This is what I'm trying to make:
In the Flutter docs for Text Fields (https://flutter.io/text-input/) it says you can remove the underline by passing null to the decoration. However, that also gets rid of the hint text. 
I do not want any underline whether the text field is focused or not.
UPDATE: updated accepted answer to reflect changes in Flutter SDK as of April 2020.

 
     
     
     
     
    
 
     
     
     
    


 
     
     
     
     
     
    


 
     
     
     
    