The simplest way to make rectifier is to make Diode first. There are several ways you can achieve that..
Using Schottky junction contacts: Use different metal contacts in S & D of Gr-FET. This will provide different Schottky junction resistance at the contact and will give you Schottky diodes.
Chemical doping method: In Gr-FET, dope half of the channel with N-type chemical dopant (such as benzyl viologen). Intrinsically, Gr is P-type in the atmosphere. by chemical doping of half of the channel, you will make a P-N diode. For example, look at my previous work, where I made high frequency rectifier using CNT diods. You can do the same thing only by replacing CNTs to Gr.
Article Chemically Doped Random Network Carbon Nanotube p-n Junction...
Electrostatic doping control: You have to make two gates in the Gr channel. One to make P-type conduction, and another to make N-type conduction. This will give you P-N diode operations as well.
Once you successfully made diode using any of the above methods, you can easily make high frequency rectifier using that diode. You can check my above paper to know how.
For graphene you just need to open the band-gap. That's it.. There are many ways to do that, either electrostatic or chemical doping or even using bi-layered Gr or Nano-ribbons. The paper only demonstrate a similar strategy. Regarding CNTs, you can find all the differences with Graphene in electronic devices, optoelectronic devices, chemical doping etc in this article below. Tried to help you and provided some information, signing-off from here. Hope this will help you further.
Good luck.
CB...
Article Graphene Versus Carbon Nanotubes in Electronic Devices