Dear Sandip,

well, I think I have one and/or two:

1. It is a Glass Transition problem, which could be loosely defined as rigidity-fluidity transition in glass forming materials.

2. Universal Relaxation Phenomenon that is often related to the glass transition phenomenon.

For both , standard experiments (Electrical Impedance Spectroscopy in particular) and the theory of nonlinear lattices might be the answer.

I hope you will find them interesting enough.

With best regards

Petr

Dear Sandip,

well, I think I have one and/or two:

1. It is a Glass Transition problem, which could be loosely defined as rigidity-fluidity transition in glass forming materials.

2. Universal Relaxation Phenomenon that is often related to the glass transition phenomenon.

For both , standard experiments (Electrical Impedance Spectroscopy in particular) and the theory of nonlinear lattices might be the answer.

I hope you will find them interesting enough.

With best regards

Petr

graphene is ambipolar, both electrons and holes are "always' present. Try to get graphene unipolar. 

It's potentially a nobel prize!

I don't want disappoint you, and I do not mean it in a negative way, but there are (from my point of view) much more unsolved problems in condensed matter physics or materials science than solved. We are everywhere trying to get closer, but even obviously "simple" problems like the martensitic transformation is not solved but only described by mainly two different and incompatible approaches/assumptions/theories. 

The problems described are facinating.. Although I have completed my research work but I intend to do further research in the field and at least give a shot in solving some unsoved mysteries. Really appreciate the inputs. Thank you much Petr Sir, Kamal Sir and Gert Sir...

The problem of the Coulomb interaction. High electron density approximation isn't valid in real substances. Accurate procedure of accounting the Coulomb interaction between electrons is unknown. This is a problem for several Nobel prizes.