How to show that the department fits my research goal? In the question about choosing research ideas to include in a statement of purpose, JeffE advised how to write the last paragraph of the SOP:


  How does my department fit your research goals? (If the rest of your statement is well-written, the reader already knows the answer to this question, but you also need convince the reader that you know.)


What should I really say here, without having repetition? This is the sum up part, which doesn't need to explain again, and should be short. I would add that this part also needs to raise the emotion of the readers. They have used their rationale enough in the main part. Whether I succeed in satisfying them or not, I have already tried my best, and there is no need to prove that I'm good anymore.

Or, as JeffE says, I need to convince the reader that I know I'm good*. My preference is to make the scarcity here, because the feeling of losing is one of the most strongest emotions. However, when I have the draft proofed, it is highly criticized that it is hubris, or at least unnecessary. I have given my rationale, but no one respond. Here is the draft:


  To sum up, I hope that If I get admitted, I will be a valuable asset to the lab, the department, and the university. I will be a new researcher with a compelling plan to maturing the theory; a new student who can enrich the diversity of the X department; and a future scientist working to accomplish the Y school’s vision: create a better world.


So:


How to write this part?
Should I use this part to raise their emotions? 
Should I use scarcity to raise their emotion?




*Emboldening is only to emphasize the needed words, not to be hubris.
Your draft paragraph says nothing specific about the department or lab beyond the "create a better world" vision statement, and it says nothing specific about you beyond that you can enrich diversity.  (Every applicant hopes to be a valuable asset and feels they have a compelling plan.)  If your paragraph were swapped with another applicant's, in many cases nobody would notice the mismatch.

I'm not convinced that's a problem.  Your statement needs a conclusion, and this is a conclusion.  Writing a better concluding paragraph will make at most a small change in your chances of admission.  If the rest of your essay is compelling, then this conclusion won't ruin it.  If it's not compelling, then the last paragraph is too late to save it.  If you have the time and energy, it could be worth trying to write the perfect conclusion (one that is specific to both you and the department), but you should keep in mind that this is a minor form of fine-tuning.


  Should I use this part to raise their emotions? 


I don't think this will be effective.  Reading statements of purpose just isn't a particularly emotional activity.  Usually, committee members are skimming through them looking for the important information and ignoring fluff, and anything that looks like an attempt to manipulate emotions will count as fluff.


  Should I use scarcity to raise their emotion?


I'm not sure I understand what you mean by using scarcity.  Are you talking about raising fears that you are a scarce commodity and they might lose you to another department?  That doesn't need to be addressed, and it can look like hubris.  Most applicants just aren't that unique: there may be dozens or even hundreds of roughly similar applications.  (Of course everyone is unique and special as a human being, but this uniqueness isn't necessarily apparent in or even relevant to graduate admissions.)  The failure mode is usually not "oh no, this amazing candidate is lost to us forever" but rather "oh well, let's accept a similar student who was almost but not quite as promising".

To the extent your application is unique, that will be readily apparent and you don't need to emphasize it.  To the extent it is not unique, trying to raise emotions with impressions of scarcity will look arrogant or out of touch.