum computation. In fact, in the coupled quantum dots, theentanglement may be influenced by many factors, such as composition fluctuations, dot sizedifferences, applied external fields, and so on. Therefore, the behavior of the entanglementcan be adjusted by optimizing the structural and the band parameters, which is important forfinding stable and controllable entanglement in qubits.In this paper, we review the fabrication and application, experimental and theoreticalstudy on the excitons in quantum dots. Two kinds of theoretical modles are proposed: onekind is the square single quantum dot and coupled quantum dots byIn0.6Ga0.4As/GaAsheterogeneous structures along the lon-gitudinal direction; another kind is the Gaussian singlequantum dot and coupled quantum dots by the Gaussian distribution of indium concentration;in this two kinds of quantum dots the lateral confinement potential is assumed to be a harmonic oscillator configuration, Such a parabolic lateral confinement is known to mimicmost of the important features of various self-assembled quantum dots and gives results thatare in a good agreement with those of experiments. Along the longitudinal direction, theexternal magnetic field is applied. Using the one-dimensional effective potential model andthe finite difference method, we theoretically study the properties of an exciton in this twokinds of models, such as the ground energies, the spatial distributions of wave functions, thetransition energies, the binding energies, the entanglement entropy, and so on. The effects dueto the applied magnetic filed and the quantum confinement on the binding energy areanalyzed, and the following results are obtained: the ground state transition energy of theheavy-hole exciton can split into four energy levels due to the Zeeman effect, which resultsare in a good agreement with those of experiments; the binding energy monotonically increasewith increasing the lateral confinement or the magnetic field; the size and shape of thequantum dot has a significant influence on the binding energy of the exciton, which can beseen both from the average distance between the electron and the hole and from the wavefunction distributions of the exciton. For the symmetrical system, the entanglement entropy ofthe exciton state can reach a value of1. However, for a system with broken symmetry, it isclose to zero. Our results are in a good agreement with previous studies.