The ABINIT Users Mailing List ( CLOSED )

[<walter.lambrecht@case.edu>]

Hi David + list, 
I still have some questions about this quantum and spontaneous polarization. 
1) As I understand it, strictly speaking only Delta P in an adiabatic
trasnformation  is well defined but the Berry phase approach calculates an
absolute P modulo a quantum 2eR/Omega with R a lattice vector or the
generalization of it that you pointed out.So, I guess that quantum drops out
somehow if we consider any physically measureable quantity like an interface
charge induced at the interface between two materials with different P. Am I
correct? And therefore the spontaneous P that people usually report is then 
the
smallest value without this quantum? 
So, for instance if we have a material with C2v symmetry with the 2 fold axis
along z, then I can 
have a non-zero P along z but not along x and y because of the mirrorplanes
according to the usual Landau Lifschitz definitions, but Berry phase could 
give
us a non-zero Px, Py. 

2) Just to feel safer, I would like to understand a little better the numbers
that come out in the tutorial 
for AsAs. What is the exact relation between what you call Berry's phase and
the spontaneous polarization?The program seems to calculate first a Berry 
phase
"corresponding to a reciprocal 
vector. "Does this mean it calculates P.Gi  with Gi the reciprocal vector or a
dot product of P
with a unit vector along Gi? I thought 
P.Gi=2e/Omega phi with phi the Bery phase. But when I put in numbers for AlAs
a=10.53 a.u. 
this does not seem to come out?  This is probably something trivial but I'd
like to understand. 
Next, given the P.Gi along three reciprocal lattice vectors (or rather G/6 for
6 points long the string)
it then can calculate the Cartesian components of P. Each of the components
seems sqrt(3) times 
the value given for the P.G for example -1.569029714E-02 *
sqrt(3)=-0.271763918E-01. 
The notes seem to say that this corresponds to a P which is (-3/4 -3/4
-3/4)a*2e/Omega. 
But I don't seem to get the right number. Can somebody throw some light on 
this
what exactly is calculated. That way I feel we could calculated by hand for
some other case, we are interested in and check whether it really is just a
quantum we need to eliminate. 


3) Finally, something on units. When converting from atomic units to SI units,
the program 
simply multiplies by e=1.602 10^-19 and divides by bohr^2=(0.529)^210^-20. 
Good but in SI units one usually writes : D=epsilon0E+P (eqSI) , whereas in 
Gaussian units (usually adopted when using atomic units) one writes D=E+4piP
(eqG)
So, the values that come out or the program, do they correspond to  eqSI or
eqG? 
Also, the value 0.029 C/m^2  for GaN given in the literature, does that
correspond to eqG 
or eqSI? In other words, if I want to calculate surface charge induced at an
interface, 
do I use 4pi Delta P.n or DeltaP.n ?

Sorry for my probably trivial questions but I just like to know what I am
doing. 
Walter