Is it a good idea to spend one year on a pre-PhD diploma to learn advance research methods? I am recently graduated with a degree of MS in Physics. I am very interested in condensed matter physics, that is why I chose a topic from this field for my MS thesis. But it was very hard for me to complete this thesis because I have not taken any advance course about condensed matter physics. I had to learn many theories by myself.

I am aiming to find a PhD position in Europe, and as you know in Europe, there is no course work in PhD program. So, before going for a PhD level research project, I want to attend a pre-PhD diploma in which research level courses of condensed matter physics will be taught.

My question is: is it a good idea to spend one year just to learn advance theories? (I am not in any rush to get a PhD degree).

Also

How should I write a motivation letter for this pre-PhD diploma? I mean everyone applying there would obviously write "I want to learn advance theories". How can my application be different than others?
I'm going to suggest that spending a year would not be a good use of your time. The end-all and be-all of doctoral education isn't the methodology, but using the methodology to do something interesting in your field. 

I would answer differently if you thought your background is weak and that you would only be accepted by spending this year, but with an MS that isn't likely true. If it were a matter of a summer spent on methodology then, again, it might be worth it. But a year feels like spinning wheels.

On the other hand, the course you suggest is in your field. If it can also get you closer to the research frontier in that field then it would have value for that, rather than methodology. At some point you need to cross that frontier so you need to approach it somehow. 

Of course, this isn't my field, and I don't know how difficult the methodology is, but I suspect that you can muddle through and pick it up - especially knowing that you have a need. It would probably delay your completion less than spending a dedicated year that might not even give you a benefit in your application.