Where in the CVX documentation to use see the function det which can take a CVX argument? There is none.
You can use log_det or det_rootn if the argument is psd and (I believe, even though not documented) concave (or affine), and constructed following CVX"s rules. I don’t know what your input data is, so I don’t know whether it satisfies the needed conditions.
Please carefully read
and re-read the CVX Users’ Guide.