  We use suspended graphene electromechanical resonators to study the variation
of resonant frequency as a function of temperature. Measuring the change in
frequency resulting from a change in tension, from 300 K to 30 K, allows us to
extract information about the thermal expansion of monolayer graphene as a
function of temperature, which is critical for strain engineering applications.
We find that thermal expansion of graphene is negative for all temperatures
between 300K and 30K. We also study the dispersion, the variation of resonant
frequency with DC gate voltage, of the electromechanical modes and find
considerable tunability of resonant frequency, desirable for applications like
mass sensing and RF signal processing at room temperature. With lowering of
temperature, we find that the positively dispersing electromechanical modes
evolve to negatively dispersing ones. We quantitatively explain this crossover
and discuss optimal electromechanical properties that are desirable for
temperature compensated sensors.
