Do I need to hook some API in file_entity to use hook_field_formatter_view to display file?

In my module drupal.org/project/pdf I declared
pdf_field_formatter_info()
pdf_field_formatter_view()
to display PDF for file_field.

function pdf_field_formatter_view($entity_type, $entity, $field, $instance, $langcode, $items, $display) {
$element = array();
switch ($display['type']) {
case 'pdf_default':
foreach ($items as $delta => $item) {
$element[$delta] = array(
'#theme' => 'pdf_formatter_default',
'#file' => $item,
);
}
break;
case 'pdf_thumbnail':
foreach ($items as $delta => $item) {
$element[$delta] = array(
'#theme' => 'pdf_formatter_thumbnail',
'#file' => $item,
);
}
break;
}
return $element;
}

When I use my owned theme_pdf_formatter_thumbnail($variables) in file_entity. I can't pass the $variables to theme function.
Do I need to use API in file_entity to re-use field_formatter?

I get the returned $element from the hook_field_formatter_view like this
Array
(
[0] => Array
(
[#theme] => pdf_formatter_thumbnail
[#file] => Array
(
[fid] => 8
[uid] => 1
[filename] => arial_unicode_en_cidfont.pdf
[uri] => public://arial_unicode_en_cidfont.pdf
[filemime] => application/pdf
[filesize] => 15779
[status] => 1
[timestamp] => 1329144740
[type] => application
[content] => Array
(
)

)

)

)

But the $variable in the theme function like this

Array
(
[file] =>
)