a) In GaAs at low temperatures the optically allowed J =1 exciton state (formed
ID: 2077229 • Letter: A
Question
a) In GaAs at low temperatures the optically allowed J =1 exciton state (formed of J_e = 1/2 electrons and J_h =3/2 holes) is triply degenerate because of the high lattice symmetry of the crystalline structure. Describe the evolution of this state in the presence of a constant magnetic field B_z applied parallel to the [100] crystalline axis. b) A structural orthorhombic distortion in the plane perpendicular to the [100] axis adds a term in the exciton Hamiltonian equal to delta_ex (J^2 _x - J^2 _y). What is the evolution of the J = 1 excitonic state with applied magnetic field B_z? Is J_z a good quantum number? What is the significance of delta_ex? How can we measure delta_ex?Explanation / Answer
Solution :- In GaAs at low temperatures the optically allowed J = 1 exciton state (formed of Je = 1/2 electrons and Jh = 3/2 holes) is triply degenerate because of the high lattice symmetry of crystalline structure.
An electron in an atom sees a constant magnetic eld Bz applied parallel to the 100 crystalline axis, because of its own orbital motion and consequently there is an interaction called the spin-orbit interaction whereby the magnetic eld due to the orbital motion of the electron tends to line up its magnetic moment along the magnetic eld
H'S.O. = µ· H.
b) A structural orthohombic distortion in the plane perpendicular to the (100) axis adds a term in the exciton Hamiltonian equal to deltaex (Jx^2-Jy^2).
The evolution of the J =1 excitonic state with applied magnetic field Bz newidth extracted from the PL spectra when excited with 1 µW/µm2.
Yes Jz is a good quantum number because it is associated with a conserved observables (= operators commute with the Hamiltonian).
The significance of delta ex is that it provides it provides useful information about the structural distrotion in the plane.
The delta ex can be measured by by the exciton Hamiltonian.
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