Is any source code available for an application that is similar to gmail in mvc 4

Sadly you cannot ask for source codes of third-party commercial web applications. Gmail doesn't provide any sample, or any third-party or indie developer has not shared any such content.

You can try to create an application which would provide same UI, but it won't be as good as you're thinking it can be. So my suggestion for you, is to avoid such thoughts and try to develop what you believe in and what you think would be helpfull. Do not re-create the wheel.