oral e hw 2

good morning everyone
my topic today is second harmonic generation in noncentrosymmetric phosphates

second harmonic generation is the measurable property of nonlinear optical materials;
and noncentrosymmetric phosphates
is a good ultraviolet nonlinear optical material.

first i'll give you the backgroud of nonlinear optical materials:
nonlinear optical materials can converting the incident light into other frequency. 
it is important in laser optical science and important military applications.

my presentation is seperated into the following part:
i'll give you the predicted conclusion and my research destination first.
and then the method and model i used to get my results
lastly, i'll show what i think is the weakness of my work and how i improve them.

The conclusion of my research is that four phosphates which are similar is structures have different SHG.
the beta phosphate tri lithum have very weak SHG while other three have measurable SHG.
I contribute the SHG of beta Vanadium tri-lithum and  phosphate Csumsium lithum mostly to reduced charge-transfer energy,
and contribute the SHG of phosphate boron to enhanced orbital hybridization.

To get the the conclusion i need to seperating the contribution into charge-transfer energy and the
orbital hybridizaion. 
And finding that berry connection and curvature interpretation of SHG is suitable for this distination.

The model i use is the simple two-band model,
starting from the hamitonian the general two-band form. 
we can write the berry connections as following.
where the alphe and beta can be writing as equation of d
for the specific point group, take mm2 of livo4 and li3po4 as example we read
d1 equals sum of ...
and d3 is the band gap
and orbital hybridization strength is ..
and charge-transfer energt is d3

as for the transverse SHG effect chi 2 along i direction. we can write it from dipole band model as ...
and under the near fermi energy approximation and long wavelength approximation. we rewrite is 
as following.

it is clearly with tx ty tz  equals t , and it indicates that lower the charge transfer energy or enhance the
orbital hybridization can enhance SHG

The first principle method is used to verify the model and used to show the conclusion.
...
...

there still some weakness i can improved in my research .
... ... ...

reshow the conclusion part