The Stability Of Electronic States In Quantum Dots

Quantum dots are special synthetic materials in which the electron spins are strongly bounded to form discrete energy levels,much like isolated atom in na-ture.The internal electron spin has good coherence and can be used as a qubit or logic gate,which has a very broad application prospect in the field of spintronics,quantum information and functional materials.However,the biggest obstacle to limiting its practical application is that the electron spin will quickly decohere under the interference of the environment,resulting in the loss of quantum infor-mation.Therefore,it is an important research topic to find electron spins that can maintain coherence under environmental disturbances.In this paper,we mainly study the Mn spin in semiconductor quantum dots and the stability of edge states in topological insulator quantum dots.Among them,the electron spins in the Mn ions in the semiconductor quantum dots have very strong locality,so their coherence is hard to be disturbed by the surrounding nuclear spins;the electron spins in the edge state of the topological insulators can remain stable under the applied electric field since its wave function is con-centrated at the edge of the quantum dot and protected by the time inversion symmetry.The electron spins in the above two materials have relatively good stability and are therefore highly promising for use in future quantum devices.The stability is defined as maintaining coherence under external disturbances.In this paper we first introduce the relevant theoretical basis of decoherence and quantum dots.Then we introduce in detail the Mn spins in semiconductor quan-tum dots and the edge states of topological insulator quantum dots.We finally conclude our research and look forward to further applications.The full text is divided into five chapters:In the first chapter,we briefly introduce the theoretical basis of the research object:electron spin and its decoherence.In the second chapter,we study the pure dephasing of Mn spin in semi-conductors(one of the mechanisms of decoherence).Firstly,we established a two-level model to describe the physics of pure dephasing of Mn spin in quan-tum dots,and provide analytical derivation and numerical calculation methods.Then we analyze in detail the rate of pure phasing of Mn spin caused by various reasons,and providing a method for suppressing the pure dephasing of Mn spin.The most important method is to add an in-plane electric field to manipulate the wave function of the electrons in the semiconductor.Finally,we analyzed the effect of surrounding nuclear spins on the pure dephasing of Mn spin at low temperatures.In the third chapter,we use the base function expansion method to calculate the energy and wave function of the quantum state of the two-dimensional topo-logical insulator,and define the reciprocal of the energy and the applied electric field as the sensitivity to describe the stability under the external electric field interference.However,due to the limitations of the accuracy of the basis function expansion method,we only discuss quantum dots with smaller radius.In the fourth chapter,in order to improve the defects of Chapter 3 work,we introduce the pattern matching method and obtain the energy and wave function in semi-analytical form.On this basis,we discuss in detail the symmetry and stability of the edge states of two-dimensional topological insulators.This includes analyzing the equal-distance of the energy levels of the edge states,the conditions on the existence of edge states in the band gap,and the influence of the parameters of the quantum dots on the stability.In the fifth chapter,we summarize the previous research and look forward to the future work.