In my view, users can search for a document and once they get the result, they can click on its id and they can download the document from specific url based on id: http://test.
Consider using Postal It's open source libriary for ASP.Net MVC allowing you to send emails very easy. For example to attach file you can use such code:
dynamic email = new Email("Example");
email.Attach(new Attachment("c:\\attachment.txt"));
email.Send();
Also you may want to use HangFire to send email in background, please take a look at the Sending Mail in Background with ASP.NET MVC
Update: In order to get the PDF file path you can use Server.MapPath method to convert virtual path to the corresponding physical directory on the server.