Does any paper use energy harvest to in the baseband? Most of RF energy harvest system just harvest $\rho$  of the RF signal for charging the battery,and the other part RF energy will be processed to baseband signal by RF Chain to do the information decoding,like this below


Now i have a new thinking,if we receive signal and use the RF chain to let the signal become the baseband signal first,then use the power splitter to let $\rho$ of baseband signal power to charge the battery(energy harvest).Can we do that?



Is there any paper which use this method to do the energy harvest?like this below
No.

Your question neglects the fact that a mixer can't transfer the whole received power to baseband (mixers are typically active, and most of the baseband energy comes from the LO that the device has to generate itself).

You can use any nonlinear device, even one without an external power source, but the mixed output's energy will always be way lower than the energy of the inputs, simply by the pure math behind what mixing does.

In general, when asking such question, you'd start with "where does what energy come from?", and with a clean, and simplified, block diagram of the receive RF chain including the mixer, and that would have answered that. If you're researching power harvesting, this is the MAIN thing you'll need to understand!