I would suggest a more practical approach.

1. What is your background and experience so far?

2. Where do you want to do research?

3. What are the possibilities of the institution you wish to join?

I think that the number of possibilities is almost infinite, so it is better to narrow down the  area by answering the above questions before you actually choose.

   Dear Alaeddine,

   There are many, but nowadays the topological insulators, semimetals (type II-Dirac and type II-Weyl fermions) and topological Majorana superconductivity are very active research in the top, or at least one of them. 

I think ther are many, to me superconductivity and nano particles...

Nano probe development is most interesting area for research. it is the key component of nanoscience, nanoengineering and nanotechnology.

I would suggest a more practical approach.

1. What is your background and experience so far?

2. Where do you want to do research?

3. What are the possibilities of the institution you wish to join?

I think that the number of possibilities is almost infinite, so it is better to narrow down the  area by answering the above questions before you actually choose.

Dear Alaeddine Kaouka,

1. From a societal point of view the sustainability of materials supply to cope with growing demands of the world's population thereby decreasing the environmental consequences seems to me the most important issue.

2. From a more strict materials science point of view the question arises: would it be possible to enhance the intrinsic/extrinsic properties of materials? This would assume more insights to the classical central question of materials science: the link between structure and properties. 

In my opinion the following topics are catching fire at present:

Fabrication of nano-materials / nanoporous materials:

- for energy and sustainability

- medical field 

- photo - catalysis

- heterogeneous catalysis

- drug delivery 

- Pharmacy

- agriculture 

- electronics

- sensor technology

- desalination of water 

many more..................................etc.

Some Hot Topics in Electroceramics Research

by LI Yong-Xiang

Please check attached papers

Thin film technology is also one of the fascinating fields in the material science having application in solar cells, photodiodes, and others.

I am with answer of Dr. Gyorgy Banhegyi you have to know the facilities available in your institution and the aim of your research.