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

[Peter Blaha]

The effect due to a magnetic field via "orb" uses a "double" approximation:
i) It applies the field only inside the spheres
ii) and it uses a "central field approximation", which is Gauge 
dependent and valid only in the case of a single atom.

This implementation was originally intended for localized 3d (4f) 
electrons, where it might catch the main effects and both approximations 
are justified to some extend.

The NMR code, which was mentioned by Robert, calculates the perturbation 
of the wave functions due to an external field and then the resulting 
current. Then it integrates this using Biot-Savarts law and calculates 
the magnetic shieldings at the positions of the nuclei.

However, we do not calculate the perturbed eigenvalues ...

Peter Blaha

Am 24.11.2015 um 17:20 schrieb 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
> -----------------------
>
>
>
>
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-- 
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-165300             FAX: +43-1-58801-165982
Email: blaha at theochem.tuwien.ac.at    WIEN2k: http://www.wien2k.at
WWW:   http://www.imc.tuwien.ac.at/staff/tc_group_e.php
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