Study On Spin Relaxation And Spin Beat In Semiconductor Quantum Dot

The traditional mechanisms for spin relaxation are suppressed in semiconductor quantum dots (QDs) with confined three-dimensional structure so the life time of spin becomes longer. Studies on spin physical properties in QDs have aroused much attention for spins of electrons or holes are promised to be used as quantum bits in application to quantum computation, quantum encryption, quantum communication, etc. It is shown in this thesis mainly about studies on spin properties in a single semiconductor QD, which include calculations and analyses in energy levels of a QD, electron spin relaxation respectively due to spin-lattice interaction and spin-orbit coupling, spin quantum beats between bright and dark excitonic states, and electron spin relaxation in an anisotropic QD.Progresses in Spintronics is briefly reviewed, involving generation of polarized spins, magneto-resistance effect, spin relaxation and dephasing, etc. It is given emphasis to four mechanisms for spin relaxation, namely, Elliott-Yafet (EY), D'yakonov-Perel'(DP), Bir-Aronov-Pikus (BAP) and hyperfine-interaction mechanisms, which are of significance to the investigation on electron spin relaxation and exciton spin beat in QDs.Energy-band structure of semiconductors can be conveniently calculated with the use of k·p perturbation method and effective mass theory. Spin-orbit (SO) interaction term is taken as small perturbation in the Hamiltonian, so the state vectors {|nk0>} can be expanded as the product of the Bloch function{|v0)} and the spin eigenstate |?>. The energy spectrum and effective mass can be obtained after diagonalizing the Hamiltonian by applying second-order perturbation theory. Using the envelope function approximation method can calculate the states of electrons and holes in electromagnetic fields which change slowly at the range of lattice constant. In a spherical QD, the Hamiltonian can be expressed as the eight-band Luttinger-Kohn Hamiltonian which involves the couplings between six valence bands and two conduction bands. Taking the advantage of matrix multiplication instead of summation in computing coefficients of wave functions, and expanding the 8×8 Hamiltonian matrix to 8N×8N matrix, we obtain the energy spectrum of the electron in QD by diagonalizing the effective-mass Hamiltonian.When dealing with the spin-lattice interaction Hamiltonian in InAs QDs, the difference between electron cyclotron tensor g??(?,?= x,y,z) and the vacuum tensor g0???can show the influence of spin-orbit coupling on spin-phonon relaxation in seemly conditions. Then abbreviation of the Hamiltonian is carried out by transforming lattice coordinates to lab ones and diagonalizing gap factor. Referring to the experimental data, a few groups of g?(?= x,y,z) are chosen to calculate the spin relaxation rate?, which is found to be determined by the values of |g?|{?= x,y,z) and markedly affected by the difference among gx,gy,gz. It's found there is a proper size for InAs QDs to minimize the rate?. In view of the influence of directions of magnetic field n(?,?) on the spin relaxation rate, several times difference in rates can be obtained by changing the directions of the magnetic field.To deal with the Hamiltonian model in GaAs and InAs QD with a single electron, we've taken the SO interaction as a perturbation term, calculated the SO matrix elements under Fock-Darwin eigenfunction which are used for second order corrections on the energies and wave functions, and considered the influence of new energy levels on g factor and effective mass m. The expression of phonon-assisted electron spin relaxation rate?is carried out. We've analyzed and compared the rates in GaAs and InAs QD, which have shown different dependences on confined potential frequency?0, magnetic field B, temperature T and vertical height z0.The excitonic energy spectrum, relevant eigenfunction and the expression of the quantum beat (QB) signal, with the parameters of magnetic field B and g factor, are derived from spin Hamiltonian in InAs QD. It's shown that the direction and strength of magnetic field, and anisotropic g factors of electrons and holes influence on quantum beat. It is found the coefficient?0 can't be neglected in magnetic field even though in a high magnetic field like B= 4T, as long as??30°. The periodic oscillations of QBs are vanished at?gx= ge,x-gh,x= 0.6, which shows that whether or not the periodic signal of QBs can be observed is related to the 'matching' of the electron and hole g factors. The signals of quantum beats show acutely fluctuated at some special ge,x while there are obvious periods of the whole waveshapes in the long timeBy introducing Schuh's algebraic solution of non-trivial oscillator, we've derived canonical transformation matrix of the Hamiltonian in anisotropic GaAs QD with a single electron and obtained the matrix elements of SO coupling under the eigenfunctions in new phase space. Taking the corrections of SO on the energy levels and wave functions, we've carried out the phonon-assisted electron spin relaxation rate?1j. To find out the anisotropic properties of electron spin relaxation, we adopt Olendiski's method that the spin relaxation rate?1j can be written as the product of two terms:?1j (?)=G1j (?)Wj. We've analyzed the geometry factors G1j(?) correlative to SO interaction change with the magnetic tilt angle?, and found in different magnetic field with?=?/2 the rate G13(0) arrive at maximum at B=1T while in other conditions G1f (0) turns into minimum. We've also studied the dependency relationship of??/?on magnetic azimuthal angle?and found that both??12/?and??13/?form two wave peaks deviated from?/2, the symmetrical point.