I am currently working in the field of my undergrad study in "computational systems and microelectronics". I have pursued my graduate masters project in Quantum Transport which have gotten me an A+ along with a Frist Class CGPA and the praise of my professors for laying the foundation of quantum transport simulation in the university in addition to publishing the quantum transport simulation paper in a high impact journal.
Now I am interested to pursue my PhD in quantum information/condensed matter/atomic and optical physics. I have emailed around 40 professors all around the world so far, around 10% of them seem interested and have called me for a PhD interview in renowned Universities (a good sign I suppose) but then they all have rejected me after the interview so far, citing a preference for more experienced candidates in the field. 20% of them outright respond back to the email enquiry, saying that I do not have the necessary background for their research. While a vast majority of professors don't even respond back (I assume they send the email to trash on sight).
I am autodidactic and have been ameliorating the courses that I didn't undertake in school such as Statistical mechanics, Optics etc. However I do have the necessary background in the mathematical and physics framework such as Tensor Calculus, Abstract Algebra, Electrodynamics, Quantum Mechanics, Solid State physics etc.
Is this a "fools errand" for a person of my background attempting to pursue the PhD in condensed matter/ atomic and optical physics or should I power through the rejections and continue approaching professors via email until one eventually hits ? I have met and seen people with my background pursue a PhD in these fields, one or two professors (no PhD openings unfortunately) on consultation even have said that my background is not an issue at all, which gives me hope.
I am currently lost and I wonder is the rejection rates I'm facing normal for PhD applications ? Should I even attempt trying or is this to be expected during the application phase? I have a preference for American or UK universities as these places offer more opportunities post graduation. I hope people who are from these fields and academics could advise me on this dilemma.