Q:

How to define Indexer behaviour to an Interface?

Is it possible to add the indexer behaviour from an interface?
something like this :
interface IIndexable<T>
{
   T this[string index];
}

A:

Yes, it is possible. In fact, all you're missing is the getter/setter on your indexer. Just add it as follows:
interface IIndexable<T>
{
     T this[string index] {get; set;}
}

A:

From MSDN:
public interface ISomeInterface
{
    //...

    // Indexer declaration:
    string this[int index]
    {
        get;
        set;
    }
}

Indexers can be declared on an interface (C# Reference). Accessors of
  interface indexers differ from the accessors of class indexers in the
  following ways:

Interface accessors do not use modifiers.
An interface accessor does not have a body.

