Can we build a more efficient airplane? Not really, says physics.
As a plane hurtles through the air, it carves out a tube of air, much of which is deflected downwards by the wings. Throw down enough air fast enough, and you can stay afloat, just as the downwards thrust of a rocket pushes it up. The key is that you have to throw down a lot of air (like a glider or an albatross), or throw it down really fast (like a helicopter or a hummingbird).
That’s how airplanes work – action and reaction.
Of course, there may be more efficient ways of throwing down air. Modern jets are more efficient because they throw more air through their engines, combining the benefits of a jet turbine and a propeller.