I can not find TTF version of popular LaTeX font family: Latin Modern Roman. I have found only OTF version. Is there any restrictions about TTF implementation or I am bad in searching?
[Tex/LaTex] Latin Modern Roman for TTF
fontslatin-moderntruetype
Related Solutions
First a side remark: With xelatex you should never load inputenc (you did it in your example).
Beside this: Theoretically it is possible to use symbols from an open type font in pdftex. But you need to create a tfm-file, you need to create enc-file(s) and a map-entry. And as pdftex can't subset open type you probably also need to split the open type and create various type1 fonts. This means a lot of work - and imho all this new files will count as "strange packages" and so your publisher will not like it. If you really don't want to use any other package you could perhaps cheat like this:
\documentclass{article}
\usepackage{lmodern}
\begin{document}
$\lbrack\!\lbrack x \rbrack\!\rbrack$
\end{document}
TeX Gyre Termes Math has blackboard bold letters similar to the amsfonts ones:
\documentclass{article}
\usepackage{unicode-math}
\setmathfont[range=\mathbb]{TeX Gyre Termes Math}
\begin{document}
$abc\mathbb{R}\mathbb{Q}\mathbb{N}$
\end{document}
Here's the result if XITS Math is used intead of Termes:
Just take your pick; you can experiment also with TeX Gyre Pagella Math or Asana Math.
Best Answer
Not a direct answer, but a workaround:
If you already have the otf font you can use e.g. FontForge to convert the files. OTF is just an extended version of TTF, the method how glyphs are specified is the same, so the characters will stay the same.