String concatenation in Wordpress
the_permalink() and the_title() does not return anything they are to print values.
You have to use their get_ version. Those are get_permalink() and get_the_title()
<?php $str .= '<a href="' . get_permalink() . '">' .get_the_title() . '</a>'; ?>
This is more of a wordpress question, but you should be using get_permalink() and get_the_title() instead of the functions you have there. Those functions will echo the link and title, and not return it in string form for use in your concatenation.