Study On The Properties Of The Negatively Charged Donor Impurity In The Quantum Tube Under The Magnetic Field

In the framework of effective-mass envelope function, the properties of Aharonov-Bohm(A-B)oscillations of the neutral donor impurity system and the charged donor impurity system in a quantum tube under the magnetic field are studied theoretically. In the numerical calculation, the two-dimensional adiabatic model of quantum tube are adopted. The Hamiltonian matrix elements will be simplified in cylindrical coordinates, at last the ground state energy can be got by using exact matrix diagonalization techniques. We analyze and discuss the calculation results in detail, which show that:(1) The ground state energy of the neutral donor impurity system and charged donor impurity system will oscillate(A-B oscillation) with the change of magnetic flux. The amplitude of A-B oscillation will increase with the decrease of radius of the quantum tube. The reason is that the oscillations of the ground state energies are generated by the transitions of the different angular momentum energies. The Coulomb interaction energy becomes weaker and weaker as the radius increases, then the different angular momentum energies intersect, which leads to the transitions more frequent, so the A-B oscillations of the ground state energies become weak and no longer clear. At the same time, as the radius increases, the total Coulomb interaction and the magnetic field intensity will decrease, but the influence on the system caused by the latter is weaker than the former, which makes the amplitude of A-B oscillation of the ground state energy small.(2) In the absence of magnetic field, the ground state energy of the neutral donor impurity system and charged donor impurity system will increases monotonically as the radius increases. When the magnetic field is added to the system, the ground state energy will decreases and then increases. This is becaues of the difference between the dependence of the kinetic energy items (including the magnetic field) and the Coulomb interaction term on the radius. When the radius is smaller, the kinetic energy items which magnetic vector potential involved in play a main role, so the energy of the system will be gradually reduced as the radius increases. When the magnetic field intensity becomes weak quickly which is resulted by the increased radius, the coulomb interaction (not the kinetic energy) will play a main role. As the radius increases, the energy of the system will increase and gradually close to the situation without magnetic field. When the radius increases to a certain size, the effect on the system made by the magnetic field almost can be ignored because the magnetic field intensity becomes very weak. Finally, the energy is almost consistent with the case of no magnetic field.(3) For the quantum tube with a negatively charged donor impurity system, the amplitude of A-B oscillation of the ground-state energy will rapidly increases with increasing length of the quantum tube. When the tube reaches to a certain length, the amplitude of oscillation will reach to a saturation state, and then does not increase with the length increase. This shows that for the same radius of quantum ring and quantum tube, the quantum tube is more available than the quantum ring with strong confinement in the axis direction for observating the A-B oscillation.(4) In the case of the same shape of quantum tubes, the amplitude of the A-B oscillation of the ground state energy in the system with a negatively charged donor impurity is greater than the system of neutral donor impurity, that is to say, the A-B oscillation of the system with a negatively charged donor impurity is more available than the neutral donor impurity system and can be easily observed in the experiment.