Acceptor excitation spectra in germanium in a uniform magnetic field

Abstract

The irreducible-spherical-tensor form of the effective-mass Hamiltonians for acceptors in cubic semiconductors in a homogeneous magnetic field parallel to a (001) direction or to a ( 111) direction has been derived. The Hamiltonians take into account the full structure of the I g SI 7+ valence-band edge, and they contain a point-charge potential with spherically symmetric qdependent dielectric screening. The eigenstates have been calculated variationally for the case of acceptors in germanium. For both orientations, the computations have been performed as a function of the magnetic-field strength, in the range from 0 to 5 T. The binding energies of the first 36 odd-parity excited states and of the first 4 even-parity states (which form the ground-state multiplet) are obtained. The oscillator strengths of the electric-dipole transitions from the ground-state sublevels to the excited states are also calculated, and the results are used to simulate theoretical acceptor excitation spectra, which are in excellent agreement with the available experimental farinfrared-absorption and photothermal-ionization-spectroscopy spectra. For the ground state and for the final states of the G and D lines, theoretical g factors are obtained which are very close to the experimental ones. In particular, the values g& = -0.45 and gz =+0.22 are computed for the acceptor ground state. It is found also that for the ground state and for the excited I 8( Td ) final states of the G, D, and B spectral lines, the ratio r =g2/4g& is always very close to the special value --', , which corresponds to a linear Zeeman splitting of the I 8 states into a degenerate doublet for B~~( 111)and into an equally spaced quartet for B~~(001 ).

Magnetoexcitons in cuprous oxide

“…After introducing relative and center of mass coordinates [27,28] and setting the position and momentum of the center of mass to zero, the complete Hamiltonian of the relative motion reads [17,[27][28][29][30][31][32] …”

“…The value of the fourth Luttinger parameter κ is unknown and will be determined in Sec. V. In the case of a finite spin-orbit coupling ∆ an additional term would generally appear in H B , which depends on the fifth Luttinger parameter q [23,32,33]. However, this term is connected with spin-orbit interactions of higher order [32] and is not considered here.…”

“…All material values used in our calculations are listed in Table I. For the case that the magnetic field is oriented along one of the directions of high symmetry, i.e., along the [001], [110] or [111] direction, we rotate the coordinate system to make the quantization axis coincide with the direction of the magnetic field and then express the Hamiltonian (7) in terms of irreducible tensors [32,36,37] (see Appendix A). We can then calculate a matrix representation of the Schrödinger equation corresponding to the Hamiltonian (7) using a complete basis.…”

Impact of the valence band structure ofCu2Oon excitonic spectra

“…Besides the p 4 -terms in Eq. (11), one could also imagine terms of the form p For subsequent calculations it is appropriate to write the Hamiltonian (7) in terms of irreducible tensors [12,36,37], where we additionally set the position and the momentum of the center of mass to zero:…”

Exciton-phonon interaction breaking all antiunitary symmetries in external magnetic fields

“…i.e., we replace x → x = R T x with x ∈ {r, p, L, I, S} to make the quantization axis coincide with the direction of the magnetic field [55,63]. Finally we express the Hamiltonian in terms of irreducible tensors (see, e.g., Refs.…”