<p>I know cutting-edge technology can be many things, but I would like to work and help create things like flexible paper-thin mobile phones, tube transport, etc.</p>
<p>Any. Pick a field. They are ALL working on cutting-edge tech.</p>
<p>Paper-thin mobile phones? Sounds like electrical and materials. Tube transport? Mechanical, civil, aerospace.</p>
<p>The real issue is going to be your relative standing. Most engineers will work on relatively mundane stuff that people need now, only a small percentage will get to work on pushing the boundaries. And that small percentage is usually drawn from those who get the best grades in undergrad and/or get advanced degrees from good schools.</p>