I think this title has changed hands several times already this century. In 2005 we were already down to the the head of a pin [SOURCE] But I think this one stands out as being best smallest and best meeting the definition of a transmitter. While we are on that topic, let's define transmitter.
"A device or set of components whose primary function is to generate and transmit electromagnetic waves via an antenna."
To satisfy any semantic arguments, I'm keeping it succinct. It's important to define that an antenna is distinguishable from it's power source, data source and antenna, since they all have different design constraints. It's also important to note that a transmitter may not be used to broadcast a signal, it may be conveyed over a wire, or point to point wirelessly. These devices all still have transmitters. Also many devices emit radio waves as a byproduct of a purpose other than emitting that signal: ex microwaves.
Their team created a voltage controlled oscillator (VCO) and manipulated graphene’s mechanical ‘stretchability’ to tune it's output frequency. Their NEMS broadcast at about 100 Mhz right in the middle of the FM band. Tests included transmitting low-tones and music. They received the signals with an "ordinary FM radio receiver." More here. I'm hoping they try to listen to it on the worlds smallest radio, developed at Berkley back in 2007, here.