Cover Letter for PhD Application
Several different templates are available on the net, it depends only on your taste!
I would like only one thing: write it in LaTeX. If you are not familiar with LaTeX or you don't feel comfortable with it, Theoretical Physics is not for you. Obviously I'm joking, but not completely...
Anyway, without too much efforts, on the net I found in particular this template that is really suitable for many purposes (actually, with some modifications, is the one I use for my letters):

As you can see this is very sober but direct and clear.
If otherwise you fell very comfortable with typing in TeX, I suggest you to try to emulate some template in LibreOffice downloadable on the net. In particular I recommend this one, in particular the one at page 23, but many others are really nice.
Therefore, I would like to quote also this answer from SE Academia that partially answer your question. In particular I stress the importance of these sentences:

What is unavoidable to write
Make your cover letter personal, remarkable (i.e., stands out from other cover letters), specific to you and specific to the position at hand. Be enthusiastic. Be specific. Show that you've put thought into the position and why you are applying.
Relate your specific skill sets and previous experience to the programme you are applying for. Relate the content of specific aspects of your CV to the programme:
&quot;During my masters, I enjoyed working on the topic of A, which relates to your programme [in this way]&quot;
&quot;I worked three summers at company B, where I gained experience in topic C ...&quot;
&quot;I visited your university in March last year and was impressed by ...&quot;
&quot;I read paper entitled 'D' published by your group at 'E' and was interested in ...&quot;
&quot;I recently published a paper 'F', which I believe compliments work by 'G' in your department on 'H' ...&quot;

Good luck for your application!