[Wien] g factors and NMR shift estimates in semiconductors with spin-orbit couplings

[Joseph Ross]

Dear Wien2k Community

We have been recently working on estimating semiconductor g-factors and 
related issues in order to estimate NMR shifts in semiconductors with spin-orbit
coupling. We took GaAs as a test case with SOC, and the band-structure
appears to be similar to what has been reported, with the split-off
hole band at about -0.33 eV. In order to estimate the g-factor in SOC
with the PBE functional (case.inso shown as the following), we applied 
magnetic field by inorb and indmc files, for example as follows:

case.inso
WFFIL
4  0  0                 llmax,ipr,kpot
-10  1.5                Emin, Emax
  0 0 1                           h,k,l (direction of magnetization)
2                       number of atoms with RLO
1 0.30 0.000 CONT             atom-number, E-param for RLO
2 0.30 0.000 CONT             atom-number, E-param for RLO
0 0      number of atoms without SO, atomnumbers

case.inorb
3  2  0                     nmod, natorb, ipr
PRATT  1.0                    BROYD/PRATT, mixing
1 3 0 1 2                       iatom nlorb, lorb
2 3 0 1 2                       iatom nlorb, lorb
1000                        Bext in T
0. 0. 1.                    direction of Bext in terms of lattice vectors

case.indmc
-12.                      Emin cutoff energy
2                       number of atoms for which density matrix is calculated
1 3 0 1 2                     iatom nlorb, lorb
2 3 0 1 2                     iatom nlorb, lorb
0 0           r-index, (l,s)index

Nominally this should give the splitting of g*H*mu_B, with the effective
g factor ~-0.44 given for the GaAs conduction band from k.P
theory. We expected to get a modified value because of the
PBE gap being incorrect, but the CB edge splitting actually gives g=+2.0
with or without SO, both in 100T and 1000T. These are big fields, but
the Zeeman splitting seems to be small enough compared to spin-orbit.
g=2 is just the Lande g value for the CB edge, and as discussed for
example in Van Bree et al., PRB 85, 165323 (2012) perhaps this is
expected since ORB does not include a field applied to the
interstitial electrons, whereas the large negative g values in some of
these systems correspond to orbital currents extending over multiple
cells. It is not clear to us whether the matching at sphere 
boundaries allows such currents to properly extend between atoms.

We are wondering, is this interpretation correct, and if so are there 
any suggested ways around this or perhaps any other suggestions if 
we want to estimate NMR Knight shifts for semiconductors? Or are 
we making a simple mistake and would expect to get splittings 
closer to the k.P values? 

Note for the hole values, the HH and LH states are more or less equally 
spaced (at least right at the edge where they are degenerate) and we 
find g=1.1, somewhat smaller than the Lande value of 4/3 for P3/2. 
(It is more difficult to tell the sign in this case.) The split-off holes 
exhibit an even smaller splitting, corresponding to g~0.06, far from 
the expected g=2/3, so maybe the guess about defaulting to the 
Lande g-factor values is not correct? Any suggestions would be 
appreciated.

-Joe Ross
-------------------------
Joseph H. Ross Jr.
Professor
Department of Physics and Astronomy
Texas A&M University
4242 TAMU
College Station TX  77843-4242
979 845 3842 / 448 MPHY
jhross at tamu.edu / http://faculty.physics.tamu.edu/ross
-----------------------